Khan Academy

Civic life, private life, politics, and government | Citizenship | High school civics | Khan Academy

Sun, 01 Nov 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/humanities/us-government-and-civics/x231f0f4241b58f49:citizens-us-gov-civics/x231f0f4241b58f49:what-does-it-mean-to-be-a-citizen-civics/e/what-makes-a-good-citizen-level-1

Uploaded 01-09-20

What's the difference between civic life and private life? What's the difference between politics and government?

View more lessons or practice this subject at: https://www.khanacademy.org/humanities/high-school-civics

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Linear models example 2 | Algebra I | Khan Academy

Sun, 01 Nov 2026 00:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-linear-eq-func/alg-linear-models-word-problems/v/linear-models-2

Uploaded 06-08-15

Marbles and water in tank

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
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Adding to 10 | Basic addition and subtraction | Early Math | Khan Academy

Sat, 31 Oct 2026 23:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-kindergarten-math/cc-kindergarten-add-subtract/kindergarten-making-5-9/v/adding-to-10-example

Uploaded 01-06-15

Learn that if we have 3 bananas, then we need 7 more bananas to make 10 bananas.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-basics/cc-early-math-make-10/e/making-ten-2?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Watch the next lesson: https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-basics/cc-early-math-add-subtract-10/v/relating-addition-and-subtraction?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Missed the previous lesson?
https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-basics/cc-early-math-make-10/v/getting-to-10-by-filling-boxes?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Early Math on Khan Academy: Math begins with counting. It's the most important skill we learn in our early years and becomes the foundation for all other math concepts. Once we can count, we can add, subtract, and measure the world around us. Shortly thereafter, we can learn about place values, plots, graphs, time, money, and shapes. These early math skills are presented in this subject's tutorials in a straightforward, understandable, and (dare we say it) fun way!

Want a virtual coach for Early Math? Unlock the Early Math mission on Khan Academy here: https://www.khanacademy.org?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Early Math channel:
https://www.youtube.com/channel/UCs8a-pNM8EHKKU28XQLetLw?sub_confirmation=1
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Dividing complex numbers | Imaginary and complex numbers | Precalculus | Khan Academy

Sat, 31 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-div/v/dividing-complex-numbers

Uploaded 12-07-11

Dividing Complex Numbers

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/multiplying-dividing-complex/e/dividing_complex_numbers?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Watch the next lesson: https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/complex_analysis/v/basic-complex-analysis?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/multiplying-dividing-complex/v/complex-conjugates-example?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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How to create a function from an equation (example) | Functions | Algebra I | Khan Academy

Sat, 31 Oct 2026 22:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:functions-and-equations/v/create-function-from-equation

Uploaded 06-08-15

Sal find the formula of a function that, given an input value "b," outputs a value "a" that satisfies the equation 4a+7b=-52.

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
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Understanding place value when adding ones | Early Math | Khan Academy

Sat, 31 Oct 2026 21:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-add-subtract-100/cc-2nd-add-100/v/understanding-place-value-when-adding-ones

Uploaded 01-06-15

Learn how to add 37 + 2 by thinking about place value.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-add-ones-tens/e/add-within-100--level-1?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Watch the next lesson: https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-add-ones-tens/v/understanding-place-value-while-adding-tens?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Missed the previous lesson?
https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-20/cc-early-math-word-problems-more-fewer-20/v/more-comparison-word-problems?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Early Math on Khan Academy: Math begins with counting. It's the most important skill we learn in our early years and becomes the foundation for all other math concepts. Once we can count, we can add, subtract, and measure the world around us. Shortly thereafter, we can learn about place values, plots, graphs, time, money, and shapes. These early math skills are presented in this subject's tutorials in a straightforward, understandable, and (dare we say it) fun way!

Want a virtual coach for Early Math? Unlock the Early Math mission on Khan Academy here: https://www.khanacademy.org?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Early Math channel:
https://www.youtube.com/channel/UCs8a-pNM8EHKKU28XQLetLw?sub_confirmation=1
Subscribe to KhanAcademy: http://www.youtube.com/subscription_center?add_user=khanacademy

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What is citizenship? | Citizenship | High school civics | Khan Academy

Sat, 31 Oct 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/humanities/us-government-and-civics/x231f0f4241b58f49:citizens-us-gov-civics/x231f0f4241b58f49:what-does-it-mean-to-be-a-citizen-civics/v/civil-society

Uploaded 01-09-20

A person has citizenship as a member of a state, which confers on them rights, responsibilities, and privileges. An individual practices good citizenship by being an informed and active member of a political community.

View more lessons or practice this subject at: https://www.khanacademy.org/humanities/high-school-civics

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Subtracting ten or one hundred | Addition and subtraction within 100 | Early Math | Khan Academy

Sat, 31 Oct 2026 20:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-add-subtract-1000/cc-2nd-sub-ones-tens-hundreds/v/subtracting-hundreds-and-tens

Uploaded 01-06-15

Learn how to subtract 1, 10, or 100 from a number.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-sub-ones-tens-hundreds/e/subtract-within-1000--level-1?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Watch the next lesson: https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-sub-ones-tens-hundreds/v/subtracting-3-digits?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Missed the previous lesson?
https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-add-ones-tens-hundreds/v/adding-hundreds-tens-and-ones?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Early Math on Khan Academy: Math begins with counting. It's the most important skill we learn in our early years and becomes the foundation for all other math concepts. Once we can count, we can add, subtract, and measure the world around us. Shortly thereafter, we can learn about place values, plots, graphs, time, money, and shapes. These early math skills are presented in this subject's tutorials in a straightforward, understandable, and (dare we say it) fun way!

Want a virtual coach for Early Math? Unlock the Early Math mission on Khan Academy here: https://www.khanacademy.org?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Early Math channel:
https://www.youtube.com/channel/UCs8a-pNM8EHKKU28XQLetLw?sub_confirmation=1
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How to determine the domain of a modeling function (example with a function) | Khan Academy

Sat, 31 Oct 2026 19:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:determining-the-domain-of-a-function/v/domain-of-a-modeling-function-example-1

Uploaded 06-08-15

Sal determines the domain of a function that models the height of a plant over time.

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Completing Perfect Square Trinomials

Sat, 31 Oct 2026 18:06:00 -0000

u16_l5_t1_we2 Completing Perfect Square Trinomials
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education

Uploaded 12-07-11

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Fence posts for horses | Addition and subtraction within 100 | Early Math | Khan Academy

Sat, 31 Oct 2026 18:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-add-subtract-100/cc-2nd-add-sub-100-word-problems/v/fence-posts-for-horses

Uploaded 01-06-15

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-add-sub-100-word-problems/e/addition-and-subtraction-word-problems-within-100--level-1?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Watch the next lesson: https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-add-sub-100-word-problems/v/snow-on-friday?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Missed the previous lesson?
https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-add-sub-100-word-problems/v/losing-tennis-balls?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Early Math on Khan Academy: Math begins with counting. It's the most important skill we learn in our early years and becomes the foundation for all other math concepts. Once we can count, we can add, subtract, and measure the world around us. Shortly thereafter, we can learn about place values, plots, graphs, time, money, and shapes. These early math skills are presented in this subject's tutorials in a straightforward, understandable, and (dare we say it) fun way!

Want a virtual coach for Early Math? Unlock the Early Math mission on Khan Academy here: https://www.khanacademy.org?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Early Math channel:
https://www.youtube.com/channel/UCs8a-pNM8EHKKU28XQLetLw?sub_confirmation=1
Subscribe to KhanAcademy: http://www.youtube.com/subscription_center?add_user=khanacademy

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Example 5: Adding polynomials with two variables | Algebra I | Khan Academy

Sat, 31 Oct 2026 17:00:00 -0000

Simplify (4x^2y - 3x^2 - 2y) + (8xy - 3x^2 + 2x^2y + 4)

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/introduction-to-polynomials-and-factorization/adding-and-subtracting-polynomials/e/adding-and-subtracting-polynomials-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-polynomials-and-factorization/adding-and-subtracting-polynomials/v/subtracting-polynomials-with-multiple-variables?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Missed the previous lesson?
https://www.khanacademy.org/math/algebra/introduction-to-polynomials-and-factorization/adding-and-subtracting-polynomials/v/adding-and-subtracting-polynomials-3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

Uploaded 06-08-15

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy Sample Zoom Class

Sat, 31 Oct 2026 16:06:00 -0000

Want to see how to integrate Khan Academy with your live video sessions?

Uploaded 27-08-20

I'm going to teach a sample lesson to show you how to:

-Reduce lecture time during live sessions
-Make your sessions highly interactive
-Drill down on the areas where your students need the most help

PS: Our advice is video conference platform agnostic. So whether you use Zoom, Google Meet, WebEx, or anything else, all the advice will still apply!

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org and Novartis. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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Recognizing shapes | Geometry | Early Math | Khan Academy

Sat, 31 Oct 2026 16:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-2nd-grade-math/x3184e0ec:geometry/cc-2nd-shapes/v/recognizing-shapes

Uploaded 01-06-15

Learn how to identify circles, triangles, squares, rectangles, rhombuses, and trapezoids.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/early-math/cc-early-math-geometry-topic/cc-early-math-shapes/e/naming-shapes?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Watch the next lesson: https://www.khanacademy.org/math/early-math/cc-early-math-geometry-topic/cc-early-math-properties-shapes/v/sides-corners?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Missed the previous lesson?
https://www.khanacademy.org/math/early-math/cc-early-math-geometry-topic/cc-early-math-shapes/v/sides-corners?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Early Math on Khan Academy: Math begins with counting. It's the most important skill we learn in our early years and becomes the foundation for all other math concepts. Once we can count, we can add, subtract, and measure the world around us. Shortly thereafter, we can learn about place values, plots, graphs, time, money, and shapes. These early math skills are presented in this subject's tutorials in a straightforward, understandable, and (dare we say it) fun way!

Want a virtual coach for Early Math? Unlock the Early Math mission on Khan Academy here: https://www.khanacademy.org?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Early Math channel:
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Introduction to rates | Ratios, rates, and percentages | 6th grade | Khan Academy

Sat, 31 Oct 2026 15:00:00 -0000

Learn how rates and how they're related to ratios.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-rates/e/rate_problems_0.5?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade

Watch the next lesson: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-rates/v/finding-unit-rates?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade

Missed the previous lesson? https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-ratio-word-problems/v/ratio-word-problem-exercise-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade

Grade 6th on Khan Academy: By the 6th grade, you're becoming a sophisticated mathemagician. You'll be able to add, subtract, multiply, and divide any non-negative numbers (including decimals and fractions) that any grumpy ogre throws at you. Mind-blowing ideas like exponents (you saw these briefly in the 5th grade), ratios, percents, negative numbers, and variable expressions will start being in your comfort zone. Most importantly, the algebraic side of mathematics is a whole new kind of fun! And if that is not enough, we are going to continue with our understanding of ideas like the coordinate plane (from 5th grade) and area while beginning to derive meaning from data! (Content was selected for this grade level based on a typical curriculum in the United States.)

Uploaded 06-08-15

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Example: Quadratics in standard form | Quadratic equations | Algebra I | Khan Academy

Sat, 31 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-quadratics/alg-solving-quadratics-using-the-quadratic-formula/v/quadratic-equations-in-standard-form

Uploaded 12-07-11

Quadratic Equations in Standard Form

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/e/quadratic_equation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Watch the next lesson: https://www.khanacademy.org/math/algebra/quadratics/quadratic-formula/v/proof-of-quadratic-formula?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Missed the previous lesson?
https://www.khanacademy.org/math/algebra/quadratics/quadratic-formula/v/using-the-quadratic-formula?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Halves and fourths | Geometry | Early Math | Khan Academy

Sat, 31 Oct 2026 14:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-1st-grade-math/cc-1st-measurement-geometry/cc-1st-fractions-of-shapes/v/halves-and-fourths

Uploaded 01-06-15

Learn how to divide shapes into two or four equal sections.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/early-math/cc-early-math-geometry-topic/cc-early-math-fractions-of-shapes/e/halves-and-fourths?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Watch the next lesson: https://www.khanacademy.org/math/early-math/cc-early-math-geometry-topic/cc-early-math-fractions-of-shapes/v/filling-rectangles-with-squares?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

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https://www.khanacademy.org/math/early-math/cc-early-math-geometry-topic/cc-early-math-composing-shapes/v/compose-shapes?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Early Math on Khan Academy: Math begins with counting. It's the most important skill we learn in our early years and becomes the foundation for all other math concepts. Once we can count, we can add, subtract, and measure the world around us. Shortly thereafter, we can learn about place values, plots, graphs, time, money, and shapes. These early math skills are presented in this subject's tutorials in a straightforward, understandable, and (dare we say it) fun way!

Want a virtual coach for Early Math? Unlock the Early Math mission on Khan Academy here: https://www.khanacademy.org?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Substitution and income effects and the Law of Demand | APⓇ Microeconomics | Khan Academy

Sat, 31 Oct 2026 13:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/unit-2-supply-and-demnd/micro-demand/e/markets--property-rights--and-the-law-of-demand

Uploaded 12-12-18

The law of demand states that quantity demanded increases when price decreases, but why? Two reasons why the demand curve slopes downward are the substitution effect and the income effect. Learn about both in this video.
AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Distillation | Intermolecular forces and properties | AP Chemistry | Khan Academy

Sat, 31 Oct 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:separation-of-solutions-and-mixtures-chromatography/v/distillation-curves

Uploaded 26-08-20

Distillation is the process of separating the components of a liquid mixture through selective evaporation and condensation. The basis of separation is the difference in the vapor pressures (volatilities) of the respective components. To improve the separation in a distillation, chemists often use a fractionating column, which allows for multiple cycles of evaporation and condensation (this is known as fractional distillation). View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:separation-of-solutions-and-mixtures-chromatography/v/distillation

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Estimating lengths | Measurement and data | Early Math | Khan Academy

Sat, 31 Oct 2026 12:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-measurement-data/cc-2nd-compare-estimate-length/v/estimating-lengths

Uploaded 01-06-15

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/early-math/cc-early-math-measure-data-topic/cc-early-math-compare-estimate-length/e/estimating-lengths?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Watch the next lesson: https://www.khanacademy.org/math/early-math/cc-early-math-measure-data-topic/cc-early-math-length-word-problems/v/length-word-problems?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

Missed the previous lesson?
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Early Math on Khan Academy: Math begins with counting. It's the most important skill we learn in our early years and becomes the foundation for all other math concepts. Once we can count, we can add, subtract, and measure the world around us. Shortly thereafter, we can learn about place values, plots, graphs, time, money, and shapes. These early math skills are presented in this subject's tutorials in a straightforward, understandable, and (dare we say it) fun way!

Want a virtual coach for Early Math? Unlock the Early Math mission on Khan Academy here: https://www.khanacademy.org?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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How to evaluate a piecewise function (example) | Functions | Algebra I | Khan Academy

Sat, 31 Oct 2026 11:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:absolute-value-piecewise-functions/x2f8bb11595b61c86:piecewise-functions/v/evaluating-piecewise-functions-example

Uploaded 28-05-15

Sal evaluates a piecewise function at a given input.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/algebra-functions/piecewise-functions/e/evaluating-piecewise-functions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Watch the next lesson: https://www.khanacademy.org/math/algebra/algebra-functions/piecewise-functions/v/graphing-piecewise-function?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Example 5: Using the quadratic formula | Quadratic equations | Algebra I | Khan Academy

Sat, 31 Oct 2026 10:06:00 -0000

Applying the Quadratic Formula

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https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/e/quadratic_equation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Watch the next lesson: https://www.khanacademy.org/math/algebra/quadratics/features-of-quadratic-functions/v/ex3-completing-the-square?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Missed the previous lesson?
https://www.khanacademy.org/math/algebra/quadratics/quadratic-formula/v/application-problem-with-quadratic-formula?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

Uploaded 12-07-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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How to determine the domain of a modeling function | Functions | Algebra I | Khan Academy

Sat, 31 Oct 2026 10:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:determining-the-domain-of-a-function/v/domain-of-a-modeling-function-example-2

Uploaded 28-05-15

Sal determines the domain of a function that models the price of candy bars.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/algebra-functions/determining-the-domain-of-a-function/e/interpreting-domain?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Watch the next lesson: https://www.khanacademy.org/math/algebra/algebra-functions/determining-the-domain-of-a-function/v/domain-of-a-modeling-function-example-3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Missed the previous lesson?
https://www.khanacademy.org/math/algebra/algebra-functions/determining-the-domain-of-a-function/v/domain-of-a-modeling-function-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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How to determine the domain of algebraic functions (examples) | Functions | Algebra I | Khan Academy

Sat, 31 Oct 2026 09:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-functions/alg-determining-the-domain-of-a-function/v/domain-of-algebraic-function-examples

Uploaded 27-05-15

Sal gives many examples where he determines the domains of functions according to mathematical limitations.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/algebra-functions/determining-the-domain-of-a-function/e/domain-of-algebraic-functions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Watch the next lesson: https://www.khanacademy.org/math/algebra/algebra-functions/determining-the-domain-of-a-function/v/domain-of-a-modeling-function-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Missed the previous lesson?
https://www.khanacademy.org/math/algebra/algebra-functions/determining-the-domain-of-a-function/v/domain-of-a-radical-function?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Solubility and intermolecular forces | AP Chemistry | Khan Academy

Sat, 31 Oct 2026 08:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:solubility/e/solubility

Uploaded 26-08-20

Want to explore more? Check out the full Solutions, acids, and bases playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAHzfFIPU3q0hDdHKTEPrz5&si=ODwD0LbDD3IH8KdB

Substances with similar polarities tend to be soluble in one another ("like dissolves like"). Nonpolar substances are generally more soluble in nonpolar solvents, while polar and ionic substances are generally more soluble in polar solvents. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:solubility/v/solubility

Sections:
00:00 - Introduction to solubility
00:26 - Water’s structure and polarity
01:01 - Why sodium chloride dissolves in water
01:56 - Ion-dipole attraction and dissolution
02:13 - Solubility with nonpolar substances
02:40 - Mixing pentane and hexane
03:08 - Hexane does not dissolve in water
03:35 - Polar organic molecules like ethanol
03:58 - Ethanol’s solubility in water
04:12 - Effect of larger nonpolar chains on solubility
04:18 - Key concept: like dissolves like

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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What is the domain of a function? | Functions | Algebra I | Khan Academy

Sat, 31 Oct 2026 08:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/domain-of-a-function-intro

Uploaded 27-05-15

Sal introduces the concept of "domain" of a function and gives various examples for functions and their domains.

Watch the next lesson: https://www.khanacademy.org/math/algebra/algebra-functions/domain-and-range/v/range-of-a-function?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Missed the previous lesson?
https://www.khanacademy.org/math/algebra/algebra-functions/domain-and-range/v/introduction-to-interval-notation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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11 Computing with set members

Sat, 31 Oct 2026 07:00:00 -0000

More free lessons at: http://www.khanacademy.org/video?v=1hihcoJPzz0

Uploaded 26-05-15

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Example 3: Completing the square | Quadratic equations | Algebra I | Khan Academy

Sat, 31 Oct 2026 06:06:00 -0000

Completing the Square to Solve Quadratic Equations

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https://www.khanacademy.org/math/algebra/quadratics/completing_the_square/e/completing_the_square_in_quadratic_expressions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

Uploaded 12-07-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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6 Area of small circles

Sat, 31 Oct 2026 06:00:00 -0000

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Uploaded 26-05-15

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Example: Amplitude and period transformations | Trigonometry | Khan Academy

Sat, 31 Oct 2026 05:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb89:period/v/example-amplitude-and-period-transformations

Uploaded 26-05-15

Understanding how the amplitude and period changes as coefficients change.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/trigonometry/trig-function-graphs/trig_graphs_tutorial/e/graphs_of_sine_and_cosine?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Watch the next lesson: https://www.khanacademy.org/math/trigonometry/trig-function-graphs/trig_graphs_tutorial/v/amplitude-and-period-cosine-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

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Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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The kinetic molecular theory of gases | AP Chemistry | Khan Academy

Sat, 31 Oct 2026 04:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:kinetic-molecular-theory/v/kinetic-molecular-theory-and-the-gas-laws

Uploaded 21-08-20

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The kinetic molecular theory (KMT) describes the behavior of ideal gases at the particle level. The five main postulates of the KMT are as follows: (1) the particles in a gas are in constant, random motion, (2) the combined volume of the particles is negligible, (3) the particles exert no forces on one another, (4) any collisions between the particles are completely elastic, and (5) the average kinetic energy of the particles is proportional to the temperature in kelvins.

Sections:
00:00 - Introduction to kinetic molecular theory
00:18 - Measurable macroscopic properties of gases
01:43 - The ideal gas law and macro relationships
03:00 - Connecting molecular behavior to gas properties
03:47 - Assumptions of elastic collisions
04:24 - Temperature and average kinetic energy
05:02 - Key assumptions of kinetic molecular theory
06:07 - Temperature and kinetic energy relationship

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Liters of soda for the party

Sat, 31 Oct 2026 04:00:00 -0000

Uploaded 26-05-15

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Ways to represent data | Data and statistics | 6th grade | Khan Academy

Sat, 31 Oct 2026 03:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/dot-plot/v/ways-to-represent-data

Uploaded 26-05-15

Here are a few of the many ways to look at data. Which is your favorite?

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/dot-plot/e/intro-to-simple-data?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade

Watch the next lesson: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/dot-plot/v/frequency-tables-and-dot-plots?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade

Missed the previous lesson? https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-geometry-topic/cc-6th-polygons-in-the-coordinate-plane/v/constructing-polygon-on-coordinate-plane-example?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade

Grade 6th on Khan Academy: By the 6th grade, you're becoming a sophisticated mathemagician. You'll be able to add, subtract, multiply, and divide any non-negative numbers (including decimals and fractions) that any grumpy ogre throws at you. Mind-blowing ideas like exponents (you saw these briefly in the 5th grade), ratios, percents, negative numbers, and variable expressions will start being in your comfort zone. Most importantly, the algebraic side of mathematics is a whole new kind of fun! And if that is not enough, we are going to continue with our understanding of ideas like the coordinate plane (from 5th grade) and area while beginning to derive meaning from data! (Content was selected for this grade level based on a typical curriculum in the United States.)

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Discriminant for types of solutions for a quadratic | Algebra II | Khan Academy

Sat, 31 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/in-in-grade-10-ncert/x573d8ce20721c073:quadratic-equations/x573d8ce20721c073:nature-of-roots/v/discriminant-for-types-of-solutions-for-a-quadratic

Uploaded 12-07-11

Discriminant for Types of Solutions for a Quadratic

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/e/solutions_to_quadratic_equations?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_ineq/v/quadratic-inequalities?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/v/discriminant-of-quadratic-equations?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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15 Possible values for expression

Sat, 31 Oct 2026 02:00:00 -0000

More free lessons at: http://www.khanacademy.org/video?v=0Z63Mv8hGnU

Uploaded 26-05-15

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Inverse of a 2x2 matrix | Matrices | Precalculus | Khan Academy

Sat, 31 Oct 2026 01:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:practice-finding-inverses-of-2x2-matrices/v/inverse-of-a-2x2-matrix

Uploaded 26-05-15

Example of calculating the inverse of a 2x2 matrix

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/precalc-matrices/inverting_matrices/e/matrix_inverse_2x2?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Watch the next lesson: https://www.khanacademy.org/math/precalculus/precalc-matrices/inverting_matrices/v/inverse-matrix-part-1?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Missed the previous lesson?
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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Kinetic molecular theory and the gas laws | AP Chemistry | Khan Academy

Sat, 31 Oct 2026 00:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:kinetic-molecular-theory/v/maxwell-boltzmann-distribution

Uploaded 20-08-20

Want to explore more? Check out the full States of matter playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAcadC8xfE0VtGhfHdrECNO&si=aLyVfcDx3Xp257S6

The kinetic molecular theory (KMT) can be used to explain the macroscopic behavior of ideal gases. In this video, we'll see how the KMT accounts for the properties of gases as described by the various gas laws (Boyle's law, Gay-Lussac's law, Charles's law, Avogadro's law, and Dalton's law of partial pressures).

Sections:
00:00 - Kinetic molecular theory overview
01:00 - Pressure from particle collisions
01:46 - Connecting KMT to the ideal gas law
02:59 - Boyle’s Law: Pressure vs Volume
04:12 - Gay-Lussac’s Law: Pressure vs Temperature
05:13 - Charles’s Law: Volume vs Temperature
05:59 - Avogadro’s Law: Volume vs Moles
06:44 - Dalton’s Law: Partial pressures add up
07:57 - Summary: Ideal gas law through KMT lens

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Identifying Champions and Exemplar Educators

Sat, 31 Oct 2026 00:00:00 -0000

Join Crystal from Khan Academy as we explore how administrators can identify and empower champions and exemplar educators within their schools. In this video, you’ll learn what strong implementation looks like in practice, how to recognize effective instructional use of Khan Academy and Khanmigo, and strategies for leveraging teacher leaders to support school-wide adoption. Discover how celebrating educator success and fostering peer collaboration can help build sustainable, student-centered implementation practices across your school or district.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khancademy.org/khan-for-educators

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Intro to 30-60-90 triangles | Right triangles and trigonometry | Geometry | Khan Academy

Fri, 30 Oct 2026 23:00:00 -0000

A few more 45-45-90 examples and an introduction to 30-60-90 triangles.

Watch the next lesson: https://www.khanacademy.org/math/geometry/right_triangles_topic/cc-geometry-trig/v/basic-trigonometry?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

Uploaded 15-05-07

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Example: Complex roots for a quadratic | Algebra II | Khan Academy

Fri, 30 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-eq/v/complex-roots-from-the-quadratic-formula

Uploaded 12-07-11

Complex Roots from the Quadratic Formula

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/e/quadratic-formula-with-complex-solutions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/v/discriminant-of-quadratic-equations?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Is rising inequality necessarily bad

Fri, 30 Oct 2026 22:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macroeconomics-income-inequality/piketty-capital/v/inequality-good-or-bad

Uploaded 16-04-19

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US and Japanese Quantitative Easing

Fri, 30 Oct 2026 21:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/federal-reserve/v/us-and-japanese-quantitative-easing

Uploaded 26-05-11

Comparing quantitative easing in Japan to "credit easing" in the United States
More free lessons at: http://www.khanacademy.org/video?v=a-R8qpea6lc

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Representing solutions using particulate models | AP Chemistry | Khan Academy

Fri, 30 Oct 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:representations-of-solutions/e/representations-of-solutions

Uploaded 18-08-20

A solution is a homogeneous mixture composed of two or more pure substances. In this video, we'll learn how to represent the relative concentrations of the substances in a solution as well as the interactions between them using a particulate model. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:representations-of-solutions/v/representing-solutions-using-particulate-models

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Gilded Age versus Silicon Valley | GDP: Measuring national income | Macroeconomics | Khan Academy

Fri, 30 Oct 2026 20:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macroeconomics-income-inequality/piketty-capital/v/gilded-age-silicon-valley

Uploaded 16-04-19

Macroeconomics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Human evolution overview | Life on earth and in the universe | Cosmology and Astronomy | Khan Academy

Fri, 30 Oct 2026 19:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/biology/history-of-life-on-earth/the-diversification-of-life/v/human-evolution-overview

Uploaded 28-05-11

An overview of human evolution. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/understanding-calendar-notation?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/history-life-earth-tutorial/v/first-living-things-on-land-clarification?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Example 4: Applying the quadratic formula | Quadratic equations | Algebra I | Khan Academy

Fri, 30 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:standard-form-quadratic/v/application-problem-with-quadratic-formula

Uploaded 12-07-11

Application Problem with Quadratic Formula

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/e/quadratic_equation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Watch the next lesson: https://www.khanacademy.org/math/algebra/quadratics/quadratic-formula/v/applying-the-quadratic-formula?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Missed the previous lesson?
https://www.khanacademy.org/math/algebra/quadratics/quadratic-formula/v/quadratic-formula-3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Convergence on macro scale | GDP: Measuring national income | Macroeconomics | Khan Academy

Fri, 30 Oct 2026 18:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macroeconomics-income-inequality/piketty-capital/v/convergence-macro

Uploaded 16-04-19

Macroeconomics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's Macroeconomics channel: https://www.youtube.com/channel/UCBytY7pnP0GAHB3C8vDeXvg
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Understanding calendar notation | Cosmology and Astronomy | Khan Academy

Fri, 30 Oct 2026 17:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/understanding-calendar-notation

Uploaded 30-05-11

Difference between BC, BCE, AD and CE. A little bit about the birth of Jesus as well. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/correction-calendar-notation?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/human-evolution-overview?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Cosmology and Astronomy channel: https://www.youtube.com/channel/UChNPnEkW8LYZ5Rwi8_A2-DA?sub_confirmation=1
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Molarity | AP Chemistry | Khan Academy

Fri, 30 Oct 2026 16:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:solutions-and-mixtures/v/dilution

Uploaded 18-08-20

Want to explore more? Check out the full Solutions, acids, and bases playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAHzfFIPU3q0hDdHKTEPrz5&si=ODwD0LbDD3IH8KdB

The most common way to express solution concentration is molarity (M), which is defined as the amount of solute in moles divided by the volume of solution in liters: M = moles of solute/liters of solution. A solution that is 1.00 molar (written 1.00 M) contains 1.00 mole of solute for every liter of solution. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:solutions-and-mixtures/v/molarity

Sections:
00:00 - Introduction to molarity
00:09 - Molarity definition and formula
00:34 - Problem setup: sodium sulfate in water
01:20 - Identifying solute and solvent
01:43 - Converting mass to moles using molar mass
02:26 - Molar mass of sodium sulfate
02:54 - Calculating moles of solute
03:30 - Converting volume to liters
03:45 - Final molarity calculation
04:38 - Result and interpretation of molarity

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Inverse relationship between capital price and returns | Macroeconomics | Khan Academy

Fri, 30 Oct 2026 16:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macroeconomics-income-inequality/piketty-capital/v/price-return-relationship

Uploaded 16-04-19

Macroeconomics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's Macroeconomics channel: https://www.youtube.com/channel/UCBytY7pnP0GAHB3C8vDeXvg
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May 29th, 2011 CNN Piece

Fri, 30 Oct 2026 15:00:00 -0000

Follow up CNN piece to Dan Simon's story on the Khan Academy from last year

Uploaded 01-06-11

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Dependent probability example 2 | Probability and Statistics | Khan Academy

Fri, 30 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/statistics-probability/probability-library/multiplication-rule-dependent/v/dependent-probability-example-2

Uploaded 23-05-11

It's important to practice these probability problems as they get more complex eventually. Take a stab on this one...with our help, of course.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/independent-dependent-probability/dependent_probability/e/identifying-dependent-and-independent-events?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/independent-dependent-probability/dependent_probability/v/independent-events-1?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/independent-dependent-probability/dependent_probability/v/dependent-probability-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
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Indifference curves and marginal rate of substitution | Microeconomics | Khan Academy

Fri, 30 Oct 2026 14:00:00 -0000

We can graph how we value tradeoffs between two goods

Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/microeconomics/choices-opp-cost-tutorial/marginal-utility-tutorial/v/optimal-point-on-budget-line?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics

Missed the previous lesson? https://www.khanacademy.org/economics-finance-domain/microeconomics/choices-opp-cost-tutorial/marginal-utility-tutorial/v/budget-line?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics

Microeconomics on Khan Academy: Topics covered in a traditional college level introductory microeconomics course

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

Uploaded 16-04-19

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's Microeconomics channel: https://www.youtube.com/channel/UC_6zQ54DjQJdLodwsxAsdZg
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Khan Academy on Perry's Principles (6/2/2011)

Fri, 30 Oct 2026 13:00:00 -0000

Khan Academy on Perry's Principles

Uploaded 03-06-11

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Dilution | Intermolecular forces and properties | AP Chemistry | Khan Academy

Fri, 30 Oct 2026 12:06:00 -0000

A common method of making a solution of a given concentration involves taking a more concentration solution and adding water until the desired concentration is reached. This process is known as dilution. We can relate the concentrations and volumes before and after a dilution using the following equation: M₁V₁ = M₂V₂ where M₁ and V₁ represent the molarity and volume of the initial concentrated solution and M₂ and V₂ represent the molarity and volume of the final diluted solution. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:solutions-and-mixtures/v/dilution

Uploaded 18-08-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Capital by Thomas Piketty | Macroeconomics | Khan Academy

Fri, 30 Oct 2026 12:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macroeconomics-income-inequality/piketty-capital/v/piketty-capital

Uploaded 16-04-19

Macroeconomics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's Macroeconomics channel: https://www.youtube.com/channel/UCBytY7pnP0GAHB3C8vDeXvg
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Correction calendar notation | Cosmology and Astronomy | Khan Academy

Fri, 30 Oct 2026 11:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/correction-calendar-notation

Uploaded 03-06-11

Correcting the time difference calculation by taking into account that there is no year 0. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/development-of-agriculture-and-writing?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/understanding-calendar-notation?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Cosmology and Astronomy channel: https://www.youtube.com/channel/UChNPnEkW8LYZ5Rwi8_A2-DA?sub_confirmation=1
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Converting fractions to decimals (ex2)

Fri, 30 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/how-earth-s-tilt-causes-seasons

Uploaded 13-07-11

How being Earth's tilt causes seasons. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/are-southern-hemisphere-seasons-more-severe?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/seasons-aren-t-dictated-by-closeness-to-sun?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Cosmology and Astronomy channel: https://www.youtube.com/channel/UChNPnEkW8LYZ5Rwi8_A2-DA?sub_confirmation=1
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Return on capital and economic growth

Fri, 30 Oct 2026 10:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macroeconomics-income-inequality/piketty-capital/v/r-greater-but-less-inequality

Uploaded 16-04-19

More free lessons at: http://www.khanacademy.org/video?v=ir-ISPDjGno

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Salman Khan at TiEcon 2011

Fri, 30 Oct 2026 09:00:00 -0000

Talk and Q and A (with Raj Mithai)

Uploaded 03-06-11

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Types of mixtures | Intermolecular forces and properties | AP Chemistry | Khan Academy

Fri, 30 Oct 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:solutions-and-mixtures/v/molarity

Uploaded 18-08-20

A mixture is composed of one or more pure substances in varying composition. There are two types of mixtures: heterogeneous and homogeneous. Heterogeneous mixtures have visually distinguishable components, while homogeneous mixtures appear uniform throughout. The most common type of homogenous mixture is a solution, which can be a solid, liquid, or gas. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:solutions-and-mixtures/v/types-of-mixtures

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Critically looking at data on ROC and economic growth over millenia | Macroeconomics | Khan Academy

Fri, 30 Oct 2026 08:00:00 -0000

Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/macroeconomics/gdp-topic/piketty-capital/v/piketty-spreadsheet-1?utm_source=YT&utm_medium=Desc&utm_campaign=macroeconomics

Missed the previous lesson? https://www.khanacademy.org/economics-finance-domain/macroeconomics/gdp-topic/piketty-capital/v/r-greater-but-less-inequality?utm_source=YT&utm_medium=Desc&utm_campaign=macroeconomics

Macroeconomics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

Uploaded 16-04-19

For free. For everyone. Forever. #YouCanLearnAnything

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Khan Academy on California Report (June 2011)

Fri, 30 Oct 2026 07:00:00 -0000

Khan Academy on California Report (June 2011)

Uploaded 03-06-11

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Converting fractions to decimals (ex2)

Fri, 30 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/milankovitch-cycles-precession-and-obliquity

Uploaded 13-07-11

How changes in Earth's rotation can effect Earth's seasons and climate. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/precession-causing-perihelion-to-happen-later?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/are-southern-hemisphere-seasons-more-severe?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Gini Coefficient and Lorenz Curve

Fri, 30 Oct 2026 06:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/ap-consumer-producer-surplus/inequality/e/inequality

Uploaded 16-04-19

How the Gini Coefficient and Lorenz Curves are used to measure income inequality.

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Backwardation bullish or bearish | Finance and Capital Markets | Khan Academy

Fri, 30 Oct 2026 05:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/backwardation-bullish-or-bearish

Uploaded 06-06-11

Thinking about why backwardation in commodities markets is bullish. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/futures-curves-ii?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/severe-contango-generally-bearish?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: In many commodities markets, it is very helpful for buyers or sellers to lock-in future prices. This is what both forwards and futures allow for. This tutorial explains how they work and what the difference is between the two.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Introduction to real gases | Intermolecular forces and properties | AP Chemistry | Khan Academy

Fri, 30 Oct 2026 04:06:00 -0000

Real gases do not always follow the assumptions of the kinetic molecular theory. While the particles of an ideal gas are assumed to occupy no volume and experience no interparticle attractions, the particles of a real gas do have finite volumes and do attract one another. As a result, real gases are often observed to deviate from ideal behavior. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:deviation-from-ideal-gas-law/v/real-gas-vs-ideal-gas

Uploaded 28-07-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Connecting income to capital growth and potential inequality | Macroeconomics | Khan Academy

Fri, 30 Oct 2026 04:00:00 -0000

Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/macroeconomics/gdp-topic/piketty-capital/v/price-return-relationship?utm_source=YT&utm_medium=Desc&utm_campaign=macroeconomics

Missed the previous lesson? https://www.khanacademy.org/economics-finance-domain/macroeconomics/gdp-topic/piketty-capital/v/r-greater-than-g?utm_source=YT&utm_medium=Desc&utm_campaign=macroeconomics

Macroeconomics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

Uploaded 16-04-19

For free. For everyone. Forever. #YouCanLearnAnything

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Appomattox Court House and Lincoln's Assassination

Fri, 30 Oct 2026 03:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/us-history/history-survey/us-history-survey/v/appomattox-court-house-and-lincoln-s-assassination

Uploaded 07-06-11

From Lee's Surrender to Grant to Lincoln's Assassination
More free lessons at: http://www.khanacademy.org/video?v=Frpq_A7Ky_Q

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Introduction to the semicolon | The Colon and semicolon | Punctuation | Khan Academy

Fri, 30 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/grammar/punctuation-the-colon-semicolon-and-more/introduction-to-semicolons/v/introduction-to-the-semicolon-the-colon-and-semicolon-punctuation-khan-academy

Uploaded 17-04-19

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/grammar/punctuation-the-colon-semicolon-and-more/introduction-to-semicolons/v/introduction-to-the-semicolon-the-colon-and-semicolon-punctuation-khan-academy

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/grammar/punctuation-the-colon-semicolon-and-more/introduction-to-semicolons/v/introduction-to-the-semicolon-the-colon-and-semicolon-punctuation-khan-academy

Paige introduces a piece of punctuation called the semicolon; this punctuation can link closely related independent clauses together in a sentence.

Practice this yourself on Khan Academy right now: https://www.khanacademy.org/the-colon-and-semicolon/e/introduction-to-semicolons

Watch the next lesson: https://www.khanacademy.org/humanities/grammar/punctuation/the-colon-and-semicolon/v/semicolons-and-complex-lists-the-colon-and-semicolon-punctuation-khan-academy

Missed the previous lesson? Watch here: https://www.khanacademy.org/humanities/grammar/punctuation/the-colon-and-semicolon/v/introduction-to-the-semicolon-the-colon-and-semicolon-punctuation-khan-academy

Punctuation on Khan Academy: Punctuation is the collection of squiggles, dots, and lines that we use to separate sentences and their parts. Is a question mark punctuation? Yes, and so is an exclamation point!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Review of revenue and cost graphs for a monopoly | Microeconomics | Khan Academy

Fri, 30 Oct 2026 02:00:00 -0000

Let's review what we've learned about monopolies

Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/microeconomics/perfect-competition-topic/monopolistic-competition-oligop/v/oligopolies-and-monopolisitc-competition?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics

Missed the previous lesson? https://www.khanacademy.org/economics-finance-domain/microeconomics/perfect-competition-topic/monopolies-tutorial/v/optional-calculus-proof-to-show-that-mr-has-twice-slope-of-demand?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics

Microeconomics on Khan Academy: Topics covered in a traditional college level introductory microeconomics course

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

Uploaded 16-04-19

For free. For everyone. Forever. #YouCanLearnAnything

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Severe contango generally bearish | Finance and Capital Markets | Khan Academy

Fri, 30 Oct 2026 01:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/severe-contango-generally-bearish

Uploaded 07-06-11

Thinking about why a severe contango could be bearish. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/backwardation-bullish-or-bearish?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/contango-from-trader-perspective?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: In many commodities markets, it is very helpful for buyers or sellers to lock-in future prices. This is what both forwards and futures allow for. This tutorial explains how they work and what the difference is between the two.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Interpreting expressions with multiple variables: Cylinder | Modeling | Algebra 2 | Khan Academy

Fri, 30 Oct 2026 00:06:00 -0000

Given the vale and the expression for the radius of a cylinder, find the radius of a cylinder with the same volume and 100 times the height. This involves analyzing the expression for the radius to see how changing the height affects the radius.

Uploaded 27-07-20

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Change in expected future prices and demand | Microeconomics | Khan Academy

Fri, 30 Oct 2026 00:00:00 -0000

Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/microeconomics/supply-demand-equilibrium/demand-curve-tutorial/v/changes-in-income-population-or-preferences?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics

Missed the previous lesson? https://www.khanacademy.org/economics-finance-domain/microeconomics/supply-demand-equilibrium/demand-curve-tutorial/v/price-of-related-products-and-demand?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics

Microeconomics on Khan Academy: Topics covered in a traditional college level introductory microeconomics course

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

Uploaded 16-04-19

For free. For everyone. Forever. #YouCanLearnAnything

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Contango from trader perspective | Finance and Capital Markets | Khan Academy

Thu, 29 Oct 2026 23:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/contango-from-trader-perspective

Uploaded 07-06-11

What a trader means when they say that a market is in contango. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/severe-contango-generally-bearish?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/futures-and-forward-curves?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: In many commodities markets, it is very helpful for buyers or sellers to lock-in future prices. This is what both forwards and futures allow for. This tutorial explains how they work and what the difference is between the two.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Abstract-ness

Thu, 29 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/precession-causing-perihelion-to-happen-later

Uploaded 14-07-11

Clarifying the effect of axial precession on the calendar and the date of perihelion and aphelion. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/what-causes-precession-and-other-orbital-changes?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/milankovitch-cycles-precession-and-obliquity?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Cosmology and Astronomy channel: https://www.youtube.com/channel/UChNPnEkW8LYZ5Rwi8_A2-DA?sub_confirmation=1
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Socially efficient and inefficient outcomes

Thu, 29 Oct 2026 22:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/ap-consumer-producer-surplus/socially-efficient-and-inefficient-market-outcomes/e/socially-efficient-and-inefficient-market-outcomes

Uploaded 16-04-19

Capturing positive and negative externalities by thinking through marginal social benefit (MSB) and marginal social cost (MSC).

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Estate tax introduction | Taxes | Finance and Capital Markets | Khan Academy

Thu, 29 Oct 2026 21:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/taxes-topic/taxes/v/estate-tax-introduction

Uploaded 07-06-11

Overview of the estate tax. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/taxes-topic/taxes/v/tax-brackets-and-progressive-taxation?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/taxes-topic/taxes/v/alternative-minimum-tax?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Benjamin Franklin (and several other writers/philosophers) tells us that "In this world nothing can be said to be certain, except death and taxes." He's right. This tutorial focus on personal income tax. Very important to watch if you ever plan on earning money (some of which the government will take for itself).

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
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Sal Discusses the Safety of Reopening Schools on the Situation Room With Wolf Blitzer

Thu, 29 Oct 2026 20:06:00 -0000

Uploaded 27-07-20

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A monopsonistic market for labor | Microeconomics | Khan Academy

Thu, 29 Oct 2026 20:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/factor-markets/monopsonistic-markets/v/monopsony-employers-and-minimum-wages

Uploaded 16-04-19

When there is a single buyer of labor this type of market is called a monopsonistic labor market. Learn how this changes the analysis of labor markets and why marginal factor cost is higher than the supply of labor in such markets.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Risk and reward introduction | Finance and Capital Markets | Khan Academy

Thu, 29 Oct 2026 19:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/risk-and-reward-introduction

Uploaded 07-06-11

Basic introduction to risk and reward. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/human-capital?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/hedge-funds/v/hedge-fund-strategies-merger-arbitrage-1?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: When are you using capital to create more things (investment) vs. for consumption (we all need to consume a bit to be happy). When you do invest, how do you compare risk to return? Can capital include human abilities? This tutorial hodge-podge covers it all.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Abstract-ness

Thu, 29 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/what-causes-precession-and-other-orbital-changes

Uploaded 14-07-11

What causes precession and other orbital changes. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/apsidal-precession-perihelion-precession-and-milankovitch-cycles?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/precession-causing-perihelion-to-happen-later?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Cosmology and Astronomy channel: https://www.youtube.com/channel/UChNPnEkW8LYZ5Rwi8_A2-DA?sub_confirmation=1
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Human capital | Finance and Capital Markets | Khan Academy

Thu, 29 Oct 2026 18:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/human-capital

Uploaded 07-06-11

Basic overview of capital and human capital. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/return-on-capital?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/risk-and-reward-introduction?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: When are you using capital to create more things (investment) vs. for consumption (we all need to consume a bit to be happy). When you do invest, how do you compare risk to return? Can capital include human abilities? This tutorial hodge-podge covers it all.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
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Factor markets worked example | Microeconomics | Khan Academy

Thu, 29 Oct 2026 17:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/factor-markets/profit-maximizing-behavior-in-perfectly-competitive-factor-markets/e/profit-maximizing-behavior-in-perfectly-competitive-factor-markets

Uploaded 15-04-19

In this video, learn how to apply the analysis of factor markets to a sample problem.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Identifying value in digits

Thu, 29 Oct 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-place-value/x3184e0ec:intro-to-place-value/e/identify-the-value-of-a-digit

Uploaded 27-07-20

Identifying value in digits

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Inflation Overview | Inflation | Finance and Capital Markets | Khan Academy

Thu, 29 Oct 2026 16:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-basics-tutorial/v/inflation-overview

Uploaded 08-06-11

Basic understanding of Inflation. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-basics-tutorial/v/what-is-inflation?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: $1 went a lot further in 1900 than today (you could probably buy a good meal for the family for $1 back then). Why? And how do we measure how much more expensive things have gotten (i.e., inflation)?

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
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Shifts in demand for labor | Microeconomics | Khan Academy

Thu, 29 Oct 2026 15:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/factor-markets/ap-labor-marginal-product-rev/e/changes-in-factor-demand-and-supply

Uploaded 15-04-19

Changes in the demand for labor affect wage rates. Learn why labor demand changes, and the effect of changes in the demand for labor on labor markets.

Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Abstract-ness

Thu, 29 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/apsidal-precession-perihelion-precession-and-milankovitch-cycles

Uploaded 14-07-11

Apsidal Precession (Perihelion Precession). Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/history-life-earth-tutorial/v/earth-formation?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/earth-history-topic/earth-title-topic/v/what-causes-precession-and-other-orbital-changes?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Cosmology and Astronomy channel: https://www.youtube.com/channel/UChNPnEkW8LYZ5Rwi8_A2-DA?sub_confirmation=1
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Time value of money | Interest and debt | Finance and Capital Markets | Khan Academy

Thu, 29 Oct 2026 14:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/present-value/v/time-value-of-money

Uploaded 08-06-11

Why when you get your money matters as much as how much money. Present and future value also discussed. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/present-value/v/introduction-to-present-value?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/cont-comp-int-and-e/v/continuously-compounding-interest-formula-e?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: If you gladly pay for a hamburger on Tuesday for a hamburger today, is it equivalent to paying for it today? A reasonable argument can be made that most everything in finance really boils down to "present value". So pay attention to this tutorial.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
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Changes in labor supply | Microeconomics | Khan Academy

Thu, 29 Oct 2026 13:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/factor-markets/ap-labor-marginal-product-rev/v/shifts-in-demand-for-labor

Uploaded 15-04-19

Changes in the supply of labor have an effect on the wage rate. The supply of labor shifts when there are changes in the population, changes in preferences and social norms, and changes in wage rates and opportunities in other markets. Learn how to show the effects of changes in labor supply on wage rates in this video.

Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Inches and feet

Thu, 29 Oct 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-measurement-data/x3184e0ec:units-of-length/e/units-of-length-inch-ft

Uploaded 23-07-20

Inches and feet

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Mortgage Interest Rates | Housing | Finance and Capital Markets | Khan Academy

Thu, 29 Oct 2026 12:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/housing/mortgages-tutorial/v/mortgage-interest-rates

Uploaded 09-06-11

Understanding how mortgage interest rates are quoted. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/housing/mortgages-tutorial/v/short-sale-basics?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/housing/mortgages-tutorial/v/introduction-to-mortgage-loans?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Most people buying a home need a mortgage to do so. This tutorial explains what a mortgage is and then actually does some math to figure out what your payments are (the last video is quite mathy so consider it optional).

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
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Introduction to labor markets | Microeconomics | Khan Academy

Thu, 29 Oct 2026 11:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/factor-markets/introduction-to-factor-markets/e/introduction-to-factor-markets

Uploaded 15-04-19

Just like goods and services, the factors of production are exchanged in markets. This video focuses on such market -- the market for labor. The supply of labor is based on people's willingness to tradeoff labor for leisure. The demand for labor is based on labor's marginal revenue product.

Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Solving a proportion with an unknown variable (example) | 7th grade | Khan Academy

Thu, 29 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-write-and-solve-proportions/v/find-an-unknown-in-a-proportion

Uploaded 15-07-11

Here's a great video where we explain the reasoning behind solving proportions. We'll put some algebra to work to get our answers, too.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-write-and-solve-proportions/e/proportions_1?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Watch the next lesson: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-write-and-solve-proportions/v/writing-proportions?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Missed the previous lesson?
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-graphs-proportions/v/identifying-proportional-relationships-visually?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Grade 7th on Khan Academy: 7th grade takes much of what you learned in 6th grade to an entirely new level. In particular, you'll now learn to do everything with negative numbers (we're talking everything--adding, subtracting, multiplying, dividing, fractions, decimals... everything!). You'll also take your algebraic skills to new heights by tackling two-step equations. 7th grade is also when you start thinking about probability (which is super important for realizing that casinos and lotteries are really just ways of taking money away from people who don't know probability) and dig deeper into the world of data and statistics. Onward! (Content was selected for this grade level based on a typical curriculum in the United States.)

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÂ Ã Âªs 7th grade channel:
https://www.youtube.com/channel/UCzKsXcrLSLDG7VN1LODlRkw?sub_confirmation=1
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Development of agriculture and writing | Cosmology and Astronomy | Khan Academy

Thu, 29 Oct 2026 10:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/development-of-agriculture-and-writing

Uploaded 09-06-11

The Paleolithic and Neolithic eras of the Stone Age. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/firestick-farming?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/correction-calendar-notation?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Cosmology and Astronomy channel: https://www.youtube.com/channel/UChNPnEkW8LYZ5Rwi8_A2-DA?sub_confirmation=1
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Game theory worked example from A P Microeconomics

Thu, 29 Oct 2026 09:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/imperfect-competition/oligopoly-and-game-theory/e/oligopoly-and-game-theory--foundational-concepts

Uploaded 22-03-19

Game theory worked example from A P Microeconomics

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Length word problem example

Thu, 29 Oct 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:\
https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-measurement-data/cc-2nd-length-word-problems/e/length-word-problem-us-customary

Uploaded 23-07-20

Length word problem example

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Intro to vectors and scalars | One-dimensional motion | Physics | Khan Academy

Thu, 29 Oct 2026 08:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/introduction-to-vectors-and-scalars

Uploaded 11-06-11

Distance, displacement, speed and velocity. Difference between vectors and scalars. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/calculating-average-velocity-or-speed?utm_source=YT&utm_medium=Desc&utm_campaign=physics

Missed the previous lesson? https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/introduction-to-physics?utm_source=YT&utm_medium=Desc&utm_campaign=physics

Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

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Long term economic profit for monopolistic competition | Microeconomics | Khan Academy

Thu, 29 Oct 2026 07:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/imperfect-competition/monopolistic-competition/e/monopolistic-competition

Uploaded 22-03-19

Compare and contrast the long run outcomes for monopolistic competition, monopolies, and perfect competition in this video.

Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Converting Fahrenheit to Celsius | Pre-Algebra | Khan Academy

Thu, 29 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/8th-engage-ny/engage-8th-module-4/8th-module-4-topic-d/v/converting-farenheit-to-celsius

Uploaded 15-07-11

Converting Fahrenheit to Celsius

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Solving for time | One-dimensional motion | Physics | Khan Academy

Thu, 29 Oct 2026 06:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/physics/one-dimensional-motion/acceleration-tutorial/v/acceleration

Uploaded 11-06-11

Simple example of solving for time given distance and rate. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/displacement-from-time-and-velocity-example?utm_source=YT&utm_medium=Desc&utm_campaign=physics

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Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Monopolies vs. perfect competition | Microeconomics | Khan Academy

Thu, 29 Oct 2026 05:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/imperfect-competition/ap-monopolies-tutorial/v/economic-profit-for-a-monopoly

Uploaded 15-03-19

Learn about the key differences between the two extremes of competition: monopolies and perfect competitition

Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Partitioning rectangles

Thu, 29 Oct 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-2nd-grade-math/x3184e0ec:geometry/x3184e0ec:partition-rectangles/e/partitioning-rectangles

Uploaded 23-07-20

Partitioning rectangles

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Displacement from time and velocity example | One-dimensional motion | Physics | Khan Academy

Thu, 29 Oct 2026 04:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/displacement-from-time-and-velocity-example

Uploaded 11-06-11

Worked example of calculating displacement from time and velocity. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/instantaneous-speed-and-velocity?utm_source=YT&utm_medium=Desc&utm_campaign=physics

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Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Economic profit for a monopoly | Microeconomics | Khan Academy

Thu, 29 Oct 2026 03:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/imperfect-competition/ap-monopolies-tutorial/v/monopolist-optimizing-price-part-1-total-revenue

Uploaded 15-03-19

Learn about how to represent a monopoly market graphically in this video. Topics covered include the profit-maximizing quantity, pricing decisions, and deadweight loss associated with monopolies.

Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Proportion word problem (example 1) | 7th grade | Khan Academy

Thu, 29 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-write-and-solve-proportions/v/find-an-unknown-in-a-proportion-2

Uploaded 15-07-11

A recipe for oatmeal cookies calls for 2 cups of flour for every 3 cups of oatmeal. How much flour is needed for a big batch of cookies that uses 9 cups of oatmeal?

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-write-and-solve-proportions/e/constructing-proportions-to-solve-application-problems?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

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Grade 7th on Khan Academy: 7th grade takes much of what you learned in 6th grade to an entirely new level. In particular, you'll now learn to do everything with negative numbers (we're talking everything--adding, subtracting, multiplying, dividing, fractions, decimals... everything!). You'll also take your algebraic skills to new heights by tackling two-step equations. 7th grade is also when you start thinking about probability (which is super important for realizing that casinos and lotteries are really just ways of taking money away from people who don't know probability) and dig deeper into the world of data and statistics. Onward! (Content was selected for this grade level based on a typical curriculum in the United States.)

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Gravity for astronauts in orbit | Centripetal force and gravitation | Physics | Khan Academy

Thu, 29 Oct 2026 02:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/gravity-newtonian/v/gravity-for-astronauts-in-orbit

Uploaded 12-06-11

Why do astronauts appear weightless despite being near the Earth? Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/gravity-newtonian/v/would-a-brick-or-feather-fall-faster?utm_source=YT&utm_medium=Desc&utm_campaign=physics

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Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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AP Microeconomics FRQ on perfect competition | AP(R) Microeconomics | Khan Academy

Thu, 29 Oct 2026 01:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/production-cost-and-the-perfect-competition-model-temporary/ap-perfect-competition/e/perfect-competition-in-the-short-run-and-long-run

Uploaded 14-03-19

Walk through the solution to a free response question (FRQ) like the ones you may see on an AP Microeconomics exam. Topics include why price equals marginal revenue (P=MR) for a perfectly competitive firm, how to draw side-by-side market and firm graphs, and how to find several points of interest in the firm graph.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Shapes and angles

Thu, 29 Oct 2026 00:06:00 -0000

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https://www.khanacademy.org/math/cc-2nd-grade-math/x3184e0ec:geometry/cc-2nd-shapes/e/analyze-shapes-by-angles

Uploaded 23-07-20

Shapes and angles

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Race cars with constant speed around curve | Physics | Khan Academy

Thu, 29 Oct 2026 00:00:00 -0000

When acceleration could involve a change in direction and not speed. Created by Sal Khan.

Uploaded 13-06-11

Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Long run supply when industry costs are increasing or decreasing | Microeconomics | Khan Academy

Wed, 28 Oct 2026 23:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/production-cost-and-the-perfect-competition-model-temporary/ap-perfect-competition/v/frq-microecononomics-on-perfect-competition

Uploaded 13-03-19

In some industries, the number of firms in the market has an impact on the costs that firms face. For example, when firms have to compete with each other over resources, firms' costs increase as more firms enter the market. But in other industries, more firms actually lower costs for firms. Learn about the implications of each of these situations on the long-run supply curve in an industry.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Compound inequalities 3 | Linear inequalities | Algebra I | Khan Academy

Wed, 28 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:compound-inequalities/v/compound-inequalities-3

Uploaded 15-07-11

Compound Inequalities 3

Practice this lesson yourself on KhanAcademy.org right now:
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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Airbus A380 take-off time | One-dimensional motion | Physics | Khan Academy

Wed, 28 Oct 2026 22:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/physics/one-dimensional-motion/acceleration-tutorial/v/airbus-a380-take-off-time

Uploaded 13-06-11

Figuring how long it takes an a380 to take off given a constant acceleration. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/physics/one-dimensional-motion/acceleration-tutorial/v/airbus-a380-take-off-distance?utm_source=YT&utm_medium=Desc&utm_campaign=physics

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Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Long run supply curve in constant cost perfectly competitive markets | Microeconomics | Khan Academy

Wed, 28 Oct 2026 21:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/production-cost-and-the-perfect-competition-model-temporary/ap-perfect-competition/v/long-run-supply-when-industry-costs-are-increasing-or-decreasing

Uploaded 13-03-19

A constant cost industry is an industry where each firm's costs aren't impacted by the entry or exit of new firms. Learn about the difference between the short run market supply curve and the long run market supply curve for perfectly competitive firms in constant cost industries in this video.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Adding two digit numbers on a number line

Wed, 28 Oct 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-add-subtract-100/cc-2nd-more-fewer-100/e/adding-and-subtracting-on-the-number-line-word-problems

Uploaded 22-07-20

Adding two digit numbers on a number line

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Why distance is area under velocity-time line | Physics | Khan Academy

Wed, 28 Oct 2026 20:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/physics/one-dimensional-motion/acceleration-tutorial/v/why-distance-is-area-under-velocity-time-line

Uploaded 13-06-11

How long of a runway does an A380 need? Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/physics/one-dimensional-motion/acceleration-tutorial/v/why-distance-is-area-under-velocity-time-line?utm_source=YT&utm_medium=Desc&utm_campaign=physics

Missed the previous lesson? https://www.khanacademy.org/science/physics/one-dimensional-motion/acceleration-tutorial/v/airbus-a380-take-off-time?utm_source=YT&utm_medium=Desc&utm_campaign=physics

Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Economic profit for firms in perfectly competitive markets

Wed, 28 Oct 2026 19:00:00 -0000

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Locate integers on a number line

Wed, 28 Oct 2026 18:06:00 -0000

u9_l1_t2_we1 Locate integers on a number line

Uploaded 15-07-11

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Long-run economic profit for perfectly competitive firms | Microeconomics | Khan Academy

Wed, 28 Oct 2026 18:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/production-cost-and-the-perfect-competition-model-temporary/ap-perfect-competition/v/long-run-supply-curve-in-constant-cost-perfectly-competitive-markets

Uploaded 12-03-19

A firm in a perfectly competitive market might be able to earn economic profit in the short run, but not in the long run. Learn about the process that brings a firm to normal economic profits in this video.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Logistic growth versus exponential growth | Ecology | AP Biology | Khan Academy

Wed, 28 Oct 2026 17:00:00 -0000

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https://www.khanacademy.org/science/ap-biology/ecology-ap/population-ecology-ap/a/hs-population-ecology-review

Uploaded 11-03-19

Logistic growth versus exponential growth (for familiarity with AP Biology formula sheet).

View more lessons or practice this subject at https://www.khanacademy.org/science/ap-biology/ecology-ap/population-ecology-ap/v/logistic-growth-versus-exponential-growth

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Multi step addition word problem

Wed, 28 Oct 2026 16:06:00 -0000

Multi step addition word problem

Uploaded 22-07-20

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Per capita population growth and exponential growth | Ecology | AP Biology | Khan Academy

Wed, 28 Oct 2026 16:00:00 -0000

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https://www.khanacademy.org/science/ap-biology/ecology-ap/population-ecology-ap/v/logistic-growth-versus-exponential-growth

Uploaded 11-03-19

Understanding per capita population growth and exponential growth.

View more lessons or practice this subject at https://www.khanacademy.org/science/ap-biology/ecology-ap/population-ecology-ap/v/per-capita-population-growth-and-exponential-growth

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Population growth rate based on birth and death rates | Ecology | AP Biology | Khan Academy

Wed, 28 Oct 2026 15:00:00 -0000

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https://www.khanacademy.org/science/ap-biology/ecology-ap/population-ecology-ap/v/per-capita-population-growth-and-exponential-growth

Uploaded 08-03-19

Seeing that the formula for population growth rate based on birth and death rates given in AP Biology exams is actually quite intuitive.

View more lessons or practice this subject at https://www.khanacademy.org/science/ap-biology/ecology-ap/population-ecology-ap/v/population-growth-rate-based-on-birth-and-death-rates

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Number sets | Fractions | Pre-Algebra | Khan Academy

Wed, 28 Oct 2026 14:06:00 -0000

Number Sets

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/number-sets-pre-alg/v/number-sets-1?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

Uploaded 15-07-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Impact of changes to trophic pyramids | High school biology | Khan Academy

Wed, 28 Oct 2026 14:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:energy-and-matter-in-biological-systems/x230b3ff252126bb6:flow-of-matter-and-energy-through-ecosystems/v/impact-of-changes-to-trophic-pyramids

Uploaded 06-03-19

The trophic pyramid illustrates energy transfer within ecosystems, highlighting primary producers, consumers, and decomposers. Energy from the sun is stored as biomass, with only 10% transferred between trophic levels. Ecosystem changes, such as reduced sunlight or pesticide use, can impact the entire pyramid, emphasizing the interconnectedness of ecosystems and the importance of energy cycling.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Cellular evidence of common ancestry | High school biology | Khan Academy

Wed, 28 Oct 2026 13:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:common-ancestry-and-phylogeny/x230b3ff252126bb6:evidence-for-evolution/v/cellular-evidence-of-common-ancestry

Uploaded 06-03-19

All living organisms share a common ancestor, evidenced by cellular similarities like DNA, RNA, and glycolysis. Evolutionary trees depict these relationships, with branches representing different species. Eukaryotes, a distinct group, possess membrane-bound organelles, linear chromosomes, and introns. DNA and RNA sequencing refines our understanding of these connections, enabling more precise evolutionary tree construction.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Multi step subtraction word problem

Wed, 28 Oct 2026 12:06:00 -0000

Multi step subtraction word problem

Uploaded 22-07-20

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Artificial selection and domestication | Natural selection | AP Biology | Khan Academy

Wed, 28 Oct 2026 12:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-biology/natural-selection/artificial-selection/e/artificial-selection

Uploaded 06-03-19

How humans have shaped plants and animals through artificial selection and domestication.

View more lessons or practice this subject at https://www.khanacademy.org/science/ap-biology/natural-selection/artificial-selection/v/artificial-selection-and-domestication

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Perfect competition | Microeconomics | Khan Academy

Wed, 28 Oct 2026 11:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/production-cost-and-the-perfect-competition-model-temporary/ap-perfect-competition/v/economic-profit-for-firms-in-perfectly-competitive-markets

Uploaded 04-03-19

Perfect competition, sometimes called pure competition, is a theoretical market structure in which there are many buyers and sellers selling homogeneous goods, no barriers to entry, and perfect information. In this video, explore the precise definition of perfect competition, and how these assumptions are captured on graphs.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Subtracting Real Numbers

Wed, 28 Oct 2026 10:06:00 -0000

u9_l2_t3_we1 Subtracting Real Numbers

Uploaded 15-07-11

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Four factors of production | AP Microeconomics | Khan Academy

Wed, 28 Oct 2026 10:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-macroeconomics/basic-economics-concepts-macro/introduction-to-the-economic-way-of-thinking-macro/v/normative-and-positive-statements

Uploaded 12-02-19

Economists traditionally divide the factors of production into four categories: land, labor, capital, and entrepreneurship. Learn how each of these are defined in this video.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Slope and intercepts from tables

Wed, 28 Oct 2026 09:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:applying-intercepts-and-slope/e/interpreting-tables

Uploaded 11-02-19

Slope and intercepts from tables

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Adding four two digit numbers

Wed, 28 Oct 2026 08:06:00 -0000

Adding four two digit numbers

Uploaded 22-07-20

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Slope and y intercept from equation

Wed, 28 Oct 2026 08:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:intro-to-slope-intercept-form/v/slope-intercept-intro-examples

Uploaded 11-02-19

Slope and y intercept from equation

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Linear equation word problems

Wed, 28 Oct 2026 07:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:intro-to-slope-intercept-form/e/interpreting-features-of-linear-functions

Uploaded 11-02-19

Linear equation word problems

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Adding negative numbers (example) | Negative numbers and absolute value | Pre-Algebra | Khan Academy

Wed, 28 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-add-negatives/v/adding-negative-numbers

Uploaded 15-07-11

Use a number line to add -15 + (-46) + (-29)

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/add-subtract-negatives-pre-alg/e/adding_negative_numbers?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/add-subtract-negatives-pre-alg/v/adding-integers-with-different-signs?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
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Constructing linear equation from context

Wed, 28 Oct 2026 06:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:writing-slope-intercept-equations/e/constructing-linear-functions-word-problems

Uploaded 11-02-19

Constructing linear equation from context

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Khan Stories: Anjali

Wed, 28 Oct 2026 05:00:00 -0000

From facing the fear of asking questions to taking a leadership role in her school, Anjali is using Khan Academy to change her life. She says “People think that a girl can’t study; she has to do household work. I want to change the world, so I started with myself.” 🙋🏽‍♀️

Uploaded 08-02-19

Do you have a story about Khan Academy you’d like to share? Visit https://www.khanacademy.org/stories.

Khan Academy is a 501(c)(3) nonprofit organization that relies on support from people like you. Help make a difference in the lives of students around the world by donating today. http://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc&campaign=khanstories

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Adding multiple two digit numbers word problem

Wed, 28 Oct 2026 04:06:00 -0000

Adding multiple two digit numbers word problem

Uploaded 22-07-20

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Rounding to the nearest 10

Wed, 28 Oct 2026 04:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-third-grade-math/imp-addition-and-subtraction/imp-rounding/v/rounding-to-the-nearest-100-number-line

Uploaded 17-01-19

Rounding to the nearest 10

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Three digit addition word problems

Wed, 28 Oct 2026 03:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/mappers/number-and-operations-192-202/x261c2cc7:addition-and-subtraction-word-problems/v/three-digit-subtraction-word-problems

Uploaded 17-01-19

Three digit addition word problems

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Multi-step inequalities 3 | Linear inequalities | Algebra I | Khan Academy

Wed, 28 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:multistep-inequalities/v/multi-step-inequalities-3

Uploaded 15-07-11

Multi-Step Inequalities

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/e/linear_inequalities?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

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https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Estimating adding large numbers by rounding

Wed, 28 Oct 2026 02:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-third-grade-math/imp-addition-and-subtraction/estimate-to-add-multi-digit-numbers/e/estimate-to-add-multi-digit-whole-numbers-

Uploaded 17-01-19

Estimating adding large numbers by rounding

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Three digit subtraction word problems

Wed, 28 Oct 2026 01:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-third-grade-math/imp-addition-and-subtraction/addition-and-subtraction-word-problems/e/add-and-subtract-within-1000-word-problems

Uploaded 17-01-19

Three digit subtraction word problems

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Getting a sense of meters and centimeters

Wed, 28 Oct 2026 00:06:00 -0000

Getting a sense of meters and centimeters

Uploaded 22-07-20

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Rounding to the nearest 100

Wed, 28 Oct 2026 00:00:00 -0000

Rounding to the nearest 100

Uploaded 17-01-19

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Methods for subracting 3 digit numbers

Tue, 27 Oct 2026 23:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-third-grade-math/imp-addition-and-subtraction/strategies-for-subtracting-two-and-three-digit-numbers/e/select-strategies-for-subtracting-within-1000

Uploaded 17-01-19

Methods for subracting 3 digit numbers

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Perimeter and unit conversion | Ratios, proportions, units, and rates | Pre-Algebra | Khan Academy

Tue, 27 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-area-perimeter/geometry-perimeter/v/perimeter-and-unit-conversion

Uploaded 15-07-11

Perimeter and Unit Conversion

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/metric-system-tutorial/v/applying-the-metric-system?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Subtraction by breaking apart

Tue, 27 Oct 2026 22:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-third-grade-math/imp-addition-and-subtraction/strategies-for-subtracting-two-and-three-digit-numbers/e/break-apart-3-digit-subtraction-problems

Uploaded 17-01-19

Subtraction by breaking apart

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Missing numbers in three digit subtraction

Tue, 27 Oct 2026 21:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-third-grade-math/imp-addition-and-subtraction/imp-addition-and-subtraction-missing-value-problems/e/find-the-missing-number--addition-and-subtraction-within-1000-

Uploaded 17-01-19

Missing numbers in three digit subtraction

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Reasoning with systems of equations | Systems of equations | Algebra I | Khan Academy

Tue, 27 Oct 2026 20:06:00 -0000

When we perform operations on a system of equations, some operations produce an equivalent system, while others don't necessarily produce an equivalent system. When we're solving a system of equations, we need to use operations that guarantee equivalence.

Uploaded 13-07-20

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Types of competition and marginal revenue | APⓇ Microeconomics | Khan Academy

Tue, 27 Oct 2026 20:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/imperfect-competition/introduction-to-imperfect-competition/v/marginal-revenue-and-marginal-cost-in-imperfect-competition

Uploaded 21-12-18

In imperfect competition firms have some control over the price they charge, so the individual firm's demand curve is not horizontal. Learn how that fact also changes the marginal revenue curve in this video.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Marginal revenue and marginal cost in imperfect competition | APⓇ Microeconomics | Khan Academy

Tue, 27 Oct 2026 19:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/imperfect-competition/introduction-to-imperfect-competition/e/imperfect-competition

Uploaded 21-12-18

This video discusses the differences in a graph of marginal cost and marginal revenue for an imperfectly competitive firm compared to a perfectly competitive firm.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Identifying percent amount and base | Decimals | Pre-Algebra | Khan Academy

Tue, 27 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/7th-grade-foundations-engageny/7th-m4-engage-ny-foundations/7th-m4-ta-foundations/v/identifying-percent-amount-and-base

Uploaded 15-07-11

Identifying Percent Amount and Base

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/percent-intro-pre-alg/e/converting_decimals_to_fractions_1?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/percent-intro-pre-alg/v/representing-a-number-as-a-decimal-percent-and-fraction-2?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
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Profit maximization worked example Free Response Question | Microeconomics | Khan Academy

Tue, 27 Oct 2026 18:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/production-cost-and-the-perfect-competition-model-temporary/profit-maximization/e/profit-maximization

Uploaded 20-12-18

Work through a free response question about profit maximization in this video.

Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from both a college level or an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Perfect and imperfect competition

Tue, 27 Oct 2026 17:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/imperfect-competition/introduction-to-imperfect-competition/v/types-of-competition-and-marginal-revenue

Uploaded 18-12-18

Perfect competition, monopolies, oligopolies, monopsony and monopolistic competition.

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Interpret quadratic models: Factored form | Algebra I | Khan Academy

Tue, 27 Oct 2026 16:06:00 -0000

Given a quadratic function that models a relationship, we can rewrite the function to reveal certain properties of the relationship. Factored form helps us identify the x-intercepts or zeros of the function.

Uploaded 13-07-20

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Shutting down or exiting industry based on price | APⓇ Microeconomics | Khan Academy

Tue, 27 Oct 2026 16:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/production-cost-and-the-perfect-competition-model-temporary/36/e/firms-short-run-decisions-to-produce-and-long-run-decisions-to-enter-or-exit-a-market

Uploaded 18-12-18

Whether a firm decides to produce in the short run depends on the relationship between price and average variable cost, but whether a firm decides to produce in the long run depends on the relationship between price and average total cost. Learn about the shut-down rule and the industry exit rule in this video.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Profit maximization | APⓇ Microeconomics | Khan Academy

Tue, 27 Oct 2026 15:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/production-cost-and-the-perfect-competition-model-temporary/profit-maximization/v/profit-maximization-worked-example

Uploaded 18-12-18

Learn about the profit maximization rule, and how to implement this rule in a graph of a perfectly competitive firm, in this video.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Dividing a decimal by a power of 10 | Decimals | Pre-Algebra | Khan Academy

Tue, 27 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/6th-grade-foundations-engageny/6th-m4-engage-ny-foundations/6th-m4-tb-foundations/v/dividing-a-decimal-by-a-power-of-10

Uploaded 15-07-11

When we were multiplying, we moved the decimal to the right for each power of ten. Guess what? When dividing, we move the decimal to the left for each power of ten.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/mult-div-by-10-dec-pre-alg/e/converting_fractions_to_decimals_0.5?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/mult-div-by-10-dec-pre-alg/v/dividing-decimals-2-1?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
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Khan Stories: Brooke Hogan

Tue, 27 Oct 2026 14:00:00 -0000

Middle school teacher Brooke Hogan makes teaching personal by getting to know every student at an individual level. She says it’s important to “recognize them as a person, not just as my student." 💛

Uploaded 14-12-18

We're humbled to empower teachers like Brooke Hogan with personalized practice, so every student can succeed!

Do you have a story about Khan Academy you’d like to share? Visit https://www.khanacademy.org/stories.

Khan Academy is a 501(c)(3) nonprofit organization that relies on support from people like you. Help make a difference in the lives of students around the world by donating today: http://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc&campaign=khanstories

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Tariff and imports worked example | APⓇ Microeconomics | Khan Academy

Tue, 27 Oct 2026 13:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/unit-2-supply-and-demnd/29-international-trade-and-public-policy/e/international-trade-and-public-policy

Uploaded 07-12-18

Walk through the solution to a question on the effect of tariffs from the 2012 AP(R) Microeconomics exam.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Using text features to locate information | Reading | Khan Academy

Tue, 27 Oct 2026 12:06:00 -0000

Nonfiction texts contain useful features that organize information. You can learn to read these text features like a map to help point you towards the things you want to know!

Uploaded 13-07-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Trade and tariffs | APⓇ Microeconomics | Khan Academy

Tue, 27 Oct 2026 12:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/unit-2-supply-and-demnd/29-international-trade-and-public-policy/v/tariff-and-imports-worked-example

Uploaded 07-12-18

When governments impose restrictions on international trade, this affects the domestic price of the good and reduces total surplus. One such imposition is a tariff (a tax on imported or exported goods and services). See how a tariff impacts price, consumer surplus, producer surplus, tax revenue, and deadweight loss in this video.

AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Mutation as a source of variation | Gene expression and regulation | AP Biology | Khan Academy

Tue, 27 Oct 2026 11:00:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-biology/ecology-ap/disruptions-to-ecosystems/v/introduced-species-and-biodiversity

Uploaded 05-12-18

Mutation in genotype as a source of variation in phenotype

View more lessons or practice this subject at https://www.khanacademy.org/science/ap-biology/gene-expression-and-regulation/mutations-ap/v/mutation-as-a-source-of-variation

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Unit conversion word problem: yards to inches | Introduction to algebra | Algebra I | Khan Academy

Tue, 27 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-fifth-grade-math/imp-measurement-and-data-3/imp-unit-measurement-word-problems/v/unit-conversion-with-fractions

Uploaded 15-07-11

In this example, we need to convert from yards to inches. We'll do it a couple of ways.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/introduction-to-algebra/units-algebra/e/units?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

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Missed the previous lesson?
https://www.khanacademy.org/math/algebra/introduction-to-algebra/units-algebra/v/unit-conversion-example-drug-dosage?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Chronometric revolution | Cosmology and Astronomy | Khan Academy

Tue, 27 Oct 2026 10:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/biology/history-of-life-on-earth/radiometric-dating/v/chronometric-revolution

Uploaded 24-10-11

Discussion of the relatively recent changes in our ability as a species to shine light on our deep past. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/measuring-age-tutorial/v/carbon-14-dating-1?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/random-predictions-for-2060?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Cosmology and Astronomy channel: https://www.youtube.com/channel/UChNPnEkW8LYZ5Rwi8_A2-DA?sub_confirmation=1
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Euler's line proof | Special properties and parts of triangles | Geometry | Khan Academy

Tue, 27 Oct 2026 09:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/triangle-property-review/v/euler-s-line-proof

Uploaded 24-10-11

Proving the somewhat mystical result that the circumcenter, centroid and orthocenter

Watch the next lesson: https://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/quadrilaterals/v/quadrilateral-overview?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/triangle_property_review/v/euler-line?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Different mediums and the tone of the text | Reading | Khan Academy

Tue, 27 Oct 2026 08:06:00 -0000

How does a text change when it goes from one medium to another, when it changes from a written work to a visual or audio one? That feeling it gives off can change—this might be why you were disappointed by the film adaptation of a favorite book, or why you love the adaptational changes someone made to a book you *didn’t* especially like.

Uploaded 13-07-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions:

GREENHOUSE BLUES was illustrated by Cour Billadeau and written by me, David Rheinstrom, as a comics project for the science fiction podcast OUR FAIR CITY.
Cour is great! You can follow their fantastic illustration work by visiting http://billet-deaux.com

Hands off My Phone! is an excerpt from an audio play that goes alongside a series of reading exercises for Khan Academy's ELA curriculum! To learn more, visit: https://www.khanacademy.org/ela/cc-6th-reading-vocab/x8c8165c7dcd5e900:learn-by-topic-banning-behavior

This play stars:
Lisette Alvarez as Valentina
Jordan Cobb as Jamila
Felipe Escamilla as Principal Rosario, and
David Rheinstrom as Sebastian

Lisette's work can be found all over the internet, but especially on their urban fantasy podcast, KALILA STORMFIRE'S ECONOMICAL MAGICK SERVICES.
Jordan is a writer, director, and actor—her production company, NO SUCH THING AUDIO DRAMA PRODUCTIONS, creates engrossing and terrifying stories for the ear.
Felipe and David work at Khan Academy!

“Cafeteria AMB” licensed under an attribution license from https://freesound.org/people/RorisangKgatle/sounds/366607/
“crazy feet, sensible shoes” by Curlew licensed under a CC 3.0 Attribution-Noncommercial-NoDerivativeWorks license: https://freemusicarchive.org/music/Curlew/Live_at_WFMU_on_Storks_show_6221997/Crazy_Feet_Sensible_Shoes

Other sound effects and music from non-copyrighted (Creative Commons Zero license) sources

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Common orthocenter and centroid | Geometry | Khan Academy

Tue, 27 Oct 2026 08:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/altitudes/v/common-orthocenter-and-centroid

Uploaded 25-10-11

Showing that a triangle with the same point as the orthocenter and centroid is equilateral

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/triangle_property_review/v/review-of-triangle-properties?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/altitudes/v/proof-triangle-altitudes-are-concurrent-orthocenter?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Currency Exchange Introduction

Tue, 27 Oct 2026 07:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/currency-exchange-introduction

Uploaded 24-10-10

Introduction to how exchange rates can fluctuate
More free lessons at: http://www.khanacademy.org/video?v=itoNb1lb5hY

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Multiplying a decimal by a power of 10 | Decimals | Pre-Algebra | Khan Academy

Tue, 27 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/6th-grade-foundations-engageny/6th-m4-engage-ny-foundations/6th-m4-tb-foundations/v/multiplying-a-decimal-by-a-power-of-10

Uploaded 15-07-11

You will notice in this word problem that moving the decimal to the right the same number of times as the number of zeros you multiplying by gets you the answer you desire. Check this out!

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/mult-div-by-10-dec-pre-alg/e/converting_fractions_to_decimals_0.5?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/mult-div-by-10-dec-pre-alg/v/dividing-a-decimal-by-a-power-of-10?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/sig-figs-pre-alg/v/multiplying-and-dividing-with-significant-figures?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Currency Effect on Trade

Tue, 27 Oct 2026 06:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/currency-effect-on-trade

Uploaded 25-10-10

Currency Effect on Trade
More free lessons at: http://www.khanacademy.org/video?v=5HVCFrXQ9pw

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Pegging the yuan | Money, banking and central banks | Finance and Capital Markets | Khan Academy

Tue, 27 Oct 2026 05:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/pegging-the-yuan

Uploaded 25-10-10

How the Chinese Central Bank could peg the Yuan to the dollar by printing Yuan and buying dollars (building up a dollar reserve). Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/chinese-central-bank-buying-treasuries?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/currency-effect-on-trade-review?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: This tutorial walks through how China's undervaluing of its currency impacts trade and prices (which also fuels cheap borrowing for the U.S.).

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Evaluating a source’s reasoning and evidence | Reading | Khan Academy

Tue, 27 Oct 2026 04:06:00 -0000

Don’t believe everything you read! A source has to give you a reason to trust it before you can accept what it’s trying to tell you. You can’t just accept it on faith when someone tells you there are goblins on the moon. How do they know that, and how can they prove to you that it’s true? (They can’t!)

Uploaded 13-07-20

But you need to learn to trust SOME sources, or you won't be able to do everyday tasks without an overwhelming sense of doubt. So let's figure out how to evaluate sources.

Use your brain, your heart, and your reading skills, Readers! You’ve got this.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Currency Effect on Trade Review

Tue, 27 Oct 2026 04:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/currency-effect-on-trade-review

Uploaded 25-10-10

Currency Effect on Trade Review
More free lessons at: http://www.khanacademy.org/video?v=Ysk1ySejuCQ

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Chinese Central Bank Buying Treasuries

Tue, 27 Oct 2026 03:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/chinese-central-bank-buying-treasuries

Uploaded 25-10-10

Chinese Central Bank Buying Treasuries
More free lessons at: http://www.khanacademy.org/video?v=MN4SWiEEqKo

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Converting mixed numbers to improper fractions | Fractions | Pre-Algebra | Khan Academy

Tue, 27 Oct 2026 02:06:00 -0000

Converting Mixed Numbers to Improper Fractions

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/mixed-numbers-pre-alg/e/converting_mixed_numbers_and_improper_fractions?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/mixed-numbers-pre-alg/v/changing-a-mixed-number-to-an-improper-fraction?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/mixed-numbers-pre-alg/v/proper-and-improper-fractions?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

Uploaded 15-07-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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American-Chinese Debt Loop

Tue, 27 Oct 2026 02:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/american-chinese-debt-loop

Uploaded 25-10-10

How the Chinese buying of American debt leads to lower interest rates
More free lessons at: http://www.khanacademy.org/video?v=m5xu4r0szaA

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Debt Loops Rationale and Effects

Tue, 27 Oct 2026 01:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/debt-loops-rationale-and-effects

Uploaded 25-10-10

Positive and negative effects of China's devaluing of their currency
More free lessons at: http://www.khanacademy.org/video?v=XBI7DqttyOQ

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Reasoning with linear equations | Solving equations and inequalities | Algebra 1 | Khan Academy

Tue, 27 Oct 2026 00:06:00 -0000

When we perform operations to manipulate equations, some operations produce equivalent equations, while others don't necessarily produce equivalent equations. When we're solving an equation, we need to use operations that guarantee equivalence.

Uploaded 09-07-20

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Monitoring Khanmigo Progress Reports

Tue, 27 Oct 2026 00:00:00 -0000

Unlock the full potential of your district's AI implementation by mastering Khanmigo Usage and Activity Reports. This video shows administrators how to drill down into schoolwide, teacher, and classroom data to understand exactly when and how Khanmigo is being used. By combining high-level metrics with specific activity tracking, you can uncover powerful engagement patterns across your schools. Learn to navigate your dashboard features with confidence and turn data into a go-to resource for district success.

Uploaded 05-10-26

00:00 Opening/Intro
00:10 Admin Dashboard
00:37 Khanmigo Usage
02:01 Khanmigo Activity:
02:50 Connecting Khanmigo to Success
03:48 Closing

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30-60-90 Triangles II

Mon, 26 Oct 2026 23:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/geometry-home/right-triangles-topic/special-right-triangles/v/intro-to-30-60-90-triangles

Uploaded 15-05-07

More examples using 30-60-90 triangles.
More free lessons at: http://www.khanacademy.org/video?v=3mLUJSoh6i0

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Comparing fractions with different denominators | Fractions | Pre-Algebra | Khan Academy

Mon, 26 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/arithmetic-home/arith-review-fractions/arith-comparing-fractions/v/comparing-fractions-2

Uploaded 15-07-11

Need help comparing fractions? Try simplifying them first then finding a common denominator. The result are two fractions you can really compare.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/e/comparing_fractions_2?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/v/ordering-fractions?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/v/comparing-fractions?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Administrator Skills Reports

Mon, 26 Oct 2026 22:00:00 -0000

In this video, administrators will explore Khan Academy’s Progress by Skills Report and learn how to use skill level data to better understand student learning and mastery. We’ll walk through how to filter and customize the report, analyze mastery trends, identify students who may need additional support, and drill down into individual student progress. This powerful report helps educators make informed instructional decisions, support meaningful data conversations, and monitor student growth across schools, grade levels, and courses.

Uploaded 05-10-26

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Introduction to Logarithms

Mon, 26 Oct 2026 21:00:00 -0000

An introduction to logarithms

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

Uploaded 16-05-07

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Defining appropriate quantities for modeling | Working with units | Algebra I | Khan Academy

Mon, 26 Oct 2026 20:06:00 -0000

Examples for different ways to define how quantities of interest are calculated in a modeling problem.

Uploaded 06-07-20

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Administrator Progress Reports on Khan Academy

Mon, 26 Oct 2026 20:00:00 -0000

In this video, administrators will explore Khan Academy’s Progress Reports and learn how to use real time data to monitor student engagement, skill growth, and learning trends across schools, grades, teachers, and individual students. We’ll walk through Progress by Course, School, Grade, and Teacher reports, including how to filter data, review learning metrics, and drill down into detailed student progress. Whether you’re supporting a single school or an entire district, these reports provide powerful insights to help inform instructional decisions, celebrate growth, and better support student success with Khan Academy.

Uploaded 05-10-26

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Quadratic inequalities (visual explanation) | Algebra II | Khan Academy

Mon, 26 Oct 2026 19:00:00 -0000

How to solve a quadratic inequality. Visual intuition of what a quadratic inequality means.

Uploaded 06-06-07

Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial_tutorial/v/terms-coefficients-and-exponents-in-a-polynomial?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_ineq/v/quadratic-inequalities?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1
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Recognizing prime and composite numbers | Factors and multiples | Pre-Algebra | Khan Academy

Mon, 26 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-fourth-grade-math/imp-factors-multiples-and-patterns/imp-prime-and-composite-numbers/v/recognizing-prime-numbers

Uploaded 18-07-11

Can you recognize the prime numbers in this group of numbers? Which are prime, composite, or neither?

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/factors-multiples/prime_numbers/e/prime_numbers?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/factors-multiples/prime_factorization/v/prime-factorization?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/factors-multiples/prime_numbers/v/prime-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Activation Report for school leaders

Mon, 26 Oct 2026 18:00:00 -0000

In this video, school and district administrators will learn how to use Khan Academy’s Activation Reports to monitor teacher and student account activation progress across their organization. We’ll explore Activation by Site, Activation by Grade, and Activation by Teacher reports, and how these tools can help identify progress, support implementation goals, and ensure educators and students are set up for success with Khan Academy. Whether you’re leading a single school or an entire district, these reports provide valuable insights to support a strong launch and ongoing implementation.

Uploaded 05-10-26

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Basic Trigonometry

Mon, 26 Oct 2026 17:00:00 -0000

An introduction to trigonometric functions: sine, cosine, and tangent.

Uploaded 13-08-07

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

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Formulas and units: Volume of a pool | Working with units | Algebra I | Khan Academy

Mon, 26 Oct 2026 16:06:00 -0000

When using formulas to calculate real-world quantities, we need to make sure our units are consistent. In this video, the base area of a pool is given in square meters while its height is given in centimeters. In order to use the formula for volume, we need to convert one of the measurements to units that match the other measurement.

Uploaded 06-07-20

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Administrator dashboard overview for school leaders

Mon, 26 Oct 2026 16:00:00 -0000

Join Michele, a Professional Learning Specialist at Khan Academy, for a guided tour of the Khan Academy Administrator Dashboard! In this video, school based administrators will learn how to activate their account, navigate key dashboard features, and use important data insights like activation, learning minutes, proficiency progress, and Khanmigo usage to support successful implementation across their school.

Uploaded 05-10-26

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Basic Trigonometry II

Mon, 26 Oct 2026 15:00:00 -0000

Another example of figuring out the sine, cosine, and tangent of an angle in a right triangle

Uploaded 13-08-07

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Least common multiple exercise: 3 numbers | Factors and multiples | Pre-Algebra | Khan Academy

Mon, 26 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-lcm/v/least-common-multiple-lcm

Uploaded 18-07-11

This least common multiple example gives us 3 numbers from which to find the lcm. This is a challenge, but fun. Do it with us!

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/factors-multiples/least_common_multiple/e/least_common_multiple?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/factors-multiples/greatest_common_divisor/v/greatest-common-divisor-factor-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/factors-multiples/least_common_multiple/v/least-common-multiple-exercise-2?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
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Communicate the 'Why?' for district leaders

Mon, 26 Oct 2026 14:00:00 -0000

Discover why "communicating the why" is a crucial leadership move for a successful Khan Academy implementation. This video explores how a clear, shared purpose helps teachers make stronger instructional decisions, aligns staff messaging, and prevents the platform from feeling like just another task. Learn how to build a unified vision with your leadership team and craft a consistent message that transforms families into true partners in student learning. By establishing this clear connection, you will foster a robust school culture centered on confidence and visible student growth.

Uploaded 05-10-26

00:00 Opening/Intro
00:17 Why the Message Matters
00:51 A Clear Why
01:30 Consistent Message to Families
02:13 Home-School Connection
02:59 Closing/Final Call to Action

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Radian and degree | Unit circle definition of trig functions | Trigonometry | Khan Academy

Mon, 26 Oct 2026 13:00:00 -0000

What a radian is. Converting radians to degrees and vice versa.

Uploaded 13-08-07

Watch the next lesson: https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/v/unit-circle-definition-of-trig-functions-1?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Missed the previous lesson?
https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/radian-and-degree-conversion-practice?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Trigonometry channel:
https://www.youtube.com/channel/UCYQSs1lFJZKpyqNQQHYFGjw?sub_confirmation=1
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Formulas and units: Comparing rates | Working with units | Algebra I | Khan Academy

Mon, 26 Oct 2026 12:06:00 -0000

When using formulas to calculate real-world quantities, we need to make sure our units are consistent. In this video, one growth rate is given in centimeters per week and the other is given in millimeters per day. In order to compare which rate is faster, we need to convert one of the rates to units that match the other rate.

Uploaded 06-07-20

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Activation and goal setting for school leaders

Mon, 26 Oct 2026 12:00:00 -0000

Learn how to configure district learning targets in Khan Academy to ensure your school leaders and teachers are aligned on measurable student growth from day one. This video walks administrators through the setup process—including activating your account via Clever, ClassLink, or email invitation—and demonstrates how to define primary goals and core targets like course mastery, weekly skills proficiency, Khanmigo usage, and learning minutes. Discover how to tailor these metrics to your district’s specific implementation model, whether you are using Khan Academy as a supplement to your core curriculum, for MTSS interventions, or for SAT prep.

Uploaded 05-10-26

00:20 Efficacious Use
00:51 Activating Your Administrator Account:
02:05 Setting a primary goal
02:46 Adding/editing goals
04:36 Implementation models:
05:38 Assign courses
06:04 Closing

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Using Trig Functions

Mon, 26 Oct 2026 11:00:00 -0000

Using Trigonometric functions to solve the sides of a right triangle

Uploaded 14-08-07

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Comparing with multiplication: age | Multiplication and division | Arithmetic | Khan Academy

Mon, 26 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/5th-grade-foundations-engageny/5th-m4-engage-ny-foundations/5th-m4-tf-foundations/v/multiplying-whole-numbers-and-applications-6

Uploaded 18-07-11

Multiplication helps us compare ages. Hint: learn those multiplication tables. They really help on problems like these.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-word-problems/e/arithmetic_word_problems?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic

Watch the next lesson: https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-word-problems/v/multiplication-word-problem-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic

Missed the previous lesson?
https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-word-problems/v/comparing-with-multiplication-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic

Arithmetic on Khan Academy: So you're ready to have some arithmetic fun? You've come to the right spot! It's the first "official" math topic and chalked full of fun exercises and great videos which help you start your journey towards math mastery. We'll cover the big ones: addition, subtraction, multiplication, and division, of course. But we don't stop there. We'll get into negative numbers, absolute value, decimals, and fractions, too. Learning math should be fun, and we plan on having some with you. Ready to get started?

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Arithmetic channel: https://www.youtube.com/channel/UCFlJkgTNeC-FYYIQnyE5yzQ?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Paving an implementation path for school leaders

Mon, 26 Oct 2026 10:00:00 -0000

Join Diona as she introduces Khan Academy’s District Implementation Framework, a strategy for creating consistent, high-quality learning experiences by pairing AI-powered support like Khanmigo with strategic leadership actions. Dioan will outline specific instructional priorities, including Supplementing Core Instruction, MTSS and Intervention, ELA and Writing, and Test Prep. She’ll also describe the administrative role in ensuring success through proactive routines, such as protecting dedicated weekly practice time and leading data discussions focused on student proficiency gains and differentiation. By aligning Khan Academy to district goals, leaders provide students with a clear path to mastery.

Uploaded 05-10-26

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Using Trig Functions Part II

Mon, 26 Oct 2026 09:00:00 -0000

A couple of more examples of using Trig functions to solve the sides of a triangle.

Uploaded 14-08-07

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Using units to solve problems: Road trip | Working with units | Algebra I | Khan Academy

Mon, 26 Oct 2026 08:06:00 -0000

In word problems that involve multiple quantities, we can use the units of the quantities to guide our solution. In this video, we find the cost of fuel for a road trip, using information that involves many different quantities, not all of which are useful for our problem.

Uploaded 06-07-20

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Khan Academy for district needs

Mon, 26 Oct 2026 08:00:00 -0000

Join Crystal, a Professional Learning Specialist from Khan Academy, in this video and learn how Khan Academy can support your students and teachers through meaningful practice, classroom routines, Khanmigo support, and administrator dashboard insights. This video gives school and district leaders a quick overview of how Khan Academy can connect to priorities like core instruction, MTSS, writing support, and test preparation.

Uploaded 05-10-26

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Unit Circle Definition of Trig Functions

Mon, 26 Oct 2026 07:00:00 -0000

Using the unit circle to define the sine, cosine, and tangent functions

Uploaded 20-08-07

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Subtraction Word Problem

Mon, 26 Oct 2026 06:06:00 -0000

u01_l2_t2_we3 Subtraction Word Problem
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education

Uploaded 18-07-11

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Khanmigo for students teachers and administrators

Mon, 26 Oct 2026 06:00:00 -0000

Discover Khanmigo, Khan Academy’s AI-powered tool, and how it supports the entire educational ecosystem. The video explores Khanmigo's function as a safe, ethical tutor for students, guiding productive struggle and giving real-time feedback without providing shortcuts. It also serves as an instructional assistant for teachers, helping to streamline planning, generate lesson materials like differentiated practice, and monitor classroom progress with tools like the Class Snapshot. Finally, for school and district leaders, Khanmigo offers tools to streamline administrative tasks, enhance communication, and enable data-driven decision-making through features like the SMART Goal Writer and Course Snapshot reports.

Uploaded 05-10-26

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Graph of the sine function

Mon, 26 Oct 2026 05:00:00 -0000

Using the unit circle definition of the sine function to make a graph of it.

Uploaded 20-08-07

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Using units to solve problems: Toy factory | Working with units | Algebra I | Khan Academy

Mon, 26 Oct 2026 04:06:00 -0000

In word problems that involve multiple quantities, we can use the units of the quantities to guide our solution. In this video, we find the value of toys produced at a factory using information that involves many different quantities, not all of which are useful for our problem.

Uploaded 06-07-20

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The AI-enhanced mastery learning approach for school leaders

Mon, 26 Oct 2026 04:00:00 -0000

Join Rachel as she presents Khan Academy’s AI-enhanced mastery learning approach, a strategic framework designed to drive instructional rigor and ensure educational equity by allowing students to demonstrate full content mastery before advancing. This system leverages Khanmigo, a purpose-built Socratic AI coach with a compliance-first architecture that supports productive struggle while maintaining full administrative oversight of student interactions and data. Leaders can utilize the Administrator Dashboard to analyze system-wide mastery metrics across distinct levels (Attempted, Familiar, Proficient, Mastered) to set data-informed priorities, allocate resources effectively, and design clear implementation plans that reinforce high expectations and link classroom-level practice to established district goals for long-term success.

Uploaded 05-10-26

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Graphs of trig functions

Mon, 26 Oct 2026 03:00:00 -0000

Exploring the graphs of trig functions

Uploaded 21-08-07

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Subtracting Whole Numbers

Mon, 26 Oct 2026 02:06:00 -0000

u01_l2_t2_we1 Subtracting Whole Numbers
More free lessons at: http://www.khanacademy.org/video?v=sAw71J2kYJE
Content provided by TheNROCproject.org - (c) Monterey Institute for Technology and Education

Uploaded 18-07-11

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Schoolwide discussions

Mon, 26 Oct 2026 02:00:00 -0000

Leading effective schoolwide discussions about Khan Academy is less about platform expertise and more about facilitating the right conversations. This video provides practical strategies for team leads to shift meetings from compliance-based check-ins to collaborative, student-centered sessions by establishing common weekly routines, using shared data indicators to identify patterns, and communicating clear, actionable barriers to leadership. By keeping your team focused on the rhythm of student learning—practicing, checking progress, and selecting targeted instructional +moves—you can build momentum, celebrate successes, and ensure your team has the support they need to help students thrive.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khancademy.org/khan-for-educators

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Graphing trig functions

Mon, 26 Oct 2026 01:00:00 -0000

Analyzing the amplitude and periods of the sine and cosine functions.

Uploaded 21-08-07

Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/graphs_of_sine_and_cosine?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription

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Interpret quadratic models: Vertex form | Algebra I | Khan Academy

Mon, 26 Oct 2026 00:06:00 -0000

Given a quadratic function that models a relationship, we can rewrite the function to reveal certain properties of the relationship. Vertex form helps us identify the minimum or maximum of the function.

Uploaded 06-07-20

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Celebrating success and identifying challenges

Mon, 26 Oct 2026 00:00:00 -0000

This reflective video guides educators in evaluating their Khan Academy classroom implementation. By examining established routines, student progress data, and the use of support tools, teachers can identify their successes and areas for growth. The activity encourages a constructive, iterative approach to teaching, asking viewers to pinpoint one practice to maintain and one to refine to help students master new skills.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khancademy.org/khan-for-educators

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More trig graphs

Sun, 25 Oct 2026 23:00:00 -0000

Determining the equations of trig functions by inspecting their graphs.

Uploaded 21-08-07

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Subtraction with Borrowing or Regrouping

Sun, 25 Oct 2026 22:06:00 -0000

u01_l2_t2_we2 Subtraction with Borrowing or Regrouping

Uploaded 18-07-11

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Embracing the struggle

Sun, 25 Oct 2026 22:00:00 -0000

Learn how productive struggle can support deeper thinking, stronger problem-solving, and meaningful learning.Explore how to distinguish productive struggle from unproductive frustrations, and identify ways to support students when they get stuck. See how Khanmigo can help students through productive struggle while keeping the cognitive work with the student.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khancademy.org/khan-for-educators

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Determining the equation of a trigonometric function

Sun, 25 Oct 2026 21:00:00 -0000

Determining the amplitude and period of sine and cosine functions.

Uploaded 22-08-07

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Interpreting a parabola in context | Quadratic functions and equations | Algebra I | Khan Academy

Sun, 25 Oct 2026 20:06:00 -0000

Given a parabola that models a context, we can relate key features of the parabola — like the y-intercept, vertex, and x-intercepts — to what they represent in the given context.

Uploaded 06-07-20

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Celebrating student achievements

Sun, 25 Oct 2026 20:00:00 -0000

Learn how to recognize and celebrate a wide range of student achievements in Khan Academy. This video guides teachers in using progress data to identify meaningful milestones and connect celebrations to student goals. By celebrating effort, persistence, and growth (not just completion or correctness) teachers can reinforce motivation, encourage student ownership, and build a stronger culture of learning.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khancademy.org/khan-for-educators

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The unit circle definition of trigonometric function

Sun, 25 Oct 2026 19:00:00 -0000

Using the unit circle to extend the SOH CAH TOA definition of the basic trigonometric functions.

Uploaded 22-08-07

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Finding common denominators | Fractions | Pre-Algebra | Khan Academy

Sun, 25 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-fourth-grade-math/comparing-fractions-and-equivalent-fractions/imp-common-denominators/v/finding-common-denominators

Uploaded 18-07-11

Finding Common Denominators

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/equivalent-fractions-pre-alg/e/equivalent_fractions?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/v/comparing-fractions-with-greater-than-and-less-than-symbols?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/equivalent-fractions-pre-alg/v/equivalent-fractions-example?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Communicating Expectations

Sun, 25 Oct 2026 18:00:00 -0000

Join Kate, a former classroom educator and Teacher Resources Content Creator at Khan Academy, as she explores how clear expectations and routines can help students use Khan Academy successfully and independently.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khancademy.org/khan-for-educators

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Return on capital | Finance and Capital Markets | Khan Academy

Sun, 25 Oct 2026 17:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/economics-finance-domain/ap-macroeconomics/ap-long-run-consequences-of-stabilization-policies/public-policy-and-economic-growth/v/return-on-capital

Uploaded 30-08-07

Introduction to return on capital and cost of capital. Using these concepts to decide where to invest. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/investment-vs-consumption-1?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/human-capital?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: When are you using capital to create more things (investment) vs. for consumption (we all need to consume a bit to be happy). When you do invest, how do you compare risk to return? Can capital include human abilities? This tutorial hodge-podge covers it all.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Sequences and domain | Sequences | Algebra I | Khan Academy

Sun, 25 Oct 2026 16:06:00 -0000

We can generate the same sequence with different functions and different domains.

Uploaded 06-07-20

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Connecting topics with student interests

Sun, 25 Oct 2026 16:00:00 -0000

Learn how to use Khanmigo teacher tools to connect Khan Academy course topics to students’ interests and real-world contexts. This video highlights ways to develop relevant examples, prompts, and lesson ideas that help students see purpose in what they’re learning. By making intentional connections to students’ lives and the world around them, teachers can improve engagement, support persistence, and build a stronger culture of learning.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khancademy.org/khan-for-educators

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Order of operations

Sun, 25 Oct 2026 15:00:00 -0000

Using the order of operations to evaluate expressions

Uploaded 30-08-07

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Identifying Rational Numbers

Sun, 25 Oct 2026 14:06:00 -0000

u09_l1_t3_we5 Identifying Rational Numbers

Uploaded 18-07-11

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Turning Data Into Instructional Action

Sun, 25 Oct 2026 14:00:00 -0000

Learn how to turn student data into purposeful instructional decisions. Discover how to group students using Get Ready, Get Unstuck, and Go Further, choose the right instructional response for each group, plan and lead a focused small group lesson, address common misconceptions, and monitor progress so you can regroup students as their needs change.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khancademy.org/khan-for-educators

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Order of operations II

Sun, 25 Oct 2026 13:00:00 -0000

More examples for "order of operations"

Uploaded 30-08-07

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Using inequalities to solve problems | Solving equations and inequalities | Algebra I | Khan Academy

Sun, 25 Oct 2026 12:06:00 -0000

We can use inequalities to solve problems in a given context.

Uploaded 06-07-20

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Individual Student Data

Sun, 25 Oct 2026 12:00:00 -0000

Learn how to use Khan Academy’s individual student reports to understand each learner’s progress and needs. This video guides teachers through the Activity, Skills, and Assignments reports, along with student Chat History. See how to review engagement, mastery, assignment performance, and learning conversations so you can celebrate growth, identify areas for support, and make informed instructional decisions.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khancademy.org/khan-for-educators

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Mortgage-backed securities I | Finance and Capital Markets | Khan Academy

Sun, 25 Oct 2026 11:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/economics-finance-domain/core-finance/current-economics/credit-crisis/v/mortgage-backed-securities-i

Uploaded 30-08-07

Part I of the introduction to mortgage-backed securities. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/mort-backed-secs-tut/v/mortgage-backed-securities-ii?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/mort-backed-secs-tut/v/mortgage-back-security-overview?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: In many commodities markets, it is very helpful for buyers or sellers to lock-in future prices. This is what both forwards and futures allow for. This tutorial explains how they work and what the difference is between the two.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Comparing decimals: place value difference | Decimals | Pre-Algebra | Khan Academy

Sun, 25 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: It's not uncommon to be asked to compare two decimals and judge which one is larger. How do you do that? This video will gave you the confidence to answer that question.

Uploaded 18-07-11

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/e/comparing_decimals_2?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/v/ordering-decimals-example?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/v/comparing-decimals-2-example?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khanmigo Reports

Sun, 25 Oct 2026 10:00:00 -0000

Learn how to navigate and leverage Khanmigo reports to deepen student support and guide targeted instruction. This video walks teachers through the Khanmigo Usage and Activity reports to analyze student engagement, track interaction depth, and flag critical check-in moments. Discover how to connect this data with broader Skills and Activity reports to gain a complete picture of student progress and make check-ins more meaningful.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khanacademy.org/khan-for-educators

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Mortgage-backed securities II | Finance and Capital Markets | Khan Academy

Sun, 25 Oct 2026 09:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/economics-finance-domain/core-finance/current-economics/credit-crisis/v/mortgage-backed-securities-ii

Uploaded 30-08-07

Part II of the introduction to mortgage-backed securities. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/mort-backed-secs-tut/v/mortgage-backed-securities-iii?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/mort-backed-secs-tut/v/mortgage-backed-securities-i?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: In many commodities markets, it is very helpful for buyers or sellers to lock-in future prices. This is what both forwards and futures allow for. This tutorial explains how they work and what the difference is between the two.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Solve by completing the square: Non-integer solutions | Algebra I | Khan Academy

Sun, 25 Oct 2026 08:06:00 -0000

We can use the strategy of completing the square to solve quadratic equations even when the solutions aren't integers.

Uploaded 06-07-20

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Mastery Learning Reports

Sun, 25 Oct 2026 08:00:00 -0000

Join Kate, a former classroom educator and Teacher Resources Content Creator at Khan Academy, as she explores how Khan Academy's reporting tools can help teachers monitor engagement, track mastery, and make informed instructional decisions.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khanacademy.org/khan-for-educators

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Mortgage-backed securities III | Finance and Capital Markets | Khan Academy

Sun, 25 Oct 2026 07:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/economics-finance-domain/core-finance/current-economics/credit-crisis/v/mortgage-backed-securities-iii

Uploaded 01-09-07

Part III of the introduction to mortgage-backed securities. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/cdo-tutorial/v/collateralized-debt-obligation-overview?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/mort-backed-secs-tut/v/mortgage-backed-securities-ii?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: In many commodities markets, it is very helpful for buyers or sellers to lock-in future prices. This is what both forwards and futures allow for. This tutorial explains how they work and what the difference is between the two.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Comparing Rational Numbers | 7th grade | Khan Academy

Sun, 25 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-add-sub-rational-numbers/v/comparing-rational-numbers

Uploaded 18-07-11

Comparing Rational Numbers

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-add-sub-rational-numbers/e/comparing-rational-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Watch the next lesson: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-add-sub-rational-numbers/v/adding-and-subtracting-a-decimal-percentage-and-fraction?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Missed the previous lesson?
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-fracs-to-decimals/v/converting-fractions-to-decimals-ex1?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Grade 7th on Khan Academy: 7th grade takes much of what you learned in 6th grade to an entirely new level. In particular, you'll now learn to do everything with negative numbers (we're talking everything--adding, subtracting, multiplying, dividing, fractions, decimals... everything!). You'll also take your algebraic skills to new heights by tackling two-step equations. 7th grade is also when you start thinking about probability (which is super important for realizing that casinos and lotteries are really just ways of taking money away from people who don't know probability) and dig deeper into the world of data and statistics. Onward! (Content was selected for this grade level based on a typical curriculum in the United States.)

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÂ Ã Âªs 7th grade channel:
https://www.youtube.com/channel/UCzKsXcrLSLDG7VN1LODlRkw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Evaluating Khanmigo activity assignment reports

Sun, 25 Oct 2026 06:00:00 -0000

Join Rachel as she walks you through evaluating Khanmigo activity assignment reports. This video covers how to locate assignments, interpret Khanmigo's summaries, and—most importantly—use the rich qualitative data from student-AI conversations to assess student learning. Learn strategies for transitioning AI-enhanced learning back into the classroom routine to strengthen student understanding, encourage ownership of their work, and support productive struggle. Discover how leveraging these reports gives you the precise insights you need to further support your students.

Uploaded 05-10-26

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Collateralized debt obligation (CDO) | Finance and Capital Markets | Khan Academy

Sun, 25 Oct 2026 05:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/economics-finance-domain/core-finance/current-economics/credit-crisis/v/collateralized-debt-obligation-cdo

Uploaded 01-09-07

Introduction to collateralized debt obligations (to be listened to after series on mortgage-backed securities. Created by Sal Khan).

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/credit-default-swaps-tut/v/credit-default-swaps-cds-intro?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/cdo-tutorial/v/collateralized-debt-obligation-overview?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Strategy in solving quadratic equations | Quadratic functions and equations | Algebra I | Khan Academy

Sun, 25 Oct 2026 04:06:00 -0000

Based on the initial form of a quadratic equation, we can determine which solution methods are and aren't appropriate.

Uploaded 06-07-20

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Responding to student chat trends

Sun, 25 Oct 2026 04:00:00 -0000

Join Michele to learn how Khanmigo's teacher tools can help you uncover meaningful insights from student conversations. In this video, you'll explore how to use the Student Chat History Summary and Teacher Reports to identify learning trends, understand what students are asking about, recognize when additional support may be needed, and make small instructional adjustments that can have a big impact on student learning.

Uploaded 05-10-26

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Domain of a function | Functions and their graphs | Algebra II | Khan Academy

Sun, 25 Oct 2026 03:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/algebra-home/alg-functions/alg-domain-of-advanced-functions/v/domain-of-a-function

Uploaded 15-09-07

Figuring out the domain of a function

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/functions_and_graphs/domain_range/e/domain_and_range_0.5?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Watch the next lesson: https://www.khanacademy.org/math/algebra2/functions_and_graphs/domain_range/v/domain-and-range-of-a-relation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/functions_and_graphs/function_expressions/v/modeling-with-combined-functions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Fraction to decimal | Decimals | Pre-Algebra | Khan Academy

Sun, 25 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-fracs-to-decimals/v/converting-fractions-to-decimals-example

Uploaded 18-07-11

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-fracs-to-decimals/v/converting-fractions-to-decimals-example

Converting fractions to decimals sometimes requires us to brush up on our long division skills. We'll walk you through it.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/decimal-to-fraction-pre-alg/e/converting_fractions_to_decimals?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/decimal-to-fraction-pre-alg/v/decimals-and-fractions?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/decimal-to-fraction-pre-alg/v/converting-fractions-to-decimals?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
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Assignment progress

Sun, 25 Oct 2026 02:00:00 -0000

Join Tim Williams, a former classroom educator and Teacher Resources content creator at Khan Academy, as he explores the tools that let teachers monitor assignment progress using the teacher dashboard. In this video, Tim demonstrates where to find assignment data, how to interpret progress and mastery information, and how to use reports to identify trends. Discover how timely insights can help you respond to student needs and make informed instructional decisions that support student success.

Uploaded 05-10-26

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Introduction to limits 2 | Limits | Precalculus | Khan Academy

Sun, 25 Oct 2026 01:00:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/calculus-all-old/limits-and-continuity-calc/limits-introduction-calc/v/introduction-to-limits

Uploaded 30-09-07

Introduction to the intuition behind limits

Watch the next lesson: https://www.khanacademy.org/math/precalculus/limit_topic_precalc/limits_precalc/v/2-sided-limit-from-graph?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/limit_topic_precalc/limits_precalc/v/introduction-to-limits-hd?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Precalculus channel:
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Solve by completing the square: Integer solutions | Algebra I | Khan Academy

Sun, 25 Oct 2026 00:06:00 -0000

We can use the strategy of completing the square to solve quadratic equations. If the solutions are integers, we can solve by factoring as well.

Uploaded 06-07-20

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Actionable insights and Class snapshot

Sun, 25 Oct 2026 00:00:00 -0000

Join Katie, a former science teacher and Teacher Resources and Development Content Creator at Khan Academy, as she explores how to use actionable insights and the Class Snapshot to monitor student learning in real time. In this video, Katie explains how to identify key data points, interpret patterns in student progress, and use that information to make informed instructional decisions. She also shares practical ways to respond in the moment, plan next steps, and use Khanmigo to support data-informed instruction. Discover how these tools can fit into your existing classroom routines, helping you provide timely support and reinforce the instruction and high expectations you already have in place. To learn more with the full Khan Academy for Educators course, visit: khanacademy.org/khan-for-educators

Uploaded 05-10-26

00:00 Opening/Intro
00:22 What These Tools Show
00:53 What to Look for First
01:22 Making Real-Time Decisions
01:56 Using Khanmigo to Go Deeper
02:32 Connecting Data to Instruction
03:06 Closing

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Getting help with Tutor Me

Sun, 25 Oct 2026 00:00:00 -0000

Join Michele, a professional learning specialist with Khan Academy as she provides teachers with a comprehensive guide on how students can effectively utilize Khanmigo’s Tutor Me feature, an always-ready AI tutor designed to strengthen learning. Michele covers how students can easily access the tool, prompt it with various schoolwork topics, and use input options like voice, image and math keys. Michele highlights Khanmigo’s method of using guiding questions and scaffolding to support independent thinking without giving away answers, as well as features like action bubbles for focused conversation. Finally, Michele details the platform's moderation system for safe learning and the Summarize Student Chat History tool that allows teachers to monitor student use and address any concerns.

Uploaded 05-10-26

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Limit examples (part 2) | Limits | Differential Calculus | Khan Academy

Sat, 24 Oct 2026 23:00:00 -0000

More limit examples

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/limits_topic/old-limits-tutorial/v/limit-examples-part3?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/limits_topic/old-limits-tutorial/v/limit-examples-part-1?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

Uploaded 30-09-07

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Calculus channel:
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The Indefinite Integral or Anti-derivative

Sat, 24 Oct 2026 23:00:00 -0000

An introduction to indefinite integration of polynomials.

Uploaded 18-10-07

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Futures fair value in the pre-market | Finance and Capital Markets | Khan Academy

Sat, 24 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/futures-fair-value-in-the-pre-market

Uploaded 20-07-11

What is the Futures Fair Value and how to traders use it as an indicator for stock price direction at market opening. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/interpretting-futures-fair-value-in-the-premarket?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/arbitraging-futures-contracts-ii?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: In many commodities markets, it is very helpful for buyers or sellers to lock-in future prices. This is what both forwards and futures allow for. This tutorial explains how they work and what the difference is between the two.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
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Working through content

Sat, 24 Oct 2026 22:00:00 -0000

Join Tim Williams, a former classroom educator Teacher Resources content creator at Khan Academy, as he explores how students navigate lessons and interact with Khanmigo in student mode. In this video, Tim explains how students move through Khan Academy content, access supporting lessons, and review their progress after completing tasks. He also demonstrates how Khanmigo acts as a context-aware tutor, offering guiding questions, hints, and structured support rather than simply giving answers. Discover how students can use Khanmigo as a thinking partner to clarify concepts, check their reasoning, and deepen understanding while working through Khan Academy lessons.

Uploaded 05-10-26

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Facilitate student ownership of progress

Sat, 24 Oct 2026 22:00:00 -0000

Join Tim Williams, a former classroom educator and Teacher Resources content creator at Khan Academy, as he explores how the Khan Academy learner experience helps students take ownership of their learning. In this video, Tim highlights how students can track their progress, use mastery data to guide their next steps, and connect their daily activities to meaningful learning goals. Discover how making progress visible can empower students to reflect, adjust their goals, and build confidence as independent learners.

Uploaded 05-10-26

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Indefinite integrals (part II)

Sat, 24 Oct 2026 21:00:00 -0000

Examples of taking the indefinite integral (or anti-derivative) of polynomials.

Uploaded 18-10-07

Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/intro-to-integration?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription

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Limit examples (part 1) | Limits | Differential Calculus | Khan Academy

Sat, 24 Oct 2026 21:00:00 -0000

Some limit exercises

Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/limits-basics-challenge?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/limits_topic/old-limits-tutorial/v/limit-examples-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/limits_topic/old-limits-tutorial/v/introduction-to-limits?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

Uploaded 30-09-07

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Calculus channel:
https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan for Educators: Where do I go from here?

Sat, 24 Oct 2026 20:06:00 -0000

Where do I go from here? is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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Activation and Learner Home

Sat, 24 Oct 2026 20:00:00 -0000

Join Khan Academy professional learning specialist Michele, as she walks you through the simple steps students take to activate their new Khan Academy accounts. From seamless sign-in to choosing a voice for Khanmigo during onboarding. Then explore the engaging Learner Home, where students can find their top-priority Daily Missions, access Unit Missions to work toward mastery, and customize Khanmigo using earned Gems.

Uploaded 05-10-26

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Student goal setting

Sat, 24 Oct 2026 20:00:00 -0000

Join Kate, a former classroom educator and Teacher Resources Content Creator at Khan Academy, as she explores how Khan Academy’s goal-setting tools and strategies can help students stay motivated, track their progress, and take ownership of their learning. The video highlights tools like Khanmigo’s SMART Goal Writer and goal-setting worksheets, along with strategies for tracking progress, celebrating milestones, and building consistent learning habits. Consistent progress, like reaching proficiency in two skills per week, can lead to significant learning gains over time.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: www.khan-for-educators

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Indefinite Integration (part III)

Sat, 24 Oct 2026 19:00:00 -0000

Integration by doing the chain rule in reverse.

Uploaded 18-10-07

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Limit examples (part 3) | Limits | Differential Calculus | Khan Academy

Sat, 24 Oct 2026 19:00:00 -0000

More limit examples

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/limits_topic/old-limits-tutorial/v/limit-examples-w-brain-malfunction-on-first-prob-part-4?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/limits_topic/old-limits-tutorial/v/limit-examples-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

Uploaded 30-09-07

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Calculus channel:
https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1
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Credit default swaps (CDS) intro | Finance and Capital Markets | Khan Academy

Sat, 24 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/credit-default-swaps-tut/v/credit-default-swaps-cds-intro

Uploaded 20-07-11

Introduction to credit default swaps and why they can be dangerous. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/credit-default-swaps-tut/v/credit-default-swaps?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/cdo-tutorial/v/collateralized-debt-obligation-cdo?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Gem reward system and Gem Jam game

Sat, 24 Oct 2026 18:00:00 -0000

Join host Rachel as she dives into the Gem reward system, a fun way to gamify learning! This video explains how students earn Gems, how class totals work, and how to set up exciting class rewards. Plus, Rachel walks through running a Gem Jam—a real-time, competitive race where students work together to earn Gems. Learn how to launch a game, project the Racermigo leaderboard to boost engagement, and strategically use the school and district rankings to build positive interdependence and drive mastery.

Uploaded 05-10-26

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Class cverview and creating assignments

Sat, 24 Oct 2026 18:00:00 -0000

00:00 - Opening/Intro
00:03 Class Overview
01:28 Navigation
01:34 Course Selection
02:21 Assigning a Unit Mission
03:49 Closing

In this video, Rachel introduces you to the Class Overview page and walks you through setting up your class to begin assigning AI-enhanced mastery learning experiences. Learn how to navigate the Class Overview to track student progress, select a course for your class in the Settings, and explore the four types of assignments: Unit missions, Khanmigo activities, Content assignments, and Writing Coach activities. Rachel then provides a step-by-step guide on how to assign your first Unit Mission to start your students on their mastery learning journey.

Uploaded 05-10-26

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Calculus: Derivatives 1 | Taking derivatives | Differential Calculus | Khan Academy

Sat, 24 Oct 2026 17:00:00 -0000

Finding the slope of a tangent line to a curve (the derivative). Introduction to Calculus.

Uploaded 03-10-07

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/calculus-derivatives-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/formal-and-alternate-form-of-the-derivative-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Calculus channel:
https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Indefinite Integration (part IV)

Sat, 24 Oct 2026 17:00:00 -0000

Integration by substitution (or the reverse-chain-rule)

Uploaded 18-10-07

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Khan for Educators: Assignment reports

Sat, 24 Oct 2026 16:06:00 -0000

Assignment reports is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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Activation and Teacher Dashboard

Sat, 24 Oct 2026 16:00:00 -0000

Join Michele as she walks you through everything you need to know about getting started with your new Khan Academy teacher account. This video covers the essential steps for account activation and onboarding for various types of teacher accounts. Michele also provides a comprehensive tour of the Teacher Dashboard, highlighting key features like the main navigation, the AI-powered Khanmigo Assistant and Teacher Tools, and where to find your rostered classes and student insights.

Uploaded 05-10-26

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RISE prompts for Khanmigo activity assignments

Sat, 24 Oct 2026 16:00:00 -0000

Join Michele as she explains how to use Khanmigo and the R.I.S.E. framework to create powerful, standards-based, student-centered assignments. After selecting the appropriate Khanmigo activity (like Tutor Me), Rachel demonstrates how to design strong assignment prompts using the R.I.S.E. framework: Role (who Khanmigo acts as, e.g., a "grammar coach"), Instruction (the learning objective, e.g., "combining simple sentences into compound sentences"), Support (how Khanmigo should help students), and Expectations (the criteria for student accountability, e.g., "independently write five compound sentences"). Finally, she walks through how to use the preview function to test and iterate on the activity before assigning it to students.

Uploaded 05-10-26

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Introduction to definite integrals

Sat, 24 Oct 2026 15:00:00 -0000

Using the definite integral to solve for the area under a curve. Intuition on why the antiderivative is the same thing as the area under a curve.

Uploaded 19-10-07

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Calculus: Derivatives 2 | Taking derivatives | Differential Calculus | Khan Academy

Sat, 24 Oct 2026 15:00:00 -0000

More intuition of what a derivative is. Using the derivative to find the slope at any point along f(x)=x^2

Uploaded 03-10-07

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/visualizing-derivatives-tutorial/v/derivative-intuition-module?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/calculus-derivatives-1?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Calculus channel:
https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Mortgage-backed security overview | Finance and Capital Markets | Khan Academy

Sat, 24 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/mort-backed-secs-tut/v/mortgage-back-security-overview

Uploaded 20-07-11

Basics of how a mortgage back security works. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/mort-backed-secs-tut/v/mortgage-backed-securities-i?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/interpretting-futures-fair-value-in-the-premarket?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: In many commodities markets, it is very helpful for buyers or sellers to lock-in future prices. This is what both forwards and futures allow for. This tutorial explains how they work and what the difference is between the two.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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The Mastery Learning Journey

Sat, 24 Oct 2026 14:00:00 -0000

Join Rachel, a professional learning specialist at Khan Academy, as she dives into the core of Khan Academy's educational philosophy: Mastery Learning. This video breaks down the three essential assignment types—Unit Missions, Content, and AI-powered Khanmigo Activities—that together form the Mastery Learning Triad. Discover the purpose of each type and learn how intentionally weaving them together creates a comprehensive, personalized learning experience that boosts student success and helps students learn anything.

Uploaded 05-10-26

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Teaching students to CHAT with Khanmigo

Sat, 24 Oct 2026 14:00:00 -0000

Join Katie, a former science teacher and Teacher Resources and Development Content Creator at Khan Academy, as she shares how to teach students to communicate effectively with Khanmigo as a learning tool and thinking partner. In this video, Katie models how to guide students in asking clear, specific questions, responding thoughtfully to prompts, and using Khanmigo to support their thinking and problem-solving. She also offers practical strategies for building routines that encourage productive struggle and student ownership. Discover how teaching students to engage in meaningful back-and-forth conversations with Khanmigo can support independence and strengthen the learning already happening in your classroom.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: khanacademy.org/khan-for-educators

00:00 Intro
00:52 Why How Students Chat Matters:
01:56 Modeling Strong Prompts
03:31Teaching Students to Respond and Follow-Up
04:59 Using Khanmigo During Learning
05:41Building Independence
06:07 Closing

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Definite integrals (part II)

Sat, 24 Oct 2026 13:00:00 -0000

More on why the antiderivative and the area under a curve are essentially the same thing.

Uploaded 19-10-07

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Power rule introduction (old) | Taking derivatives | Differential Calculus | Khan Academy

Sat, 24 Oct 2026 13:00:00 -0000

Determining the derivatives of simple polynomials.

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/chain_rule/v/derivatives-of-sin-x-cos-x-tan-x-e-x-and-ln-x?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/power_rule_tutorial/v/proof-d-dx-sqrt-x?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

Uploaded 03-10-07

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Calculus channel:
https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan for Educators: Creating assignments

Sat, 24 Oct 2026 12:06:00 -0000

Creating assignments is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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Introducing students to Khanmigo

Sat, 24 Oct 2026 12:00:00 -0000

00:00 Intro
00:16 What Khanmigo is for students
00:38 Where Students Will Use Khanmigo
01:30 Choosing the Right Activity
01:54 Setting Expectations and Norms
02:52 Safety, Moderation, and Visibility

Uploaded 05-10-26

Join Katie, a former science teacher and Teacher Resources and Development Content Creator at Khan Academy, as she shares how to introduce students to Khanmigo as a learning tool and thinking partner. In this video, Katie explains how to set clear expectations and routines for student use, shows how Khanmigo supports student thinking during independent practice, and offers practical strategies for creating a safe, responsible, and productive classroom environment for AI use. Discover how thoughtful introduction and consistent routines can help Khanmigo become a meaningful part of your classroom, supporting student independence and reinforcing the instruction and high expectations you already have in place.

To learn more with the full Khan Academy for Educators course, visit: www.khanacademy.org/khan-for-educators

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The AI-enhanced mastery learning approach

Sat, 24 Oct 2026 12:00:00 -0000

Join Katie, a former science teacher and Teacher Resources and Development Content Creator at Khan Academy, as she explores how AI-enhanced mastery learning supports strong foundations and high expectations for every student. In this video, Katie defines mastery learning as it’s implemented on Khan Academy, explains how adaptive practice and real-time guidance from Khanmigo strengthen student understanding, and highlights how teachers can use mastery data to inform instruction. Discover how Khan Academy’s mastery-based approach works alongside your teaching to build confidence, support productive struggle, and promote meaningful student growth.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, visit: www.khanacademy.org/khan-for-educators

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The Chain Rule

Sat, 24 Oct 2026 11:00:00 -0000

Part 4 of derivatives. Introduction to the chain rule.

Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/chain_rule_1?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription

Uploaded 03-10-07

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Definite Integrals (area under a curve) (part III)

Sat, 24 Oct 2026 11:00:00 -0000

More on why the antiderivative and the area under a curve are essentially the same thing.

Uploaded 19-10-07

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Collateralized debt obligation overview | Finance and Capital Markets | Khan Academy

Sat, 24 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/cdo-tutorial/v/collateralized-debt-obligation-overview

Uploaded 20-07-11

How CDOs can give different investors different levels of risk and returns with the same underlying assets. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/cdo-tutorial/v/collateralized-debt-obligation-cdo?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/mort-backed-secs-tut/v/mortgage-backed-securities-iii?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Mastery learning vs traditional grades

Sat, 24 Oct 2026 10:00:00 -0000

Ready to revolutionize student learning and achieve unprecedented outcomes? Join Rachel as she dives into the game-changing difference between traditional grading and the transformative Khan Academy mastery learning model. Traditional constraints create learning gaps and discouraging labels; the mastery approach champions deep understanding, allowing every student to advance at their own pace and eliminate unfinished learning. Rachel clearly outlines the four progress signals—Attempted, Familiar, Proficient, and Mastered—that track true proficiency. The data is clear: guiding students to 60 skills to proficient in a single year can increase learning by approximately 30 percentage points! Learn how the mastery journey is powered by Unit Missions, Targeted Assignments, and breakthrough Khanmigo AI support to turn productive struggle into success. Make the essential shift to proficiency and unlock the conditions for stronger learning and long-term retention for all students.

Uploaded 05-10-26

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Khanmigo as a student tutor and teacher assistant

Sat, 24 Oct 2026 10:00:00 -0000

Join Tim Williams, a former classroom educator and Teacher Resources content creator at Khan Academy, as he explores how Khanmigo can support both students and teachers. In this video, Tim explains how Khanmigo acts as a friendly tutor for students, guiding their thinking with questions, hints, and real-time feedback. He also demonstrates how Khanmigo functions as a helpful teaching assistant, supporting educators with lesson ideas, differentiated activities, and instructional planning. Discover how Khanmigo can enhance learning, support productive struggle, and help teachers spend more time focusing on student growth.

Uploaded 05-10-26

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Chain Rule Examples

Sat, 24 Oct 2026 09:00:00 -0000

Examples using the Chain Rule

Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/chain_rule_1?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription

Uploaded 03-10-07

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Integration by Parts (part 6 of Indefinite Integration)

Sat, 24 Oct 2026 09:00:00 -0000

Example using Integration by Parts

Uploaded 21-10-07

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Khan for Educators: Course Mastery

Sat, 24 Oct 2026 08:06:00 -0000

Course Mastery is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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When to use Khan Academy

Sat, 24 Oct 2026 08:00:00 -0000

Join Kate, a former classroom educator and Teacher Resources Content Creator at Khan Academy, as she explores when Khan Academy works best as a flexible, responsive supplement to your teaching, providing structured, skill-based practice for your students. This video demonstrates how to integrate the platform for targeted practice during small group or independent work, and how to use the Class Dashboard to leverage real-time data to guide your instructional decisions.
To learn more with the full Khan Academy for Educators course, visit: www.khanacademy.org/khan-for-educators

Uploaded 05-10-26

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Electric potential energy | AP Physics | Khan Academy

Sat, 24 Oct 2026 08:00:00 -0000

The electric potential energy of a system of two point charges equals the amount of work required for an external force to bring the point charges to their current positions from infinitely far away. The total electric potential energy of a system can be determined by finding the sum of the electric potential energies of the individual interactions between each pair of charged objects in the system.

Uploaded 04-10-26

Sections:
00:00 - What is electric potential energy?
02:06 - Choosing infinity as the reference point
04:00 - Potential energy of like charges
06:48 - Potential energy of unlike charges
08:00 - Comparing electric and gravitational potential energy
09:27 - Potential energy of a system of multiple charges

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Even More Chain Rule

Sat, 24 Oct 2026 07:00:00 -0000

Even more examples using the chain rule.

Uploaded 03-10-07

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Indefinite Integration (part 7)

Sat, 24 Oct 2026 07:00:00 -0000

Another example using integration by parts.

Uploaded 21-10-07

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Relation between nominal and real returns and inflation | Finance and Capital Markets | Khan Academy

Sat, 24 Oct 2026 06:06:00 -0000

Relation between nominal and real returns and inflation. Created by Sal Khan.

Uploaded 21-07-11

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/cap-util-inflation/v/economics-of-a-cupcake-factory?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/real-nominal-return-tut/v/calculating-real-return-in-last-year-dollars?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: If the value of money is constantly changing, can we compare investment return in the future or past to that earned in the present? This tutorial focuses on how to do this (another good tutorial to watch is the one on "present value").

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Electric potential of charge distributions | AP Physics | Khan Academy

Sat, 24 Oct 2026 06:00:00 -0000

Electric potential describes the electric potential energy per unit charge at a point in space. Expressions for the electric potential of charge distributions can be found using integration and the principle of superposition.

Uploaded 10-10-26

Sections:
00:00 - Potential due to discrete charges
00:40 - Continuous charge distributions
01:47 - Comparing potential and field integrals
03:16 - Potential at the center of a charged ring
05:31 - Setting up the integral for a charged rod

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Course alignment and classroom needs

Sat, 24 Oct 2026 06:00:00 -0000

Join Tim Williams, a former classroom educator and Teacher Resources content creator at Khan Academy, as he explores how Khan Academy courses can align with your classroom goals. In this video, Tim explains how courses are organized into standards-aligned units and lessons, highlights how instructional content and practice can reinforce classroom learning, and shows how course mastery and progress data help teachers monitor student growth. Discover how Khan Academy courses can support pacing, differentiation, intervention frameworks and more while providing meaningful insights to guide instruction.

Uploaded 05-10-26

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Indefinite Integration (part V)

Sat, 24 Oct 2026 05:00:00 -0000

Introduction to Integration by Parts (kind of the reverse-product rule)

Uploaded 21-10-07

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Product rule | Taking derivatives | Differential Calculus | Khan Academy

Sat, 24 Oct 2026 05:00:00 -0000

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/quotient-rule?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/product-rule-proof?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

Uploaded 03-10-07

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Calculus channel:
https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan for Educators: Student experience

Sat, 24 Oct 2026 04:06:00 -0000

Student experience is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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Goals for using AI-enhanced learning

Sat, 24 Oct 2026 04:00:00 -0000

Join Katie, a former science teacher and Teacher Resources and Development Content Creator at Khan Academy, as she shares how to set clear, intentional goals for using AI-enhanced learning with Khanmigo. In this video, Katie walks through practical ways to align Khanmigo with mastery-based practice, support student independence, and connect AI tools to your curriculum and classroom priorities. Learn how thoughtful implementation can strengthen productive struggle, provide meaningful insight into student progress, and enhance your instructional impact.

Uploaded 05-10-26

To learn more with the full Khan Academy for Educators course, www.khanacademy.org/khan-for-educators

00:00 Intro
00:36 Start with Purpose
01:12 Align to Your Instruction:
01:55 Set Expectations:
02:28 Classroom Scenarios
02:55 Closing

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Connecting electric potential and field using calculus | AP Physics | Khan Academy

Sat, 24 Oct 2026 04:00:00 -0000

At a given location in an electrostatic field, the electric field component in a particular direction equals the negative derivative of electric potential with respect to position in that direction. The change in electric potential between two points equals the negative integral of the dot product of the electric field and the displacement along a path connecting them. This change is independent of the path chosen.

Uploaded 12-10-26

Sections:
00:00 - Finding electric field from potential
00:45 - From average field to field at a point
02:07 - Field components in two and three dimensions
03:31 - Finding potential difference from field
06:14 - Worked example with uniform electric field

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Definite Integrals (part 5)

Sat, 24 Oct 2026 03:00:00 -0000

More examples of using definite integrals to calculate the area between curves

Uploaded 22-10-07

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Quotient rule and common derivatives | Taking derivatives | Differential Calculus | Khan Academy

Sat, 24 Oct 2026 03:00:00 -0000

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/equation-of-a-tangent-line?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/product-rule?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

Uploaded 04-10-07

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Calculus channel:
https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Real and nominal return | Inflation | Finance and Capital Markets | Khan Academy

Sat, 24 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/ap-macroeconomics/ap-financial-sector/nominal-v-real-interest-rates-ap/v/real-and-nominal-return

Uploaded 21-07-11

Inflation and real and nominal return. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/real-nominal-return-tut/v/calculating-real-return-in-last-year-dollars?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-scenarios-tutorial/v/hyperinflation?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: If the value of money is constantly changing, can we compare investment return in the future or past to that earned in the present? This tutorial focuses on how to do this (another good tutorial to watch is the one on "present value").

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Conservation of electric energy | AP Physics | Khan Academy

Sat, 24 Oct 2026 02:00:00 -0000

When a charged particle moves between two locations with different electric potentials, the resulting change in the electric potential energy of the particle-field system can be found by multiplying the charge by the electric potential difference between the locations. Assuming no resistive forces, the movement of a charged particle between two points with different electric potentials results in a change in kinetic energy of the particle consistent with the conservation of energy. An electron volt (eV) is a unit of energy equal to the kinetic energy gained by an electron or proton when it accelerates through a potential difference of one volt under the electric force alone.

Uploaded 14-10-26

00:00 - Electric potential energy from potential difference
03:19 - Energy conservation: from potential energy to speed
05:23 - Negative charges and the sign of ΔU
06:29 - The electron volt
09:14 - Worked example: finding the final speed
11:22 - Conceptual example: moving a charge into a charged sphere

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Leveraging multilingual support features

Sat, 24 Oct 2026 02:00:00 -0000

00:00 - 00:25 Intro
00:25 - 02:02 Language access built into the platform
02:02 - 02:30 Sentence frames to support academic talk
02:30 - 02:55 Closing

Join Kate, a former classroom educator and Teacher Resources Content Creator at Khan Academy, as she explores how Khan Academy’s multilingual support features, including localized site language, subtitles, transcripts, and Khanmigo language capabilities can help your multilingual learners access and engage confidently with grade-level content. This video demonstrates where to find these built-in tools on the platform and provides practical examples for classroom implementation. To learn more with the full Khan Academy for Educators course, visit: www.khanacademy.org/khan-for-educators

Uploaded 05-10-26

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Definite Integrals (part 4)

Sat, 24 Oct 2026 01:00:00 -0000

Examples of using definite integrals to find the area under a curve

Uploaded 22-10-07

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Derivatives (part 9)

Sat, 24 Oct 2026 01:00:00 -0000

More examples of taking derivatives

Uploaded 04-10-07

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Khan for Educators: Creating a class

Sat, 24 Oct 2026 00:06:00 -0000

Creating a class is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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Calculating real return in last year dollars | Inflation | Finance and Capital Markets | Khan Academy

Fri, 23 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/ap-macroeconomics/ap-financial-sector/nominal-v-real-interest-rates-ap/v/calculating-real-return-in-last-year-dollars

Uploaded 21-07-11

Calculating real return in last year dollars. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/real-nominal-return-tut/v/relation-between-nominal-and-real-returns-and-inflation?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/real-nominal-return-tut/v/real-and-nominal-return?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: If the value of money is constantly changing, can we compare investment return in the future or past to that earned in the present? This tutorial focuses on how to do this (another good tutorial to watch is the one on "present value").

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan for Educators: Basic site navigation

Fri, 23 Oct 2026 20:06:00 -0000

Basic site navigation is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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Stagflation | Inflation | Finance and Capital Markets | Khan Academy

Fri, 23 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macro-economic-indicators-and-the-business-cycle/macro-price-indices-and-inflation/v/stagflation

Uploaded 21-07-11

How a supply shock can cause prices to rise and the economy to stagnate. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-scenarios-tutorial/v/hyperinflation?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-scenarios-tutorial/v/moderate-inflation-in-a-good-economy?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: You know about inflation, but now want to look at how thing might play out in different scenarios. This tutorial focuses on when inflation is "acceptable" and when it isn't (and the causes and repercussions).

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan for Educators: Our Content

Fri, 23 Oct 2026 16:06:00 -0000

Our Content is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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Moderate inflation in a good economy | Inflation | Finance and Capital Markets | Khan Academy

Fri, 23 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macro-long-run-consequences-of-stabilization-policies/macro-money-growth-and-inflation/v/moderate-inflation-in-a-good-economy

Uploaded 21-07-11

Why there tends to be moderate inflation during good economies. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-scenarios-tutorial/v/stagflation?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-basics-tutorial/v/cpi-index?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: You know about inflation, but now want to look at how thing might play out in different scenarios. This tutorial focuses on when inflation is "acceptable" and when it isn't (and the causes and repercussions).

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan for Educators: Khan Academy’s learning experience

Fri, 23 Oct 2026 12:06:00 -0000

Khan Academy’s learning experience is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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What is inflation? | Inflation | Finance and Capital Markets | Khan Academy

Fri, 23 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-basics-tutorial/v/what-is-inflation

Uploaded 21-07-11

The basics of what price inflation is and how the CPI-U is calculated. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-basics-tutorial/v/inflation-data?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-basics-tutorial/v/inflation-overview?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: $1 went a lot further in 1900 than today (you could probably buy a good meal for the family for $1 back then). Why? And how do we measure how much more expensive things have gotten (i.e., inflation)?

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan for Educators: Khan Academy's Mission

Fri, 23 Oct 2026 08:06:00 -0000

Khan Academy’s Mission is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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Inflation data | Inflation | Finance and Capital Markets | Khan Academy

Fri, 23 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/economics-finance-domain/macroeconomics/macro-economic-indicators-and-the-business-cycle/macro-price-indices-and-inflation/v/inflation-data

Uploaded 21-07-11

Looking at actual sequential and year-over-year inflation data. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-basics-tutorial/v/cpi-index?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-basics-tutorial/v/what-is-inflation?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: $1 went a lot further in 1900 than today (you could probably buy a good meal for the family for $1 back then). Why? And how do we measure how much more expensive things have gotten (i.e., inflation)?

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan for Educators: Welcome to Khan for Educators

Fri, 23 Oct 2026 04:06:00 -0000

Welcome to Khan for Educators is part of Khan for Educators, a free course for teachers to learn more about Khan Academy, the content and tools available for teachers and students, and best practices for implementing technology with students.

Uploaded 06-07-20

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Financial weapons of mass destruction | Finance and Capital Markets | Khan Academy

Fri, 23 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/credit-default-swaps-tut/v/financial-weapons-of-mass-destruction

Uploaded 22-07-11

Why Warren Buffett called Credit Default Swaps financial weapons of mass destruction.Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/interest-rate-swaps-tut/v/interest-rate-swap-1?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/credit-default-swaps-tut/v/use-cases-for-credit-default-swaps?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Incorporating opposing viewpoints | Reading | Khan Academy

Fri, 23 Oct 2026 00:06:00 -0000

Hello, Readers! LET’S ARGUE.

Incorporating opposing viewpoints in an argument can make an argument stronger—as readers, we can pay attention to how authors deploy this technique, which I compare to the martial art of Wing Chun. Block as you strike!

Uploaded 06-07-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attribution:
The Wing Chun technique of translating a block into a strike, and specifically the illustrated depiction of the two combatants, comes from this Master Wong video: https://www.youtube.com/watch?v=Nkc8R_VtrAo

Thanks, Master Wong! Please use his knowledge responsibly.

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Use cases for credit default swaps | Finance and Capital Markets | Khan Academy

Thu, 22 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/credit-default-swaps-tut/v/use-cases-for-credit-default-swaps

Uploaded 22-07-11

How credit default swaps can be used as hedges, insurance or side-bets. Created bySal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/credit-default-swaps-tut/v/financial-weapons-of-mass-destruction?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/credit-default-swaps-tut/v/credit-default-swaps-2?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Analyzing tone through word choice | Reading | Khan Academy

Thu, 22 Oct 2026 20:06:00 -0000

Tone communicates how an author feels about their topic. How do good readers pick up on tone from clues left by the words an author chooses? Let’s discuss, and find out together!

Uploaded 06-07-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

attributions and pictures of sausages:
Half smokes and Ben’s [Chili Bowl]* is licensed under an attribution/sharealike license through the Wikimedia Commons; it’s from user Joe Loong: https://www.flickr.com/photos/joelogon/3302309261/
Chicago-style hot dog courtesy of Jonathan Mauer, licensed under a CC Attribution/Sharealike 4.0 license: https://en.wikipedia.org/wiki/File:Chicago-style_hot_dog_Johnniebeefs.jpg
Classic New York Hot Dog from Gray’s Papaya licensed under a CC attribution/sharealike license from Aneil Hutchman of http://cestlavibe.com/: https://www.flickr.com/photos/72547033@N06/14487377758

* Ben’s Chili Bowl is an indispensable DC food landmark. The one in the airport is no substitute; go to the one on U Street.

Music:
Bach - Brandenburg Concerto No 3, 1 allegro by Advent Chamber Orchestra is licensed under a Attribution-Share Alike 3.0 United States License.

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Deflation | Inflation | Finance and Capital Markets | Khan Academy

Thu, 22 Oct 2026 18:06:00 -0000

Basics of deflation. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/deflation-tutorial/v/velocity-of-money-rather-than-quantity-driving-prices?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/cap-util-inflation/v/inflation-deflation-3-obama-stimulus-plan?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Prices don't always go up. They often go down. This might seem like a good thing, but it could be disastrous for a modern economy is it goes too far. This tutorial explains what deflation is, how it happens and what the effects of it might be.

Uploaded 22-07-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Interpreting trigonometric graphs in context | Trigonometry | Algebra || | Khan Academy

Thu, 22 Oct 2026 16:06:00 -0000

When a trigonometric function models a real-world relationship, we can assign meaning to its midline, amplitude and period.

Uploaded 30-06-20

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Velocity of money rather than quantity driving prices | Finance and Capital Markets | Khan Academy

Thu, 22 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macro-long-run-consequences-of-stabilization-policies/macro-money-growth-and-inflation/v/velocity-of-money-rather-than-quantity-driving-prices

Uploaded 22-07-11

How velocity of money can drive price increases. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/deflation-tutorial/v/deflation-despite-increases-in-money-supply?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/deflation-tutorial/v/deflation?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Prices don't always go up. They often go down. This might seem like a good thing, but it could be disastrous for a modern economy is it goes too far. This tutorial explains what deflation is, how it happens and what the effects of it might be.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Graph labels and scales | Modeling | Algebra II | Khan Academy

Thu, 22 Oct 2026 12:06:00 -0000

When graphing a real-world relationship, we need to pick labels and axis scales that are appropriate for the purpose of our model.

Uploaded 30-06-20

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Deflation despite increases in money supply | Inflation | Finance and Capital Markets | Khan Academy

Thu, 22 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macro-long-run-consequences-of-stabilization-policies/macro-money-growth-and-inflation/v/deflation-despite-increases-in-money-supply

Uploaded 22-07-11

How you can have deflation even if the money supply increases. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/deflation-tutorial/v/deflationary-spiral?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/deflation-tutorial/v/velocity-of-money-rather-than-quantity-driving-prices?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Prices don't always go up. They often go down. This might seem like a good thing, but it could be disastrous for a modern economy is it goes too far. This tutorial explains what deflation is, how it happens and what the effects of it might be.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Interpreting expressions with multiple variables: Resistors | Modeling | Algebra II | Khan Academy

Thu, 22 Oct 2026 08:06:00 -0000

Given the expression for the total resistance in an electric circuit with two resistors, analyze the expression to tell what happens to the total resistance when the resistance of one resistor increases and the resistance of the other resistor stays the same.

Uploaded 30-06-20

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Hyperinflation in a good economy | Inflation | Finance and Capital Markets | Khan Academy

Thu, 22 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/monetary-system-topic/macro-definition-measurement-and-functions-of-money/v/hyperinflation

Uploaded 25-07-11

Basic of hyperinflation. Weimar Germany, Hungarian Pengo and Zibabwean Dollar. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/real-nominal-return-tut/v/real-and-nominal-return?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/inflation-scenarios-tutorial/v/stagflation?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: You know about inflation, but now want to look at how thing might play out in different scenarios. This tutorial focuses on when inflation is "acceptable" and when it isn't (and the causes and repercussions).

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Modeling with multiple variables: Pancakes | Modeling | Algebra || | Khan Academy

Thu, 22 Oct 2026 04:06:00 -0000

Modeling the relationship between three quantities (or more) isn't that different from modeling the relationship between two quantities. Here is an example of a model that relates different quantities in the context of making pancakes.

Uploaded 30-06-20

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Deflationary spiral | Inflation | Finance and Capital Markets | Khan Academy

Thu, 22 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/macroeconomics/macro-economic-indicators-and-the-business-cycle/macro-price-indices-and-inflation/v/deflationary-spiral

Uploaded 25-07-11

Basics of a deflationary spiral. Created by Sal Khan.

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/inflation-tutorial/deflation-tutorial/v/deflation-despite-increases-in-money-supply?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Prices don't always go up. They often go down. This might seem like a good thing, but it could be disastrous for a modern economy is it goes too far. This tutorial explains what deflation is, how it happens and what the effects of it might be.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Modeling with multiple variables: Roller coaster | Modeling | Algebra II | Khan Academy

Thu, 22 Oct 2026 00:06:00 -0000

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Primaries and caucuses | American civics | US History | Khan Academy

Wed, 21 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/primaries-and-caucuses

Uploaded 25-07-11

How states choose their delegates for the national party conventions (video content under CC-BY-SA license). Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/humanities/us-history/american-civics-parent/american-civics/v/deficit-and-debt-ceiling?utm_source=YT&utm_medium=Desc&utm_campaign=UShistory

Missed the previous lesson? https://www.khanacademy.org/humanities/us-history/american-civics-parent/american-civics/v/electoral-college?utm_source=YT&utm_medium=Desc&utm_campaign=UShistory

US history on Khan Academy: From a mosquito-ridden backwater to the world's last remaining superpower, the United States of America is a nation with a rich history and a noble goal: government of the people, by the people, for the people. Its citizens' struggle to achieve that goal is a dramatic story stretching over hundreds of years.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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How the delivery of a speech affects the impact of the words | Reading | Khan Academy

Wed, 21 Oct 2026 20:06:00 -0000

Good public speakers use a range of techniques to convey their message to their audience, which goes beyond just the words they say. They become actors, who are telling us a story on stage not just with their lines but with their physical presence.

Uploaded 30-06-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!
Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc
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Electoral college | American civics | US History | Khan Academy

Wed, 21 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/electoral-college

Uploaded 25-07-11

How we elect our President in the United States. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/humanities/us-history/american-civics-parent/american-civics/v/primaries-and-caucuses?utm_source=YT&utm_medium=Desc&utm_campaign=UShistory

Missed the previous lesson? https://www.khanacademy.org/humanities/us-history/american-civics-parent/american-civics/v/more-fiscal-cliff-analysis?utm_source=YT&utm_medium=Desc&utm_campaign=UShistory

US history on Khan Academy: From a mosquito-ridden backwater to the world's last remaining superpower, the United States of America is a nation with a rich history and a noble goal: government of the people, by the people, for the people. Its citizens' struggle to achieve that goal is a dramatic story stretching over hundreds of years.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s US History channel: https://www.youtube.com/channel/UCurOvzSAIe84sW8zwPGHUHg?sub_confirmation=1
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Mapping shapes

Wed, 21 Oct 2026 16:06:00 -0000

Find sequences of rigid transformations that map one shape onto another shape.

Uploaded 29-06-20

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Money Market Funds

Wed, 21 Oct 2026 14:06:00 -0000

The basics of money market funds

Uploaded 26-07-11

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Radians as ratio of arc length to radius | Circles | High school geometry | Khan Academy

Wed, 21 Oct 2026 12:06:00 -0000

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality.

Uploaded 29-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-radians-intro .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Breaking the Buck

Wed, 21 Oct 2026 10:06:00 -0000

The unlikely scenario of investors of a money market fund losing money

Uploaded 26-07-11

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Dilating a triangle example

Wed, 21 Oct 2026 08:06:00 -0000

Dilating a triangle example

Uploaded 28-06-20

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Deficit and debt ceiling | American civics | US government and civics | Khan Academy

Wed, 21 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/deficit-and-debt-ceiling

Uploaded 27-07-11

Basic of the deficit, debt and debt ceiling. Created by Sal Khan.

View more lessons or practice this subject at https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/deficit-and-debt-ceiling?utm_source=youtube&utm_medium=desc&utm_campaign=usgovernmentandcivics

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today!

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Proving triangle congruence | Congruence | High school geometry | Khan Academy

Wed, 21 Oct 2026 04:06:00 -0000

Given a figure composed of 2 triangles, prove that the triangles are congruent or determine that there's not enough information to tell.

Uploaded 27-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruent-triangles .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Government's financial condition | American civics | US government and civics | Khan Academy

Wed, 21 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/government-s-financial-condition

Uploaded 27-07-11

The deficit is a measure of how much the government is overspending in a given year, or the difference between government spending and revenue. The deficit, however, does not account for the total of the government's liabilities, which include future payments to government employees and veterans and programs like Social Security. Created by Sal Khan.

View more lessons or practice this subject at https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/government-s-financial-condition?utm_source=youtube&utm_medium=desc&utm_campaign=usgovernmentandcivics

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today!

Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Applying volume of solids | Solid geometry | High school geometry | Khan Academy

Wed, 21 Oct 2026 00:06:00 -0000

Calculate the volume of a grain hopper and then use the given rate to solve an applied problem.

Uploaded 27-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-solids/hs-geo-prisms .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Ordering Numeric Expressions

Tue, 20 Oct 2026 22:06:00 -0000

Converting percentages and fractions to decimals to order numbers

Uploaded 28-07-11

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Proof: Parallel lines divide triangle sides proportionally | Similarity | Geometry | Khan Academy

Tue, 20 Oct 2026 20:06:00 -0000

Prove that a line parallel to one triangle side divides other sides proportionately.

Uploaded 27-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-proving-relationships-using-similarity .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Social security intro | American civics | US government and civics | Khan Academy

Tue, 20 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/ap-biology/chemistry-of-life/elements-of-life/v/elements-and-atoms

Uploaded 29-07-11

Basics on how social security works. Created by Sal Khan.

View more lessons or practice this subject at https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/social-security-intro?utm_source=youtube&utm_medium=desc&utm_campaign=usgovernmentandcivics

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today!

Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Multi-step word problem with Pythagorean theorem | Geometry | Khan Academy

Tue, 20 Oct 2026 16:06:00 -0000

Use the Pythagorean theorem and proportional reasoning in context.

Uploaded 27-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-pyth-theorem .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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FICA tax | American civics | US government and civics | Khan Academy

Tue, 20 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/fica-tax

Uploaded 29-07-11

How the FICA tax is calculated and what it stands for. Created by Sal Khan.

View more lessons or practice this subject at https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/fica-tax?utm_source=youtube&utm_medium=desc&utm_campaign=usgovernmentandcivics

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today!

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Proof: perpendicular radius bisects chord

Tue, 20 Oct 2026 12:06:00 -0000

Simple proof using right triangle-side-hypotenuse (RSH) congruence criterion to show that a radius perpendicular to a chord bisects it

Uploaded 27-06-20

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Medicare sustainability | American civics | US government and civics | Khan Academy

Tue, 20 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/medicare-sustainability

Uploaded 29-07-11

How medicare is funded and why it is even less sustainable than social security. Created by Sal Khan.

View more lessons or practice this subject at https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/medicare-sustainability?utm_source=youtube&utm_medium=desc&utm_campaign=usgovernmentandcivics

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today!

Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Camp Khan Parent Webinar

Tue, 20 Oct 2026 08:06:00 -0000

Parents, are you looking for fun summer opportunities and learning activities to prepare your child for the fall? If so, we invite you to join us to learn more about Camp Khan, our fun and flexible virtual camp! We walk through our new Get ready for grade level courses, and give you a preview of some of the fun activities we're excited to share with Camp Khan campers this summer.

Uploaded 26-06-20

Learn more about Camp Khan here, and enroll your child today: khan.co/CampKhan2020
You can view the slides here: khan.co/CampKhanWebinarSlides
You can view the handout here: khan.co/CampKhanHandout

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Elements and atoms | Atoms, compounds, and ions | Chemistry | Khan Academy

Tue, 20 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/ap-biology/chemistry-of-life/elements-of-life/v/elements-and-atoms

Uploaded 31-07-11

How elements relate to atoms. The basics of how protons, electrons and neutrons make up an atom.

Watch the next lesson: https://www.khanacademy.org/science/chemistry/atomic-structure-and-properties/introduction-to-the-atom/v/atomic-number-mass-number-and-isotopes?utm_source=YT&utm_medium=Desc&utm_campaign=chemistry

Chemistry on Khan Academy: Did you know that everything is made out of chemicals? Chemistry is the study of matter: its composition, properties, and reactivity. This material roughly covers a first-year high school or college course, and a good understanding of algebra is helpful.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Dividing line segments according to ratio

Tue, 20 Oct 2026 04:06:00 -0000

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Uploaded 25-06-20

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Heart disease and heart attacks | Miscellaneous | Heatlh and Medicine | Khan Academy

Tue, 20 Oct 2026 02:06:00 -0000

Basics of heart disease, heart attacks, heart failure, angina, cardiac arrest. Special thanks to Edward J Perper, MD for help in clarifying certain aspects of this video. Licensed under CC-BY-SA. Created by Sal Khan.

Uploaded 02-08-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/stenosis-ischemia-and-heart-failure?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/health-care-system/v/medicare-overview?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Classifying figures with coordinates | Analytic geometry | High school geometry | Khan Academy

Tue, 20 Oct 2026 00:06:00 -0000

Use coordinates to determine the slopes of sides of a figure in order to classify it.

Uploaded 25-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-lines .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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New operator definitions | Functions and their graphs | Algebra II | Khan Academy

Mon, 19 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-functions/alg-two-variable-functions/v/new-operator-definitions

Uploaded 02-08-11

Getting comfortable with evaluating newly defined function operators

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/functions_and_graphs/new_operators/e/new_definitions_1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Watch the next lesson: https://www.khanacademy.org/math/algebra2/functions_and_graphs/new_operators/v/new-definitions-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/functions_and_graphs/undefined_indeterminate/v/undefined-and-indeterminate?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Using related volumes | Solid geometry | High school geometry | Khan Academy

Mon, 19 Oct 2026 20:06:00 -0000

Use related volumes (using the volume of one figure to determine the volume of another).

Uploaded 25-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-solids/hs-geo-cavalieri-s-principle .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Probability explained | Independent and dependent events | Probability and Statistics | Khan Academy

Mon, 19 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics/cc-7th-basic-prob/v/basic-probability

Uploaded 03-08-11

We give you an introduction to probability through the example of flipping a quarter and rolling a die.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/independent-dependent-probability/basic_probability/e/dice_probability?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/independent-dependent-probability/basic_probability/v/probability-space-exercise-example?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Volumes of cones intuition | Solid geometry | High school geometry | Khan Academy

Mon, 19 Oct 2026 16:06:00 -0000

Use Cavalieri's Principle to establish that the formula for the volume of a cone is the same as the formula for the volume of a pyramid (1/3 * base area * height).

Uploaded 25-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-solids/hs-geo-cavalieri-s-principle .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Probability with playing cards and Venn diagrams | Probability and Statistics | Khan Academy

Mon, 19 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:addition-rule-prob-precalc/v/probability-with-playing-cards-and-venn-diagrams

Uploaded 03-08-11

Probability of compound events. The Addition Rule. Common Core Standard 457 S-CP.7

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/independent-dependent-probability/addition_rule_probability/e/adding-probability?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/independent-dependent-probability/addition_rule_probability/v/addition-rule-for-probability?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/independent-dependent-probability/basic_probability/v/events-and-outcomes-1?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Citing evidence in literary analysis | Reading | Khan Academy

Mon, 19 Oct 2026 12:06:00 -0000

In order to successfully build an argument about a text, you must make inferences and draw conclusions—and those must be built on the backs of evidence in the text. Let's talk about how to search for evidence-bearing details in text, and how to best derive support for the points you're trying to make, in the only way I know how: by talking about fictitious pirates.

Uploaded 25-06-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Sal Answers Questions from Malaysian Magazine Readers

Mon, 19 Oct 2026 10:06:00 -0000

Sal informally answers questions from Malaysian viewers for a magazine

Uploaded 04-08-11

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Part-to-whole relationships in text structure | Reading | Khan Academy

Mon, 19 Oct 2026 08:06:00 -0000

How is an informational text like Voltron, the giant robot made from other, smaller robots? Well, a text is made up of other, smaller sections of text, which are in turn made up of paragraphs and sentences—and each smaller component serves the larger component to drive towards the main point of the text. This is similar to how the lion-shaped robots combine to make a giant person-shaped robot; listen, don't think about it too hard or it falls apart.

Uploaded 25-06-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Addition rule for probability | Probability and Statistics | Khan Academy

Mon, 19 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:addition-rule-prob-precalc/v/addition-rule-for-probability

Uploaded 05-08-11

Venn diagrams and the addition rule for probability

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/independent-dependent-probability/addition_rule_probability/e/adding-probability?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/v/compound-probability-of-independent-events?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/independent-dependent-probability/addition_rule_probability/v/probability-with-playing-cards-and-venn-diagrams?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Cavalieri's principle in 3D | Solid geometry | High school geometry | Khan Academy

Mon, 19 Oct 2026 04:06:00 -0000

Cavalieri's principle tells us that if 2 figures have the same height and the same cross-sectional area at every point along that height, they have the same volume.

Uploaded 22-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-solids/hs-geo-cavalieri-s-principle .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Compound probability of independent events | Probability and Statistics | Khan Academy

Mon, 19 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:compound-probability-of-ind-events-using-mult-rule/v/compound-probability-of-independent-events

Uploaded 09-08-11

You'll become familiar with the concept of independent events, or that one event in no way affects what happens in the second event. Keep in mind, too, that the sum of the probabilities of all the possible events should equal 1.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/e/independent_probability?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/v/getting-at-least-one-heads?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/independent-dependent-probability/addition_rule_probability/v/addition-rule-for-probability?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Dilating in 3D | Solid geometry | High school geometry | Khan Academy

Mon, 19 Oct 2026 00:06:00 -0000

The cross-sections of a pyramid parallel to its base are the dilations of the base about the apex with scale factors from 0 to 1.

Uploaded 22-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-solids/hs-geo-2d-vs-3d .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Coin flipping probability | Probability and Statistics | Khan Academy

Sun, 18 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-statistics/probability-ap/probability-multiplication-rule/v/getting-at-least-one-heads

Uploaded 09-08-11

In this video, we' ll explore the probability of getting at least one heads in multiple flips of a fair coin.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/e/independent_probability?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/v/events-and-outcomes-2?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/v/compound-probability-of-independent-events?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Calculating angle measures to verify congruence | Congruence | High school geometry | Khan Academy

Sun, 18 Oct 2026 20:06:00 -0000

Calculate missing angle measures to determine which triangles must be congruent.

Uploaded 22-06-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruent-triangles .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Probability without equally likely events | Probability and Statistics | Khan Academy

Sun, 18 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/statistics-probability/probability-library/multiplication-rule-independent/v/frequency-probability-and-unfair-coins

Uploaded 09-08-11

Up until now, we've looked at probabilities surrounding only equally likely events. What about probabilities when we don't have equally likely events? Say, we have unfair coins?

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/e/independent_probability?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/v/independent-events-2?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/v/lebron-asks-about-free-throws-versus-three-pointers?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Preview Get Ready for Grade Level

Sun, 18 Oct 2026 16:06:00 -0000

We designed Get Ready for Grade Level courses to help students master the most important skills they’ll need for the next grade. If they have gaps for the grade they’re entering in the fall, students spend their time mastering the important skills they need to fill those gaps. If they don’t have gaps, students accelerate ahead and brush up on the skills they need for next school year. Teachers can also use Get Ready for Grade Level at back-to-school time to complement grade-level instruction. Get Ready for Grade Level courses are available in English and Spanish on our website and mobile app. Like all our courses, they are completely free.

Uploaded 22-06-20

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Proof by induction | Sequences, series and induction | Precalculus | Khan Academy

Sun, 18 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-induction/v/proof-by-induction

Uploaded 09-08-11

Proving an expression for the sum of all positive integers up to and including n by induction

Watch the next lesson: https://www.khanacademy.org/math/precalculus/seq_induction/proof_by_induction/v/alternate-proof-to-induction-for-integer-sum?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/prob_comb/prob_combinatorics_precalc/v/birthday-probability-problem?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Precalculus channel:
https://www.youtube.com/channel/UCBeHztHRWuVvnlwm20u2hNA?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Reading within and across genres | Reading | Khan Academy

Sun, 18 Oct 2026 12:06:00 -0000

A genre is a type of story, like fantasy or romance: stories within a genre share similar subject matter, themes, or styles. The more you read within a genre, the more you develop a schema, a set of background knowledge or expectations for that genre. And if an author's clever, they may play with your expectations...

Uploaded 19-06-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

P.S. The butler totally did it. Did you see the way he treated Mrs. Womblesby? So rude!

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Alternate proof to induction for integer sum | Precalculus | Khan Academy

Sun, 18 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-induction/v/proof-by-induction

Uploaded 09-08-11

Another way to prove the expression for the sum of all positive integers up to and including n

Watch the next lesson: https://www.khanacademy.org/math/precalculus/seq_induction/seq_and_series/v/explicit-and-recursive-definitions-of-sequences?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/seq_induction/proof_by_induction/v/proof-by-induction?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Precalculus channel:
https://www.youtube.com/channel/UCBeHztHRWuVvnlwm20u2hNA?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Quantitative information in texts | Reading | Khan Academy

Sun, 18 Oct 2026 08:06:00 -0000

How can a chart or a graph improve an argument? What's the most efficient way to describe information? How can I convince the neighborhood council to ban peanuts at the bake sale? Let's try to answer those questions the only way I know how: with made-up charts and the world's oldest GIF.

Uploaded 18-06-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attribution: Eadweard Muybridge's 1878 photographs of a running horse are some of the earliest motion pictures. They're in the public domain, and you should absolutely look them up, and yes, I know that's a really strange spelling of 'Edward'. He adopted the Anglo-Saxon spelling in 1882.

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Exactly three heads in five flips | Probability and Statistics | Khan Academy

Sun, 18 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/statistics-probability/counting-permutations-and-combinations/combinatorics-probability/v/exactly-three-heads-in-five-flips

Uploaded 10-08-11

Probability of exactly 3 heads in 5 flips using combinations

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/probability_combinatorics/e/probability_with_perm_comb?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/probability_combinatorics/v/probability-of-dependent-events?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/probability_combinatorics/v/probability-using-combinations?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Character change | Reading | Khan Academy

Sun, 18 Oct 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-5th-reading-vocab/x798e47233e450b09:cc-5th-imaginative-worlds/x798e47233e450b09:reading-for-understanding/v/reading-within-and-across-genres-reading

Uploaded 18-06-20

What does it look like when a fictional character shows change and growth? Let's begin by talking about one of David's favorite character-growth arcs, Prince Zuko from AVATAR: THE LAST AIRBENDER.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Getting exactly two heads (combinatorics) | Probability and Statistics | Khan Academy

Sun, 18 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/statistics-probability/counting-permutations-and-combinations/combinatorics-probability/v/getting-exactly-two-heads-combinatorics

Uploaded 10-08-11

A different way to think about the probability of getting 2 heads in 4 flips

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/probability_combinatorics/e/probability_with_perm_comb?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/probability_combinatorics/v/probability-and-combinations-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/probability_combinatorics/v/coin-flipping-example?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Making objective summaries of literary texts | Reading | Khan Academy

Sun, 18 Oct 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-5th-reading-vocab/x798e47233e450b09:cc-5th-imaginative-worlds/x798e47233e450b09:close-reading/v/character-actions-in-stories-reading

Uploaded 16-06-20

Being objective is *hard*, but it provides a necessary backbone for your analysis. Once you've got an objective summary, then you can bring opinions back in for your analysis. (Opinions are good! Opinions are where analysis lives!)

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

attributions: Some sounds licensed under a public domain Creative Commons 0 license
“Neighborhood Compost and Moving Trucks Ambience” licensed under an attribution license: https://freesound.org/people/Ev-Dawg/sounds/350695/

“Avalanche_land_mono_1.wav” licensed under an attribution license: https://freesound.org/people/leonsptvx/sounds/384568/

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Generalizing with binomial coefficients (bit advanced) | Probability and Statistics | Khan Academy

Sat, 17 Oct 2026 22:06:00 -0000

Conceptual understanding of where the formula for binomial coefficients come from

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/probability_combinatorics/e/probability_with_perm_comb?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/probability_combinatorics/v/conditional-probability-and-combinations?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/probability_combinatorics/v/mega-millions-jackpot-probability?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

Uploaded 10-08-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Analyzing an author's purpose | Reading | Khan Academy

Sat, 17 Oct 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-5th-reading-vocab/x798e47233e450b09:cc-5th-inventing-progress/x798e47233e450b09:close-reading-argumentative-text/v/what-is-an-argument-reading

Uploaded 16-06-20

When it comes to nonfiction texts (and especially opinion pieces), nearly everybody's selling something. Stay sharp, stay skeptical, and watch out for manipulative tactics—what an author *doesn't* say can be as important as what they do say.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions:

Uma Pândega de Paranóias, Fobias e Mania da Perseguição by Stealing Orchestra is licensed under a Attribution-NonCommercial-NoDerivatives (aka Music Sharing) 3.0 International License.

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Prudent Prescribing of Antibiotics (Experiment with Dr. Prober)

Sat, 17 Oct 2026 18:06:00 -0000

Initial experiment of Sal having conversations with people with people who are experts in their fields

Uploaded 12-08-11

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Changes in POV and dramatic irony | Reading | Khan Academy

Sat, 17 Oct 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-8th-reading-vocab/xe1f784c7c84e84fc:cc-8th-funny-business/xe1f784c7c84e84fc:close-reading/a/introduction-to-a-midsummer-nights-dream

Uploaded 12-06-20

When we analyze the perspectives of storytellers—whether that’s a point of view character, an omniscient narrator, or a narrator that attaches closely to multiple perspectives—we can understand the way that an author is controlling the flow of information. Who knows what, when? And what does that tell us?

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions for Dramatic Irony:

some sounds licensed under a public domain Creative Commons 0 license
“Wet Splat” by JustInvoke licensed under an Attribution license
https://freesound.org/people/JustInvoke/sounds/446115/

Music:

“Division” by Kevin MacLeod
Link: https://incompetech.filmmusic.io/song/3665-division
License: http://creativecommons.org/licenses/by/4.0/

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Salman Khan interviewed on NPR's On Point

Sat, 17 Oct 2026 14:06:00 -0000

August 17, 2011

Uploaded 17-08-11

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How POV affects readers | Reading | Khan Academy

Sat, 17 Oct 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-5th-reading-vocab/x798e47233e450b09:cc-5th-imaginative-worlds/x798e47233e450b09:close-reading/v/what-do-pictures-bring-to-a-story-reading

Uploaded 12-06-20

Let’s talk about point of view in literature, and how it can shape what we, as readers, take away from a story. Once we’ve sussed out whose perspective a story or a poem is being told from, what’s next? What else is there to talk about?

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Correlation and causality | Statistical studies | Probability and Statistics | Khan Academy

Sat, 17 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/probability/xa88397b6:scatterplots/estimating-trend-lines/v/correlation-and-causality

Uploaded 18-08-11

Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise)

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/statistical-studies/types-of-studies/e/types-of-statistical-studies?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/statistical-studies/types-of-studies/v/analyzing-statistical-study?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/statistical-studies/types-of-studies/v/types-statistical-studies?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Developing themes | Reading | Khan Academy

Sat, 17 Oct 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-5th-reading-vocab/x798e47233e450b09:cc-5th-imaginative-worlds/x798e47233e450b09:reading-for-understanding-creative-fiction-the-boy-in-the-painting/e/imaginative-worlds--reading-creative-fiction--the-boy-in-the-painting-5

Uploaded 09-06-20

Let’s talk about themes, and how authors can intentionally build messages into fiction. Themes link big ideas about the world we live in with the action of a text—but how does an author structure them into a story?

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Hyperplasia in colon tissue | Gastrointestinal system diseases | Health and Medicine | Khan Academy

Sat, 17 Oct 2026 06:06:00 -0000

Dr. Andy Connolly from Stanford Medical School shows Sal what hyperplasia in colon tissue looks like. Created by Sal Khan.

Uploaded 19-08-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/gastrointestinal-system-diseases/colon-diseases/v/colon-dysplasia?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/gastrointestinal-system-diseases/colon-diseases/v/normal-colon-tissue?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
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What is an argument? | Reading | Khan Academy

Sat, 17 Oct 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-5th-reading-vocab/x798e47233e450b09:cc-5th-inventing-progress/x798e47233e450b09:close-reading-argumentative-text/v/evaluating-a-sources-reasoning-and-evidence

Uploaded 08-06-20

Let's talk about how arguments work!

Argument is when an author wants to convince you of their position. “This is my position; you should share this position, and here is why.” Argument does not sneak. It does not come in through the back. It is supported by reasons, evidence, examples. Not just pure opinion, not just cherry-picked stories. Data! Fact! Observable reality.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Normal colon tissue | Gastrointestinal system diseases | Health and Medicine | Khan Academy

Sat, 17 Oct 2026 02:06:00 -0000

Dr. Andy Connolly from Stanford Medical School introduces Sal to what normal colon tissue looks like. Created by Sal Khan.

Uploaded 19-08-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/gastrointestinal-system-diseases/colon-diseases/v/hyperplasia-in-colon-tissue?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/gastrointestinal-system-diseases/celiac-disease/v/what-is-celiac-disease?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
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Figurative language | Reading | Khan Academy

Sat, 17 Oct 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-3rd-reading-vocab/xaf0c1b5d7010608e:cc-3rd-pets/xaf0c1b5d7010608e:applying-knowledge/e/pets--vocabulary--which-pet-is-right-for-you-3

Uploaded 08-06-20

We're going to talk about non-literal uses of language today, which can be difficult and confusing. Figurative language says something that isn't true in order to EXPRESS something that is true. We're basically lying in order to tell the truth, which is super weird. But it can be so powerful, once you get the hang of it.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions:

photo of the Biblioteca Vasconcelos, Ciudad de México by“Diego Delso, delso.photo, License CC-BY-SA"
Extract from 1964’s “This is Hormel” (the hot dog footage) has been released into the public domain by the Prelinger Archives.

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Colon dysplasia | Gastrointestinal system diseases | Health and Medicine | Khan Academy

Fri, 16 Oct 2026 22:06:00 -0000

Dr. Andy Connolly shows Sal what cancerous colon tissue looks like. Created by Sal Khan.

Uploaded 19-08-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/gastrointestinal-system-diseases/colon-diseases/v/cancerous-colon-tissue?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/gastrointestinal-system-diseases/colon-diseases/v/hyperplasia-in-colon-tissue?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Reporting measurements | Working with units | Algebra 1 | Khan Academy

Fri, 16 Oct 2026 20:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:working-units/x2f8bb11595b61c86:appropriate-units/v/reporting-measurements

Uploaded 05-06-20

We should think about the appropriate level of precision of different measurements in modeling problems.

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Cancerous colon tissue | Gastrointestinal system diseases | Health and Medicine | Khan Academy

Fri, 16 Oct 2026 18:06:00 -0000

Dr. Andy Connolly of Stanford Medical School shows us what cancerous colon tissue looks like. Created by Sal Khan.

Uploaded 19-08-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/advanced-muscular-system/muscular-system-introduction/v/myosin-and-actin?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/gastrointestinal-system-diseases/colon-diseases/v/colon-dysplasia?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Reasoning with systems of equations | Equivalent systems of equations | Algebra I | Khan Academy

Fri, 16 Oct 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:systems-of-equations/x2f8bb11595b61c86:equivalent-systems-equations/e/understanding-solution-methods-to-systems-of-equations

Uploaded 05-06-20

When we perform operations on a system of equations, some operations produce an equivalent system, while others don't necessarily produce an equivalent system. When we're solving a system of equations, we need to use operations that guarantee equivalence.

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Adequacy of the lateral cervical spine X-ray | Miscellaneous | Heatlh and Medicine | Khan Academy

Fri, 16 Oct 2026 14:06:00 -0000

Dr. Mahadevan from Stanford School of Medicine explains adequacy for lateral cervical (neck) x-rays. Created by Sal Khan.

Uploaded 22-08-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/assessing-alignment-of-the-lateral-cervical-spine-neck-x-ray?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/spotting-salty-foods?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Reasoning with linear equations | Solving equations and inequalities | Algebra I | Khan Academy

Fri, 16 Oct 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-parentheses/e/reasoning-with-linear-equations

Uploaded 05-06-20

When we perform operations to manipulate equations, some operations produce equivalent equations, while others don't necessarily produce equivalent equations. When we're solving an equation, we need to use operations that guarantee equivalence.

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Assessing alignment of the lateral cervical spine (neck) X-ray | Heatlh and Medicine | Khan Academy

Fri, 16 Oct 2026 10:06:00 -0000

Dr. Mahadevan of Stanford Medical School shows Sal what misalignment in the neck could look like in an X-ray. Created by Sal Khan.

Uploaded 22-08-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/cervical-spine-protection-in-airway-management-not-a-substitute-for-formal-training?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/adequacy-of-the-lateral-cervical-spine-x-ray?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Parent Quick-Start Tips: For Kids Ages 12 and Under

Fri, 16 Oct 2026 08:06:00 -0000

This video gives a quick overview of how parents can get started with using Khan Academy with their children. It is meant for parents who have kids who are 12 or younger. If you have kids who are 13 or older, please see this video: https://www.youtube.com/watch?v=Nj0_IxXk5hU

Uploaded 03-06-20

To start using Khan Academy with your children, visit www.khanacademy.org.

Get free resources to keep your kids learning during school closures:
https://keeplearning.khanacademy.org/

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Global Burden of Trauma Why Should We Care

Fri, 16 Oct 2026 06:06:00 -0000

Uploaded 22-08-11

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Parent Quick-Start Tips: For Kids Ages 13+

Fri, 16 Oct 2026 04:06:00 -0000

This video gives a quick overview of how parents can get started with using Khan Academy with their children. It is meant for parents who have kids who are 13 or older. If you have kids who are 12 or younger, please see this video: https://www.youtube.com/watch?v=KABB4Kr7WhU

Uploaded 03-06-20

To start using Khan Academy with your children, visit www.khanacademy.org.

Get free resources to keep your kids learning during school closures:
https://keeplearning.khanacademy.org/

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Cervical spine protection in airway management (not a substitute for formal training) | Khan Academy

Fri, 16 Oct 2026 02:06:00 -0000

Cervical Spine Protection in Airway Management. This is for education only. It is not a substitute for formal training or licensure. Every effort has been made in preparing this video to provide accurate and up-to-date information which is in accord accepted standards and practice at the time of production. We make no warranties on the information contained in the video because clinical standards are constantly changing through research and regulation. We disclaim all liability for direct or consequential damages resulting from the use of material contained in this video. Created by Sal Khan.

Uploaded 22-08-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/precocious-puberty?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/assessing-alignment-of-the-lateral-cervical-spine-neck-x-ray?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Latin and Greek roots and affixes | Reading | Khan Academy

Fri, 16 Oct 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-4th-reading-vocab/x5ea2e43787f7791b:cc-4th-growth-mindset/x5ea2e43787f7791b:applying-knowledge/e/growth-mindset--word-meanings-4-1

Uploaded 01-06-20

Roots and affixes are the keys to unlocking so much of English's vocabulary. For a variety of Fun History Reasons™, many of the roots we use to make words in English are derived from Latin and Greek. Understanding those word-parts can make vocabulary a lot less frustrating and scary.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions:
“crazy feet, sensible shoes” by Curlew licensed under a CC 3.0 Attribution-Noncommercial-NoDerivativeWorks license

Other sound effects and music from non-copyrighted (Creative Commons Zero license) sources

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Understanding South Indian Naming

Thu, 15 Oct 2026 22:06:00 -0000

Dr. Mahadevan explains how South Indian naming differs from North Indian or Western naming

Uploaded 22-08-11

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What are affixes? | Reading | Khan Academy

Thu, 15 Oct 2026 20:06:00 -0000

Affixes are word-parts that change the meaning of the words they attach to. "Un-" is a great example; when you're not happy, you're "unhappy". "Un-" means "not". It's a kind of affix we call a "prefix".

Uploaded 01-06-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Questions from Superinteressante (8-22-2011)

Thu, 15 Oct 2026 18:06:00 -0000

Answers for a magazine in Brazil

Uploaded 22-08-11

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Reading multiple accounts of the same topic | Reading | Khan Academy

Thu, 15 Oct 2026 16:06:00 -0000

Everyone brings a different perspective to an event. We read multiple accounts of the same topic so we can bring all those perspectives together, and in so doing, we can get a handle on the truth.

Uploaded 22-05-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

attributions:

The image of the 1962 Rashomon re-release poster is in the public domain in Japan.

illustration of the RMS Titanic licensed under a CC attribution-sharealike 3.0 license.
https://commons.wikimedia.org/wiki/File:Cd51-1000g.gif

Willy Stöwer’s 1912 engraving, Der Untergang der Titanic, is in the public domain.
https://en.wikipedia.org/wiki/File:St%C3%B6wer_Titanic.jpg

This photo of the USS Massachusetts’s fire room/boiler room is in the public domain:
https://en.wikipedia.org/wiki/File:Fire_room_Massachusetts.jpg

This photo of stateroom B-58 aboard the RMS Titanic is in the public domain in the United States:
https://en.wikipedia.org/wiki/File:B-58.jpg

Michael M. Stokes’s photo of the Somerset Patriots players arguing with an umpire is licensed under an attribution 2.0 license.
https://commons.wikimedia.org/wiki/File:Somerset_Patriots_vs_umpire_(41836541332).jpg

This image of a car hitting a tree is by Huhu Uet - Own work, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=8991289

"Bicyclist crossing the street" is licensed under a CC BY 3.0 license: https://commons.wikimedia.org/wiki/File:Bicyclist_Crossing_the_Street.jpg

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NCSU Answers

Thu, 15 Oct 2026 14:06:00 -0000

Answers for the NCSU newpaper

Uploaded 22-08-11

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Connotation | Reading | Khan Academy

Thu, 15 Oct 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:working-units/x2f8bb11595b61c86:word-problems-multiple-units/v/using-units-to-solve-problems-toy-factory

Uploaded 20-05-20

Today, let’s talk about feelings—specifically, the way that words make us feel.

We're talking about connotation, the way a word feels, the context around it. Imagine a rock in a stream: connotation is the way culture flows around a word.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

photo of a baseball by Schyler at English Wikipedia, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=13465049

photo of a soccer ball by Petey21 - Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=33477368

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Answers for Malibu Magazine

Thu, 15 Oct 2026 10:06:00 -0000

Uploaded 22-08-11

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Place value tables

Thu, 15 Oct 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-place-value/x3184e0ec:intro-to-place-value/v/use-place-value-blocks-to-show-numbers-within-1000

Uploaded 18-05-20

Introduction to place value tables

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21st Century Challenges (Royal Geographic Society)

Thu, 15 Oct 2026 06:06:00 -0000

Answers to questions from the Royal Geographic Society

Uploaded 22-08-11

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The structures of informational texts | Reading | Khan Academy

Thu, 15 Oct 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-4th-reading-vocab/x5ea2e43787f7791b:cc-4th-superheroes/x5ea2e43787f7791b:close-reading-informational-text/e/superheroes-reading-informational-text-superheroes-around-the-world-4

Uploaded 18-05-20

Buildings and essays: they’re similar in an unexpected way! They both have STRUCTURE. We’ll explore five different ways to structure a piece of nonfiction writing, using as our example the greatest food in the world… the pizza.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions:

photo of the John Hancock center licensed under a Creative Commons 3.0 Attribution-Share-Alike license: https://commons.wikimedia.org/wiki/File:John_Hancock_Center_2.jpg

photo of the Abdoun Bridge licensed from I, Producer, CC BY 2.5, https://commons.wikimedia.org/w/index.php?curid=5055834

Rebar and shingles photograph licensed under a CC 2.0 attribution license: https://commons.wikimedia.org/wiki/File:Rebar_and_shingles.jpg

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Setting up proportions to solve word problems | 7th grade | Khan Academy

Thu, 15 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-write-and-solve-proportions/v/writing-proportions

Uploaded 23-08-11

Some examples of writing two ratios and setting them equal to each other to solve proportion word problems

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-write-and-solve-proportions/e/writing_proportions?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Watch the next lesson: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-write-and-solve-proportions/v/find-an-unknown-in-a-proportion-2?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Missed the previous lesson?
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-write-and-solve-proportions/v/find-an-unknown-in-a-proportion?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Grade 7th on Khan Academy: 7th grade takes much of what you learned in 6th grade to an entirely new level. In particular, you'll now learn to do everything with negative numbers (we're talking everything--adding, subtracting, multiplying, dividing, fractions, decimals... everything!). You'll also take your algebraic skills to new heights by tackling two-step equations. 7th grade is also when you start thinking about probability (which is super important for realizing that casinos and lotteries are really just ways of taking money away from people who don't know probability) and dig deeper into the world of data and statistics. Onward! (Content was selected for this grade level based on a typical curriculum in the United States.)

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÂ Ã Âªs 7th grade channel:
https://www.youtube.com/channel/UCzKsXcrLSLDG7VN1LODlRkw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Learn How to Use Pixar in a Box with Your Students

Thu, 15 Oct 2026 00:06:00 -0000

We know this is a tough time for teachers and students alike — especially when it comes to sparking the joy of learning.

Uploaded 12-05-20

That's why we're excited to show you "Pixar in a Box" — a collaboration between Khan Academy and Pixar Animation Studios that's all about generating curiosity and excitement, even in tough times.

Covering a range of subjects — from math to science to the humanities — your students will learn how to animate bouncing balls, build a swarm of robots, and make virtual fireworks explode!

And you'll learn directly from an expert Khan Academy teacher who uses this curriculum with her own students.

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org, Novartis, and Fastly. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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More angle measurements using a protractor | Angles and intersecting lines | Geometry | Khan Academy

Wed, 14 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-fourth-grade-math/imp-geometry-2/imp-measuring-angles/v/measuring-angles

Uploaded 23-08-11

We're practicing measuring angles using the virtual protractor. Do this a few times with us and you'll use a real protractor like a pro!

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/e/measuring_angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/acute-right-and-obtuse-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/using-a-protractor?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy Best Practices for Supporting Students in Special Education

Wed, 14 Oct 2026 20:06:00 -0000

Want to learn how to use Khan Academy to best support your students in Special Education?

Uploaded 12-05-20

This is your chance to get advice directly from an expert Khan Academy Special Education teacher!

We'll cover everything you need to get started and make the most of this tool.

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org and Novartis. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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Comparing and ordering fractions | Fractions | Pre-Algebra | Khan Academy

Wed, 14 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/arithmetic-home/arith-review-fractions/arith-comparing-fractions/v/ordering-fractions

Uploaded 23-08-11

Finding common denominators of multiple fractions to order them

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/e/ordering_fractions?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/decomposing-fractions-pre-alg/v/decomposing-a-fraction-visually?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/v/comparing-fractions-2?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy Best Practices for ELA

Wed, 14 Oct 2026 16:06:00 -0000

Want to learn how to use Khan Academy to help your students master ELA skills?

Uploaded 12-05-20

This is your chance to get advice directly from an expert Khan Academy ELA teacher!

We'll cover everything you need to get started and make the most of this tool.

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org and Novartis. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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Ordering negative numbers | Negative numbers and absolute value | Pre-Algebra | Khan Academy

Wed, 14 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic/x0267d782:ordering-rational-numbers/v/ordering-negative-numbers

Uploaded 23-08-11

Is -40 bigger than -10? When ordering negative numbers from least to greatest, careful that you don't get hung up on the "amount" of the number. Think about what that negative sign really means!

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/add-sub-negatives-pre-alg/e/ordering_negative_numbers?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/add-subtract-negatives-pre-alg/v/adding-and-subtracting-negative-number-examples?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/add-sub-negatives-pre-alg/v/number-line-3-exercise-example?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy Best Practices for Supporting English Language Learners

Wed, 14 Oct 2026 12:06:00 -0000

Want to learn how to use Khan Academy to best support your ELL students?

Uploaded 12-05-20

This is your chance to get advice directly from an expert Khan Academy ELL teacher!

We'll cover everything you need to get started and make the most of this tool.

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org, Novartis, and Fastly. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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Comparing absolute values | Negative numbers and absolute value | Pre-Algebra | Khan Academy

Wed, 14 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic/x0267d782:cc-6th-comparing-absolute-values/v/comparing-absolute-values

Uploaded 23-08-11

When we compare numbers we use the concepts of greater than, less than, and equal to (=). The same is true of absolute values.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/arithmetic/absolute-value/abs_value_tutorial/e/comparing_absolute_values?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/arithmetic/absolute-value/abs_value_tutorial/v/absolute-value-word-problems-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/arithmetic/absolute-value/abs_value_tutorial/v/absolute-value-of-integers?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy Best Practices for Middle School

Wed, 14 Oct 2026 08:06:00 -0000

Want to learn how to use Khan Academy with your middle schoolers?

Uploaded 12-05-20

This is your chance to get advice directly from an expert Khan Academy middle school teacher!

We'll cover everything you need to get started and make the most of this tool.

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org and Novartis. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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Intro to lines, line segments, and rays | Geometry | Khan Academy

Wed, 14 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-fourth-grade-math/plane-figures/imp-lines-line-segments-and-rays/v/lines-line-segments-and-rays

Uploaded 23-08-11

Let's get familiar with the difference between lines, line segments, and rays. Hint: a ray is somewhere between a line and a line segment!

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/intro_euclid/e/recognizing_rays_lines_and_line_segments?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/intro_euclid/v/drawing-lines-exercise-example?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/intro_euclid/v/language-and-notation-of-basic-geometry?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Get a Tour of the Student Experience on Khan Academy

Wed, 14 Oct 2026 04:06:00 -0000

Want to see what the student experience on Khan Academy looks like?

Uploaded 12-05-20

Get a full tour from Meaghan Pattani, Khan Academy's Professional Learning Leader, to better understand everything from registration to reviewing results.

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org, Novartis, and Fastly. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

Learn more about your ad choices. Visit megaphone.fm/adchoices

Vi and Sal talk about the mysteries of Benford's law | Logarithms | Algebra II | Khan Academy

Wed, 14 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/alg-logarithmic-scale/v/vi-and-sal-talk-about-the-mysteries-of-benford-s-law

Uploaded 23-08-11

Vi Hart visits Khan Academy and talks about Benford's Law with Sal

Watch the next lesson: https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithmic-scale-patterns/v/benford-s-law-explanation-sequel-to-mysteries-of-benford-s-law?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithmic-scale-patterns/v/logarithmic-scale?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy Best Practices for Elementary School

Wed, 14 Oct 2026 00:06:00 -0000

Want to learn how to use Khan Academy with your elementary students?

Uploaded 12-05-20

This is your chance to get advice directly from an expert Khan Academy elementary school teacher!

We'll cover everything you need to get started and make the most of this tool.

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org and Novartis. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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Benford's law explanation (sequel to mysteries of Benford's law) | Algebra II | Khan Academy

Tue, 13 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/alg-logarithmic-scale/v/benford-s-law-explanation-sequel-to-mysteries-of-benford-s-law

Uploaded 23-08-11

Vi and Sal talk through the intuition of Benford's law (part 2)

Watch the next lesson: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/imaginary_unit_i-a2/v/introduction-to-i-and-imaginary-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithmic-scale-patterns/v/vi-and-sal-talk-about-the-mysteries-of-benford-s-law?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy Best Practices for Science

Tue, 13 Oct 2026 20:06:00 -0000

Want to learn how to use Khan Academy to help your students master science?

Uploaded 12-05-20

This is your chance to get advice directly from an expert Khan Academy science teacher!

We'll cover everything you need to get started and make the most of this tool.

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org and Novartis. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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Vi and Sal explore how we think about scale | Algebra II | Khan Academy

Tue, 13 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/alg-logarithmic-scale/v/vi-and-sal-explore-how-we-think-about-scale

Uploaded 23-08-11

Vi Hart (http://www.youtube.com/vihart) and Sal talk about how we humans perceive things nonlinearly

Watch the next lesson: https://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/logarithmic-equations/v/solving-logarithmic-equations_dup_1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/log_functions/v/logarithmic-function-graphs?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy Best Practices for Social Studies

Tue, 13 Oct 2026 16:06:00 -0000

Want to learn how to use Khan Academy to help your students master social studies skills?

Uploaded 12-05-20

This is your chance to get advice directly from an expert Khan Academy social studies teacher!

We'll cover everything you need to get started and make the most of this tool.

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org and Novartis. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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Firestick farming | Life on earth and in the universe | Cosmology and Astronomy | Khan Academy

Tue, 13 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/firestick-farming

Uploaded 25-08-11

How the indigenous Australians used fire to change their environment. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/collective-learning?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/development-of-agriculture-and-writing?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Cosmology and Astronomy channel: https://www.youtube.com/channel/UChNPnEkW8LYZ5Rwi8_A2-DA?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy Best Practices for High School

Tue, 13 Oct 2026 12:06:00 -0000

Want to learn how to use Khan Academy with your high schoolers?

Uploaded 12-05-20

This is your chance to get advice directly from an expert Khan Academy high school teacher!

We'll cover everything you need to get started and make the most of this tool.

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org and Novartis. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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Logarithmic scale | Logarithms | Algebra II | Khan Academy

Tue, 13 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/alg-logarithmic-scale/v/logarithmic-scale

Uploaded 25-08-11

Understanding how logarithmic scale is different from linear scale and why it could be useful

Watch the next lesson: https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_properties/v/richter-scale?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_properties/v/solving-logarithmic-equations_dup_1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Remote Learning Best Practices from a Cyber School Teacher

Tue, 13 Oct 2026 08:06:00 -0000

We know the transition to remote learning has been tough. But who better to learn from than an educator who's been offering remote learning for years?

Uploaded 12-05-20

Join our Khan Academy Ambassador, Mark Laser of Agora Cyber Charter School, to learn how best to:

-Get started with remote learning
-Engage your students
-Track and grade student progress

*About Khan Academy*
Khan Academy is a nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. With more than one billion children world-wide being impacted by school closures, we are experiencing soaring demand for our free resources. Our ability to quickly increase our services is made possible by Bank of America, AT and T, Google.org and Novartis. If you are able, please consider making a donation: https://www.khanacademy.org/donate. Together, we can keep everyone learning.

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Carry trade basics | Money, banking and central banks | Finance and Capital Markets | Khan Academy

Tue, 13 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/carry-trade-basics

Uploaded 26-08-11

The mechanics of the carry trade. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/china-us-debt-situation/v/floating-exchange-resolving-trade-imbalance?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/currency-tutorial/v/china-keeps-peg-but-diversifies-holdings?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: This tutorial walks through how China's undervaluing of its currency impacts trade and prices (which also fuels cheap borrowing for the U.S.).

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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How to Bring Mastery Learning to Your Class... And Get Results Like Tim's!

Tue, 13 Oct 2026 04:06:00 -0000

Tim Vandenberg shared his story earlier this month about using Mastery Learning to take his students from below grade level to far above it: https://www.youtube.com/watch?v=Q8YNn...

Uploaded 12-05-20

Now learn how to do the same in your own classroom or school.

And then grab Tim's slides here: http://khan.co/timimplementation - and his pacing chart here: http://bit.ly/timspacingchart

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Answers to Questions from the Independent

Tue, 13 Oct 2026 02:06:00 -0000

Sal answers questions on August 26, 2011

Uploaded 26-08-11

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How I Helped My 6th Graders Ace Math... By Taking Them Back to Kindergarten! | Mastery Learning

Tue, 13 Oct 2026 00:06:00 -0000

Tim Vandenberg has been teaching 6th grade in Hesperia, California, for nearly 20 years. But it's only been in the last three years that he's been able to help his students (100% Free/Reduced Lunch, 90% Below Grade Level in Math) outperform not just their starting points - but students across the entire state.

Uploaded 12-05-20

Come learn how Tim was able to bend the arc of his students' trajectories through the power of differentiation, mastery learning, and yes... starting over with kindergarten!

BONUS RESOURCES

1) Bring mastery learning and Khan Academy to your classroom with this quick cheatsheet: https://bit.ly/khancheatsheet

2) Check out the videos Tim references by clicking into his slides: https://bit.ly/timsdeck

3) Share a summary of Tim's story and recommendations with your school or district leaders: https://bit.ly/tim4schools

4) Go deeper on these topics here: https://www.youtube.com/watch?v=lEBMvWEgVqM&list=PLnhtSiAy9Bpx2iSprM5AdOeRHWmHNvzNP&index=6&t=0s

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The Gates Notes: Sal on Khan Academy

Mon, 12 Oct 2026 22:06:00 -0000

Salman Khan on the future of learning.
More free lessons at: http://www.khanacademy.org/video?v=raP1ZWQSXjY

Uploaded 26-08-11

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How to Engage + Motivate Your Students Even When You're Remote!

Mon, 12 Oct 2026 20:06:00 -0000

We know that keeping your students engaged and motivated can challenging, even when you're in class with them!

Uploaded 08-05-20

So doing the same when everyone is separated can feel nearly impossible.

That's why we're thrilled to have Conor Corey, one of our Khan Academy Ambassadors, share his secrets for keeping students excited, even during the toughest of times.

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The Gates Notes: Insights into students' progress

Mon, 12 Oct 2026 18:06:00 -0000

How Khan Academy is helping teachers free up classroom time, track student's progress, and pinpoint their needs
More free lessons at: http://www.khanacademy.org/video?v=zscrs94_pFc

Uploaded 26-08-11

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7 Tips for Effective Remote Learning with Khan Academy

Mon, 12 Oct 2026 16:06:00 -0000

Doing remote learning well isn't just about technology.

Join us to discover the other keys to successfully serving students from afar - including:

-Setting up a schedule + routine
-Supporting independent learning
-Staying in touch
-Using goals and milestones to keep students motivated
-Addressing the emotional impact

Uploaded 08-05-20

Get the slides here: http://khan.co/7tips-remote

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The Gates Notes: Administrators in Los Altos

Mon, 12 Oct 2026 14:06:00 -0000

Administrators in Los Altos School District share their experiences with Khan Academy
More free lessons at: http://www.khanacademy.org/video?v=2DlxIXYEu4s

Uploaded 26-08-11

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Getting Started with Khan Academy for Remote Learning

Mon, 12 Oct 2026 12:06:00 -0000

Want to learn how to use Khan Academy for remote learning?

Join us for a quick walkthrough of how to get started, including:

-Getting your students enrolled
-Finding appropriate content and exercises
-Differentiating content to help each student thrive
-Reviewing results

Uploaded 08-05-20

Then download our QuickStart Guide to get your class set-up: https://bit.ly/khanremotelearning

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The Gates Notes: Teachers in Los Altos

Mon, 12 Oct 2026 10:06:00 -0000

Teachers in Los Altos School District share their experiences with Khan Academy
More free lessons at: http://www.khanacademy.org/video?v=RoGgxrCsCEQ

Uploaded 26-08-11

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Khan Academy thanks our teachers

Mon, 12 Oct 2026 08:06:00 -0000

#TeacherAppreciationWeek is every week for the Khan Academy team. Our gratitude for everything our teachers have taught us fuels us daily.

Uploaded 08-05-20

#TeacherAppreciationWeek #ThankATeacher

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The Gates Notes: Students in Los Altos

Mon, 12 Oct 2026 06:06:00 -0000

Students in Los Altos School District share their experiences with Khan Academy
More free lessons at: http://www.khanacademy.org/video?v=q7lttowsC0Y

Uploaded 26-08-11

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Creating objective summaries | Reading | Khan Academy

Mon, 12 Oct 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-5th-reading-vocab/x798e47233e450b09:cc-5th-inventing-progress/x798e47233e450b09:inventing-progress-close-reading-informational/v/two-or-more-main-ideas-reading

Uploaded 06-05-20

All we want are the facts! Today, let's talk about what it means to be objective (and how difficult that is!). When you're summarizing a text, leave your opinions out—save them for analysis! When you summarize a text, do your best to leave judgment behind.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions: "Dragnet" is in the public domain, so I snagged the theme from the radio show!

The image of Joe Friday is one I traced from a promotional production still.

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Richter scale | Logarithms | Algebra II | Khan Academy

Mon, 12 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/alg-logarithmic-scale/v/richter-scale

Uploaded 29-08-11

The basics of the logarithmic Richter and Moment Magnitude Scales to measure earthquakes

Watch the next lesson: https://www.khanacademy.org/math/algebra2/logarithms-tutorial/natural_logarithm/v/natural-logarithm-with-a-calculator?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_properties/v/logarithmic-scale?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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How can a text have two or more main ideas? | Reading | Khan Academy

Mon, 12 Oct 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-5th-reading-vocab/x798e47233e450b09:cc-5th-athletes-in-action/x798e47233e450b09:close-reading-informational-text-title-ix/v/using-examples-reading

Uploaded 06-05-20

Unless you’re a quantum particle, you can’t be in two places at once. But your mind *CAN*. Texts can contain more than one main idea: multiple, equally-important arguments can be threaded through a single text. Let’s talk about how that works!

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions:
The public domain map of the United States comes from Wikipedia!
“How can you be in two places at once when you’re not anywhere at all?” is the name of a very goofy counterculture comedy record from the 60s by The Firesign Theatre. The song I sing a snippet of is from Track 2 on the CD version, “Zeno’s Evil”. Prepare yourself: it is very dense.

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Intro to the endocrine system | Health and Medicine | Khan Academy

Sun, 11 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/ap-biology/cell-communication-and-cell-cycle/cell-communication/v/intro-to-the-endocrine-system

Uploaded 30-08-11

Basic overview of hormones and the endocrine system. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/advanced-endocrine-system/endocrine-system-introduction/v/endocrine-gland-hormone-review?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/hematologic-system-diseases-2/myeloproliferative-disorders/v/what-is-primary-myelofibrosis?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
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How do writers use examples to get their points across? | Reading | Khan Academy

Sun, 11 Oct 2026 20:06:00 -0000

Examples are very powerful tools! As writers, we can use them to make arguments stronger. As readers, we're engaged in a push-and-pull with writers, and have to think critically about how examples are used in a text.

Uploaded 06-05-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Paying doctors | Health care system | Heatlh and Medicine | Khan Academy

Sun, 11 Oct 2026 18:06:00 -0000

Basics of how doctors get paid. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/health-care-system/v/medicare-overview?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/health-care-system/v/healthcare-system-overview?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

Uploaded 30-08-11

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
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Finding your footing in uncertain times: Balancing multiple kids with multiple schedules

Sun, 11 Oct 2026 16:06:00 -0000

We've heard lots of questions from parents about how to juggle the needs of multiple kids, while being productive at work, and managing a hundred other tasks... all while staying (relatively) sane during an apocalypse. Join us as we chat with Dr. Lindsay Portnoy, an education professor at Northeastern, a parent of multiple kids, and an author with the Association for Supervision and Curriculum Development. She shares her top tips around building clarity, curation, creativity, compassion, and curiosity for parents to support their kids and themselves.

Uploaded 05-05-20

View the slides here: https://bit.ly/FindingFootingWebinarSlides

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Healthcare system overview | Health care system | Heatlh and Medicine | Khan Academy

Sun, 11 Oct 2026 14:06:00 -0000

The different roles in the healthcare system. Created by Sal Khan.

Uploaded 30-08-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/health-care-system/v/paying-doctors?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/health-care-system/v/health-care-costs-in-us-vs-europe?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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How to motivate and engage your kids in learning while at home

Sun, 11 Oct 2026 12:06:00 -0000

We’ve received many requests from parents about ways to keep their kids engaged and learning during school closures. Join us as we chat with Conor Corey, an expert teacher, Khan Academy Ambassador, and parent of 4. Conor will share his top tips and strategies for teaching and motivating kids.

Uploaded 30-04-20

You can find the handout from the webinar here: https://bit.ly/MotivationTipsHandout

You can view the daily schedules mentioned in the webinar, and all of our other remote learning resources here:
https://keeplearning.khanacademy.org/

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Early Show

Sun, 11 Oct 2026 10:06:00 -0000

Khan Academy profiled on the Early Show

Uploaded 05-09-11

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Crystalline and amorphous polymers | AP Chemistry | Khan Academy

Sun, 11 Oct 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:solids-liquids-and-gases/e/solids-liquids-and-gases

Uploaded 28-04-20

Polymers can exist as both crystalline and amorphous solids. In fact, most polymers are semicrystalline, which means that they contain a mixture of crystalline and amorphous regions. In this video, we'll see different examples of semicrystalline and amorphous polymers and learn how their structures can be represented using particulate models. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:solids-liquids-and-gases/v/crystalline-and-amorphous-polymers

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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2011 Calculus AB free response #2 (a and b) | AP Calculus AB | Khan Academy

Sun, 11 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-2-a-b

Uploaded 07-09-11

Approximating rate of change and total area under a curve. Trapezoidal sums to approximate integrals. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-2-c-d?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-1-parts-b-c-d?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Reading (and comparing) multiple books | Reading | Khan Academy

Sun, 11 Oct 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-fairy-tales-retold/xfb4fc0bf01437792:close-reading/e/fairy-tales-retold--reading-creative-fiction--granny-the-hero-2

Uploaded 28-04-20

You know what's better than reading a book? Reading TWO BOOKS. Let's talk about how books and stories relate to one another, how book series work, and what you can learn from comparing stories from around the world.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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2011 Calculus AB free response #2 (c and d) | AP Calculus AB | Khan Academy

Sun, 11 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-2-c-d

Uploaded 07-09-11

Second fundamental theorem of calculus application. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-3-a-b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-2-a-b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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What do pictures bring to a story? | Reading | Khan Academy

Sun, 11 Oct 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-fairy-tales-retold/xfb4fc0bf01437792:close-reading-little-red-riding-hood/e/fairy-tales-retold--reading-creating-fiction--little-red-riding-hood-2

Uploaded 28-04-20

Don't skip the pictures in a book! Good readers use illustrations to fill in details about stories. Let's talk about how understanding pictures can help you understand stories even better.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attribution: This video uses images that are the original work of the Core Knowledge ® Foundation, made available through licensing under a Creative Commons Attribution-NonCommercial- ShareAlike 4.0 International License. This does not in any way imply that the Core Knowledge Foundation endorses this work.

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2011 Calculus AB free response #3 (a and b) | AP Calculus AB | Khan Academy

Sat, 10 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-3-a-b

Uploaded 07-09-11

Equation of a tangent line and area between curves. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-3-c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-2-c-d?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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The elements of a drama | Reading | Khan Academy

Sat, 10 Oct 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-fairy-tales-retold/xfb4fc0bf01437792:reading-for-understanding/e/fairy-tales-retold--reading-drama--tom-thumb-2

Uploaded 28-04-20

Let's talk about how to read a play! Dramas are special stories. They're written to be performed aloud, and that means that you read them differently from how you'd read a story or a poem.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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2011 Calculus AB free response #3 (c) | AP Calculus AB | Khan Academy

Sat, 10 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-3-c

Uploaded 07-09-11

Disk method to find the volume of a solid generated by rotation of a function. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-4a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-3-a-b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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A story's point of view | Reading | Khan Academy

Sat, 10 Oct 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-fairy-tales-retold/xfb4fc0bf01437792:close-reading/v/reading-and-comparing-multiple-books

Uploaded 28-04-20

Stories have points of view. Let's talk about the three flavors they can come in!

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions:

"Strong Surf" is licensed under an attribution license from Andrew1280 on FreeSound. This sound effect makes David miss Lake Michigan terribly:
https://freesound.org/people/andrew1280/sounds/41191/

"Full Stop" from Ketsa's "End is Beginning", licensed with permission from the Independent Music Licensing Collective - imlcollective.uk

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2011 Calculus AB Free Response #1 parts b c d | AP Calculus AB | Khan Academy

Sat, 10 Oct 2026 14:06:00 -0000

Integration to find average value of a function. Using a graphing calculator to calculate definite integrals. Created by Sal Khan.

Uploaded 08-09-11

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-2-a-b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-1a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Homeschooling your kids? Learn how to use our weekly math learning plans

Sat, 10 Oct 2026 12:06:00 -0000

Parents, for many of you, your school may be closed through the end of the year, and you may be wondering how to keep your child learning while at home. We're here to help. We've created step-by-step sample weekly math schedules for grades 3 - Algebra 2, and designed them to be a fun, structured way to keep kids learning and reduce the impact of the summer slide and school closures. In this webinar recording, we'll walk you through the schedules and give tips on how you can adapt them for your family.

Uploaded 27-04-20

View the weekly math schedules here: https://bit.ly/KA-Weekly-LPs
View the slides here: https://bit.ly/WeeklyLearningPlansSlides

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2011 Calculus AB free response #4a | AP Calculus AB | Khan Academy

Sat, 10 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-4a

Uploaded 08-09-11

Taking derivatives and integrals of strangely defined functions. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-4b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

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AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Gas mixtures and partial pressures | AP Chemistry | Khan Academy

Sat, 10 Oct 2026 08:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:ideal-gas-law/v/partial-pressure

Uploaded 23-04-20

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For a mixture of ideal gases, the total pressure exerted by the mixture equals the sum of the pressures that each gas would exert on its own. This observation, known as Dalton's law of partial pressures, can be written as follows: P(total) = P₁ + P₂ + P₃ + ... where P₁, P₂, and P₃ are the partial pressures of the different gases in the mixture, and P(total) is the total pressure of the mixture. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:ideal-gas-law/v/introduction-to-partial-pressure

Sections:
00:00 - Introduction to partial pressure
00:36 - Total pressure as sum of partial pressures
01:18 - Using ideal gas law for partial pressures
02:14 - Factoring pressure equation for multiple gases
03:37 - Applying mole values to partial pressure
04:20 - Calculating mole fraction
05:34 - Using mole fraction to find partial pressure
06:14 - Final result: partial pressure of gas three

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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2011 Calculus AB free response #4b | AP Calculus AB | Khan Academy

Sat, 10 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-4b

Uploaded 08-09-11

Absolute maximum over an interval. Critical points and differentiability. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-4c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

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AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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The ideal gas law (PV = nRT) | Intermolecular forces and properties | AP Chemistry | Khan Academy

Sat, 10 Oct 2026 04:06:00 -0000

The ideal gas law (PV = nRT) relates the macroscopic properties of ideal gases. An ideal gas is a gas in which the particles (a) do not attract or repel one another and (b) take up no space (have no volume). No gas is truly ideal, but the ideal gas law does provide a good approximation of real gas behavior under many conditions. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:ideal-gas-law/v/ideal-gas-equation-pv-nrt

Uploaded 23-04-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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2011 Calculus AB free response #4c | AP Calculus AB | Khan Academy

Sat, 10 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-4c

Uploaded 08-09-11

Finding the points of inflection for a strangely defined function. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-4d?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

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AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
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London dispersion forces | Intermolecular forces and properties | AP Chemistry | Khan Academy

Sat, 10 Oct 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:intermolecular-forces/v/dipole-dipole-forces

Uploaded 22-04-20

London dispersion forces result from the coulombic interactions between instantaneous dipoles. Dispersion forces are present between all molecules (and atoms) and are typically greater for heavier, more polarizable molecules and molecules with larger surface areas. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:intermolecular-forces/v/london-dispersion-forces

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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2011 Calculus AB free response #4d | AP Calculus AB | Khan Academy

Fri, 09 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-4d

Uploaded 09-09-11

Mean Value Theorem and differentiability. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-5a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-4c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
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Worked example: Calculating partial pressures | AP Chemistry | Khan Academy

Fri, 09 Oct 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:ideal-gas-law/e/ideal-gas-law

Uploaded 22-04-20

In a mixture of ideal gases, each gas behaves independently of the other gases. As a result, we can use the ideal gas law to calculate the partial pressure of each gas in the mixture. Once we know the partial pressures of all of the gases, we can sum them using Dalton's law to find the total pressure of the mixture. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:ideal-gas-law/v/partial-pressure

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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2011 Calculus AB free response #5a | AP Calculus AB | Khan Academy

Fri, 09 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-5a

Uploaded 09-09-11

Using a tangent line to extrapolate a function from a known initial condition. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-5b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-4d?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
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Worked example: Using the ideal gas law to calculate number of moles | AP Chemistry | Khan Academy

Fri, 09 Oct 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:ideal-gas-law/v/worked-example-using-the-ideal-gas-law-to-calculate-a-change-in-volume

Uploaded 22-04-20

The ideal gas law relates four macroscopic properties of ideal gases (pressure, volume, number of moles, and temperature). If we know the values of three of these properties, we can use the ideal gas law to solve for the fourth. In this video, we'll use the ideal gas law to solve for the number of moles (and ultimately molecules) in a sample of gas. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:ideal-gas-law/v/worked-example-using-the-ideal-gas-law-to-calculate-number-of-moles

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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2011 Calculus AB free response #5b | AP Calculus AB | Khan Academy

Fri, 09 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-5b

Uploaded 09-09-11

Using the second derivative to judge whether an approximation with the tangent line is an overestimate or underestimate. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-5c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-5a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
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Worked example: Using the ideal gas law to calculate a change in volume | Khan Academy

Fri, 09 Oct 2026 12:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:ideal-gas-law/v/introduction-to-partial-pressure

Uploaded 22-04-20

Want to explore more? Check out the full States of matter playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAcadC8xfE0VtGhfHdrECNO&si=aLyVfcDx3Xp257S6

The ideal gas law can be used to describe a change in state for an ideal gas. In this video, we'll apply the ideal gas law to the initial and final states of a gas to see how changes in temperature and pressure affect the volume of the gas. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:ideal-gas-law/v/worked-example-using-the-ideal-gas-law-to-calculate-a-change-in-volume

Sections:
00:00 - Problem setup: balloon and gas conditions
00:36 - Identifying use of ideal gas law
01:05 - Applying combined gas law
02:06 - Extracting variables from the problem
03:30 - Rearranging for final volume V₂
04:19 - Substituting known values into the equation
05:10 - Unit cancellation and calculation setup
05:48 - Solving and final answer in scientific notation
06:14 - Intuition check on the result

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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2011 Calculus AB free response #5c. | AP Calculus AB | Khan Academy

Fri, 09 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-5c

Uploaded 09-09-11

Solving a differential equation using separation of variables. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-6a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-5b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
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Tour of the Khan Academy student experience

Fri, 09 Oct 2026 08:06:00 -0000

What do students see when they log in to Khan Academy? Meaghan Pattani, who leads teacher education at Khan, walks Kim through what students see when they receive assignments, mastery goals, and mastery challenges.

Uploaded 22-04-20

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2011 Calculus AB free response #6a | AP Calculus AB | Khan Academy

Fri, 09 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-6a

Uploaded 12-09-11

Continuity of piecewise-defined functions. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-6b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-5c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Using similarity to estimate ratio between side lengths | High school geometry | Khan Academy

Fri, 09 Oct 2026 04:06:00 -0000

When two right triangles share an acute angle measure, the ratios of the corresponding side lengths within the triangles are equal.

Uploaded 21-04-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-ratios-in-right-triangles .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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2011 Calculus AB free response #6b | AP Calculus AB | Khan Academy

Fri, 09 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-6b

Uploaded 12-09-11

Derivative of a piecewise-defined function. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-6c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-6a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Determining congruent triangles example

Fri, 09 Oct 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/geometry/hs-geo-congruence/xff63fac4:hs-geo-congruent-triangles/v/congruent-triangles-and-sss

Uploaded 21-04-20

Determining congruent triangles example

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2011 Calculus AB free response #6c | AP Calculus AB | Khan Academy

Thu, 08 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-6c

Uploaded 12-09-11

Average value of a piecewise-defined function on an interval. Created by Sal Khan.

This is the last video in our AP Calculus AB subject! Now move on to our first video in AP Calculus BC: https://www.khanacademy.org/math/ap-calculus-bc/bc-limits-continuity/bc-about-the-course/v/khan-academy-in-the-classroom-bill-scott?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-6b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
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Using right triangle ratios to approximate angle measure | High school geometry | Khan Academy

Thu, 08 Oct 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/geometry/hs-geo-trig/xff63fac4:hs-geo-trig-ratios-similarity/e/use-ratios-in-right-triangles

Uploaded 21-04-20

Because of similarity, all right triangles with a given acute angle measure have equal ratios between their side lengths. So if we know two of the side lengths of a right triangle, we can figure out the angle measures, too!

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-ratios-in-right-triangles .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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2011 Calculus AB free response #1a | AP Calculus AB solved exams | AP Calculus AB | Khan Academy

Thu, 08 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-1a

Uploaded 12-09-11

Determining whether speed is increasing. Difference between speed and acceleration. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2011/v/2011-calculus-ab-free-response-1-parts-b-c-d?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams/ab-solved-exams-2015/v/2015-ap-calculus-ab-6c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
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Volume of pyramids intuition | Solid geometry | High school geometry | Khan Academy

Thu, 08 Oct 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/a/volume-of-a-pyramid-or-cone

Uploaded 21-04-20

The volume of a pyramid is a fraction of the volume of the rectangular prism that encloses it. We can find out what that fraction is by cutting a prism into several pyramids.

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-solids/hs-geo-cavalieri-s-principle .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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2011 Calculus BC free response #1a | AP Calculus BC solved exams | AP Calculus BC | Khan Academy

Thu, 08 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-solved-exams-new/ab-solved-exams-2011-new/v/2011-calculus-ab-free-response-1-parts-b-c-d

Uploaded 12-09-11

Velocity and acceleration vectors for particle. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-1-b-c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2015/v/2015-ap-calculus-bc-6c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
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Similar shapes and transformations

Thu, 08 Oct 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-similarity-definitions/e/exploring-angle-preserving-transformations-and-similarity

Uploaded 21-04-20

Given a pair of polygons, reason about whether or not they are similar in terms of rigid transformations and dilations.

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2011 Calculus BC free response #1 (b and c) | AP Calculus BC | Khan Academy

Thu, 08 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams-new/bc-solved-exams-2011-new/v/2011-calculus-bc-free-response-1-b-c

Uploaded 12-09-11

Position and slope of particle's path at a given time. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-1d?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-1a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
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US taxation trends in post war era | Macroeconomics | Khan Academy

Thu, 08 Oct 2026 08:06:00 -0000

US taxation trends in the post war era.

View more lessons or practice this subject at https://www.khanacademy.org/economics....

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Uploaded 16-04-20

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?ut...

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2011 Calculus BC free response #1d | AP Calculus BC | Khan Academy

Thu, 08 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams-new/bc-solved-exams-2011-new/v/2011-calculus-bc-free-response-1d

Uploaded 12-09-11

Arc length for a curve. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-3a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-1-b-c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
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Representing solids, liquids, and gases using particulate models | AP Chemistry | Khan Academy

Thu, 08 Oct 2026 04:06:00 -0000

In this video, we'll learn how to represent solids, liquids, and gases using particulate models. The particles in a solid are either highly ordered (if the solid is crystalline) or have no regular arrangement (if the solid is amorphous). In both cases, the motion of the particles is limited. The particles in a liquid are close together and are constantly moving and colliding. Finally, the particles in a gas are generally well-separated and are in constant, random motion. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:solids-liquids-and-gases/v/representing-solids-liquids-and-gases-using-particulate-models

Uploaded 15-04-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Bacterial meningitis | Miscellaneous | Heatlh and Medicine | Khan Academy

Thu, 08 Oct 2026 02:06:00 -0000

Dr. Charles Prober discusses prudent prescribing of antibiotics in the context of bacterial meningitis with 4th year medical student Morgan Theis. Created by Sal Khan.

Uploaded 12-09-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/ritual-of-the-bedside-exam?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/childhood-growth?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Per capita GDP trends over past 70 years | Macroeconomics | Khan Academy

Thu, 08 Oct 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/macroeconomics/macroeconomics-income-inequality/xba99f16dd99e6fe4:analysis-of-income-inequality-in-the-united-states/v/us-taxation-trends-in-post-war-era

Uploaded 15-04-20

Analysis of how well average inflation-adjusted after-tax income for the bottom 90% has tracked per capita GDP over the past 70 years.

View more lessons or practice this subject at https://www.khanacademy.org/economics-finance-domain/macroeconomics.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Precocious puberty | Miscellaneous | Heatlh and Medicine | Khan Academy

Wed, 07 Oct 2026 22:06:00 -0000

At Stanford Medical School with Morgan Theis talking to Dr. Laura Bachrach talking about precocious puberty. Created by Sal Khan.

Uploaded 12-09-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/childhood-growth?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/cervical-spine-protection-in-airway-management-not-a-substitute-for-formal-training?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Quick guide to the 2020 AP US History exam | AP US History | Khan Academy

Wed, 07 Oct 2026 20:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/humanities/ap-us-history/general-ap-us-history-skills-and-test-strategies/xb87a304a:apush-2020/v/quick-guide-to-the-2020-ap-us-history-exam

Uploaded 15-04-20

What's different in the 2020 AP US History test? Kim Kutz Elliott walks you through what to expect with the new exam format and scoring.

If you or a student you know needs help getting access to the technology they need to complete the online test, fill out the College Board's form here: https://collegeboard.tfaforms.net/74

If you'd like to check out the College Board's updated scoring rubric for the 2020 DBQ, you can find it here: https://apcentral.collegeboard.org/pdf/ap-history-rubric-2020-dbq.pdf

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Childhood growth | Miscellaneous | Heatlh and Medicine | Khan Academy

Wed, 07 Oct 2026 18:06:00 -0000

Sal talks with Dr. Laura Bachrach about childhood growth. Created by Sal Khan.

Uploaded 12-09-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/bacterial-meningitis?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/precocious-puberty?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Comparing income trends across countries | Macroeconomics | Khan Academy

Wed, 07 Oct 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/macroeconomics/macroeconomics-income-inequality/xba99f16dd99e6fe4:analysis-of-income-inequality-in-the-united-states/v/per-capita-gdp-trends-over-past-70-years

Uploaded 14-04-20

Analyzing charts from New York Times to compare income trends across several countries over a 30 year time period.

View more lessons or practice this subject at https://www.khanacademy.org/economics-finance-domain/macroeconomics.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Ritual of the bedside exam | Miscellaneous | Heatlh and Medicine | Khan Academy

Wed, 07 Oct 2026 14:06:00 -0000

Dr. Abraham Verghese explains the ritual of the bedside exam. Created by Sal Khan.

Uploaded 12-09-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/systemic-thinking-about-cancer?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/bacterial-meningitis?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Looking at trends in inflation adjusted income since 1980 | Khan Academy

Wed, 07 Oct 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/economics-finance-domain/macroeconomics/macroeconomics-income-inequality/xba99f16dd99e6fe4:analysis-of-income-inequality-in-the-united-states/v/comparing-income-trends-across-countries

Uploaded 14-04-20

Leveraging a diagram from the New York Times to look at trends in inflation adjusted income since 1980. Discussion of possible levers that could be driving the trends.

View more lessons or practice this subject at https://www.khanacademy.org/economics-finance-domain/macroeconomics.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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School Leadership Briefing (Sep 12 2011)

Wed, 07 Oct 2026 10:06:00 -0000

Sal answers questions for School Leadership Briefing

Uploaded 13-09-11

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The elements of a story | Reading | Khan Academy

Wed, 07 Oct 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-the-moon/xfb4fc0bf01437792:close-reading-fiction/v/a-storys-point-of-view-reading

Uploaded 10-04-20

Did you know that many stories have a shape? Let's discuss what that means as we explore the parts of a story.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions:
"Street Dancing" by Timecrawler 82 is licensed under a Creative Commons Attribution License, and can be found here: https://freemusicarchive.org/music/Timecrawler_82/Osaka_Lights/Street_Dancing

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School Leadership Briefing Questions (Sep 12 2011) 2

Wed, 07 Oct 2026 06:06:00 -0000

More answers for School Leadership Briefing

Uploaded 13-09-11

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Molecular solids | Intermolecular forces and properties | AP Chemistry | Khan Academy

Wed, 07 Oct 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:properties-of-solids/v/covalent-network-solids

Uploaded 09-04-20

Molecular solids are composed of discrete molecules held together by intermolecular forces. Because these interactions are relatively weak, molecular solids tend to be soft and have low to moderate melting points. Molecular solids are also poor conductors of electricity because their valence electrons are tightly held within each individual molecule. View more lessons or practice this subject at https://www.khanacademy.org/science/chemistry/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:properties-of-solids/v/molecular-solids

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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2011 Calculus BC free response #3a | AP Calculus BC | Khan Academy

Wed, 07 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams-new/bc-solved-exams-2011-new/v/2011-calculus-bc-free-response-3a

Uploaded 13-09-11

Arc length of a function. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-3-b-c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-1d?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Covalent network solids | Intermolecular forces and properties | AP Chemistry | Khan Academy

Wed, 07 Oct 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:properties-of-solids/e/properties-of-solids

Uploaded 09-04-20

Covalent network solids are composed of atoms covalently bonded together into a three-dimensional network or layers of two-dimensional networks. Due to the strength of the covalent bonds, covalent network solids tend to have high melting points. Three-dimensional network solids (such as diamond or silica) are typically hard and rigid, whereas two-dimensional network solids (such as graphite) are much softer due to the ease with which the network layers can slide past each other. View more lessons or practice this subject at https://www.khanacademy.org/science/chemistry/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:properties-of-solids/v/covalent-network-solids

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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2011 Calculus BC free response #3 (b and c) | AP Calculus BC | Khan Academy

Tue, 06 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams-new/bc-solved-exams-2011-new/v/2011-calculus-bc-free-response-3-b-c

Uploaded 13-09-11

Volume of a solid of rotation and Chain Rule for rates of change. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-6a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-3a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy learning plans for school closures

Tue, 06 Oct 2026 20:06:00 -0000

Math learning plans (grades 3-8 + Algebra I, Geometry and Algebra II):
3rd grade learning plan (https://bit.ly/KA-3-LearningPlan)
4th grade learning plan (https://bit.ly/KA-4-LearningPlan)
5th grade learning plan (https://bit.ly/KA-5-LearningPlan)
6th grade learning plan (https://bit.ly/KA-6-LearningPlan)
7th grade learning plan (https://bit.ly/KA-7-LearningPlan)
8th grade learning plan (https://bit.ly/KA-8-LearningPlan)
Geometry learning plan (https://bit.ly/KA-Geometry-LearningPlan)
Algebra 1 learning plan (https://bit.ly/KA-Algebra1-LearningPlan)
Algebra 2 learning plan (https://bit.ly/KA-Algebra2-LearingPlan)

Uploaded 08-04-20

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2011 Calculus BC free response #6a | AP Calculus BC | Khan Academy

Tue, 06 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams-new/bc-solved-exams-2011-new/v/2011-calculus-bc-free-response-6a

Uploaded 13-09-11

Taylor Series approximation of sin(x). Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-6b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-3-b-c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
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Understanding theme | Reading | Khan Academy

Tue, 06 Oct 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-3rd-reading-vocab/xaf0c1b5d7010608e:cc-3rd-extreme-environments/xaf0c1b5d7010608e:extreme-environments-close-reading-fiction/v/characters-thoughts-and-feelings-reading

Uploaded 06-04-20

A theme is an important idea that is woven throughout a story. It’s not the plot or the summary, but something a little deeper. A theme links a big idea about our world with the action of a text.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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2011 Calculus BC free response #6b | AP Calculus BC | Khan Academy

Tue, 06 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/old-ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-6b

Uploaded 14-09-11

Taylor Series for cos x at x=0. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-6c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-6a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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For parents: Setting a daily learning schedule for middle school students

Tue, 06 Oct 2026 12:06:00 -0000

Parents, are you wondering how to structure a day of learning and fun for your middle school student? We’ll walk you through a sample daily schedule and give you suggestions on ways to adapt it for your family. We’ll also take a closer look at ways you can find relevant content on Khan Academy to support your child's learning.

Uploaded 06-04-20

Get the slides here: khan.co/MiddleSchoolWebinarSlides

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2011 Calculus BC free response #6c | AP Calculus BC | Khan Academy

Tue, 06 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/old-ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-6c

Uploaded 14-09-11

Calculating the 6th derivative at 0 from the Taylor Series approximation. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-6d?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-6b?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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For parents: Setting a daily learning schedule for elementary school students

Tue, 06 Oct 2026 08:06:00 -0000

Parents, are you wondering how to structure a day of learning and fun for your elementary school student? We’ll walk you through a sample daily schedule and give you suggestions on ways to adapt it for your family. We’ll also take a closer look at ways you can find relevant content on Khan Academy to support your child's learning.

Uploaded 03-04-20

Get the slides here: http://khan.co/ElementaryWebinarSlides

And get our daily schedules and many more resources for remote learning here:
https://keeplearning.khanacademy.org/

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Brainwave Sep 2011

Tue, 06 Oct 2026 06:06:00 -0000

Sal answers questions for Brainwave Magazine

Uploaded 14-09-11

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Character actions in stories | Reading | Khan Academy

Tue, 06 Oct 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-fairy-tales-retold/xfb4fc0bf01437792:close-reading-little-red-riding-hood/v/what-do-pictures-bring-to-a-story-reading

Uploaded 03-04-20

Sound the Horn of Action, because today we’re going to be talking about character actions in stories. Understanding what characters do is key to your success as a reader. The way characters behave, towards themselves, towards others, towards objects, can tell us a lot about them—and can give us clues to the larger messages in a story.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Attributions:

"Tuohitorvi" (a Finnish hunting horn) Licensed under an attribution license: https://freesound.org/people/juskiddink/sounds/166067/

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Taylor polynomial remainder (part 1) | Series | AP Calculus BC | Khan Academy

Tue, 06 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-12/v/error-or-remainder-of-a-taylor-polynomial-approximation

Uploaded 15-09-11

The more terms we have in a Taylor polynomial approximation of a function, the closer we get to the function. But HOW close? Let's embark on a journey to find a bound for the error of a Taylor polynomial approximation. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-taylor-series/v/proof-bounding-the-error-or-remainder-of-a-taylor-polynomial-approximation?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-taylor-series/v/fourth-degree-coefficient-for-taylor-polynomial?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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For parents: setting a daily learning schedule for learners ages 2-7

Tue, 06 Oct 2026 00:06:00 -0000

Parents, are you wondering how to structure a day of learning and fun for your young children? We’ll walk you through a sample daily schedule and give you suggestions on ways to adapt it for your family. We’ll also take a closer look at the Khan Academy Kids app and explain how you can use the app to support your child’s learning.

Uploaded 02-04-20

Get the slides here: http://khan.co/KhanKidsWebinar2Handout

Learn more about Khan Academy Kids, our free educational app for children ages 2-7 at http://www.khankids.org.

Download now!
http://khan.co/KhanKids-YT-Google
http://khan.co/KhanKids-YT-Apple
http://khan.co/KhanKids-YT-Amazon

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Taylor polynomial remainder (part 2) | Series | AP Calculus BC | Khan Academy

Mon, 05 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-12/v/proof-bounding-the-error-or-remainder-of-a-taylor-polynomial-approximation

Uploaded 15-09-11

The more terms we have in a Taylor polynomial approximation of a function, the closer we get to the function. But HOW close? In this video, we prove the Lagrange error bound for Taylor polynomials. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-taylor-series/v/lagrange-error-bound-for-sine-function?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-taylor-series/v/error-or-remainder-of-a-taylor-polynomial-approximation?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Messages and morals | Reading | Khan Academy

Mon, 05 Oct 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-fairy-tales-retold/xfb4fc0bf01437792:close-reading-little-red-riding-hood/v/character-actions-in-stories-reading

Uploaded 30-03-20

Morals are lessons about how to treat other people. Many stories have these lessons embedded in them. Let's learn how to dig them out!

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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2011 Calculus BC free response #6d | AP Calculus BC | Khan Academy

Mon, 05 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams-new/bc-solved-exams-2011-new/v/2011-calculus-bc-free-response-6d

Uploaded 15-09-11

Lagrange error bound for Taylor Polynomial approximation. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2008/v/ap-calculus-bc-exams-2008-1-a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2011/v/2011-calculus-bc-free-response-6c?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Characters' thoughts and feelings | Reading | Khan Academy

Mon, 05 Oct 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-fairy-tales-retold/xfb4fc0bf01437792:close-reading/v/a-storys-point-of-view-reading

Uploaded 30-03-20

Understanding the thoughts and emotions of characters in a story: it's essentially mind-reading, and it's just as magical!

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

“Walk That Dog” by U.S. Army Blues is licensed under a Public Domain license.
“A Nice Life” by Ketsa is licensed with permission from the Independent Music Licensing Collective - imlcollective.uk

"Rain, Moderate, C.wav" by InspectorJ (www.jshaw.co.uk) of Freesound.org

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Center for Future of Museums

Mon, 05 Oct 2026 14:06:00 -0000

Sal answers questions for magazine (Sep 2011)

Uploaded 15-09-11

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Khan Academy request for donations

Mon, 05 Oct 2026 12:06:00 -0000

http://khanacademy.org/donate

Khan Academy is a non profit organization supported by philanthropic donations. We are able to create interactive software, exercises, videos and articles for the world, for free because of this support. But we were already running at a deficit before the COVID-19 crisis and now our server load is 2.5x normal (approaching 100m learning minutes on Khan Academy *per day*). Please think about donating at http://khanacademy.org/donate

Uploaded 27-03-20

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Interpreting futures fair value in the premarket | Finance and Capital Markets | Khan Academy

Mon, 05 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/interpretting-futures-fair-value-in-the-premarket

Uploaded 16-09-11

How to interpret the market price of a futures contract relative to the fair value in the premarket. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/mort-backed-secs-tut/v/mortgage-back-security-overview?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/futures-fair-value-in-the-pre-market?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: In many commodities markets, it is very helpful for buyers or sellers to lock-in future prices. This is what both forwards and futures allow for. This tutorial explains how they work and what the difference is between the two.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Summarizing informational text | Reading | Khan Academy

Mon, 05 Oct 2026 08:06:00 -0000

Summaries are retellings of texts. Let's explore how they work for informational texts!

Uploaded 27-03-20

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-3rd-reading-vocab/xaf0c1b5d7010608e:cc-3rd-extreme-environments/xaf0c1b5d7010608e:extreme-environments-close-reading-informational/v/cause-and-effect-reading

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Interest rate swap 1 | Finance and Capital Markets | Khan Academy

Mon, 05 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/interest-rate-swaps-tut/v/interest-rate-swap-1

Uploaded 16-09-11

The basic dynamic of an interest rate swap. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/interest-rate-swaps-tut/v/interest-rate-swap-2?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/credit-default-swaps-tut/v/financial-weapons-of-mass-destruction?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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What language shows cause and effect? | Reading | Khan Academy

Mon, 05 Oct 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-3rd-reading-vocab/xaf0c1b5d7010608e:cc-3rd-extreme-environments/xaf0c1b5d7010608e:extreme-environments-close-reading-informational/v/interpreting-text-features-reading

Uploaded 27-03-20

Let's use the wacky inventions of Rube Goldberg to explore cause and effect relationships in nonfiction writing!

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Credits:

Rube Goldberg's 1931 cartoon is in the public domain:
https://commons.wikimedia.org/wiki/File:Self-operating_napkin_(Rube_Goldberg_cartoon_with_caption).jpg

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Interest rate swap 2 | Finance and Capital Markets | Khan Academy

Mon, 05 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/interest-rate-swaps-tut/v/interest-rate-swap-2

Uploaded 16-09-11

Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/black-scholes/v/introduction-to-the-black-scholes-formula?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/interest-rate-swaps-tut/v/interest-rate-swap-1?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Relationships between scientific ideas in a text | Reading | Khan Academy

Mon, 05 Oct 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-the-moon/xfb4fc0bf01437792:close-reading-informational-text/v/interpreting-text-features-reading

Uploaded 27-03-20

David illustrates how ideas connect to each other in a scientific nonfiction text, using the story of Mexican chemist and Nobel laureate Mario Molina.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Credits:

"Air Hockey Saloon" by Chris Zabriskie, licensed under a Creative Commons Attribution License: https://freemusicarchive.org/music/Chris_Zabriskie/Vendaface/05_-_Air_Hockey_Saloon

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Partial quotient method of division | Multiplication and division | Arithmetic | Khan Academy

Sun, 04 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/arithmetic-home/multiply-divide/mult-digit-div-2/v/partial-quotient-division

Uploaded 19-09-11

An alternate to traditional long division

Watch the next lesson: https://www.khanacademy.org/math/arithmetic/multiplication-division/partial_quotient_division/v/partial-quotient-method-of-division-2?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic

Missed the previous lesson?
https://www.khanacademy.org/math/arithmetic/multiplication-division/lattice_multiplication/v/why-lattice-multiplication-works?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic

Arithmetic on Khan Academy: So you're ready to have some arithmetic fun? You've come to the right spot! It's the first "official" math topic and chalked full of fun exercises and great videos which help you start your journey towards math mastery. We'll cover the big ones: addition, subtraction, multiplication, and division, of course. But we don't stop there. We'll get into negative numbers, absolute value, decimals, and fractions, too. Learning math should be fun, and we plan on having some with you. Ready to get started?

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Arithmetic channel: https://www.youtube.com/channel/UCFlJkgTNeC-FYYIQnyE5yzQ?sub_confirmation=1
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What is a main idea? | Reading | Khan Academy

Sun, 04 Oct 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-the-moon/xfb4fc0bf01437792:close-reading-informational-text/v/relationships-between-scientific-ideas-in-a-text-reading

Uploaded 27-03-20

In this video, we'll discuss the main idea of a text: the key information the author wants you to understand.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Credits:

Sound effects licensed under a Creative Commons 0 License:
https://freesound.org/people/bajko/sounds/385279/

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Partial quotient method of division 2 | Multiplication and division | Arithmetic | Khan Academy

Sun, 04 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/arithmetic-home/multiply-divide/mult-digit-div-2/v/partial-quotient-division

Uploaded 19-09-11

Another example of doing long division using the partial quotient method

Watch the next lesson: https://www.khanacademy.org/math/arithmetic/multiplication-division/advanced-mult-div-word-problems/v/multi-step-word-problems-with-whole-numbers-exercise-1?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic

Missed the previous lesson?
https://www.khanacademy.org/math/arithmetic/multiplication-division/partial_quotient_division/v/partial-quotient-division?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic

Arithmetic on Khan Academy: So you're ready to have some arithmetic fun? You've come to the right spot! It's the first "official" math topic and chalked full of fun exercises and great videos which help you start your journey towards math mastery. We'll cover the big ones: addition, subtraction, multiplication, and division, of course. But we don't stop there. We'll get into negative numbers, absolute value, decimals, and fractions, too. Learning math should be fun, and we plan on having some with you. Ready to get started?

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Arithmetic channel: https://www.youtube.com/channel/UCFlJkgTNeC-FYYIQnyE5yzQ?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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First and secondhand accounts | Reading | Khan Academy

Sun, 04 Oct 2026 16:06:00 -0000

What's the difference between a firsthand account and a secondhand account? What's the difference between a story of an event that's told by someone who was there, and one told by someone who wasn't there?

Uploaded 27-03-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Inverse property of addition | Arithmetic properties | Pre-Algebra | Khan Academy

Sun, 04 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/in-class-8-math-foundation/x5ee0e3519fe698ad:rational-numbers/x5ee0e3519fe698ad:additive-and-multiplicative-inverse/v/inverse-property-of-addition

Uploaded 20-09-11

The simple idea that a number plus its negative is 0

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/order-of-operations/arithmetic_properties/v/inverse-property-of-multiplication?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson? https://www.khanacademy.org/math/pre-algebra/order-of-operations/arithmetic_properties/v/identity-property-of-0?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Reading more than one source on a topic | Reading | Khan Academy

Sun, 04 Oct 2026 12:06:00 -0000

Why is it important to read more than one text about a topic? We'll give you three reasons!

Uploaded 27-03-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Inverse property of multiplication | Arithmetic properties | Pre-Algebra | Khan Academy

Sun, 04 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/in-class-8-math-foundation/x5ee0e3519fe698ad:rational-numbers/x5ee0e3519fe698ad:additive-and-multiplicative-inverse/v/inverse-property-of-multiplication

Uploaded 20-09-11

Simple idea that multiplying by a numbers multiplicative inverse gets you back to one

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/order-of-operations/arithmetic_properties/v/properties-of-numbers-2?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson? https://www.khanacademy.org/math/pre-algebra/order-of-operations/arithmetic_properties/v/inverse-property-of-addition?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Looking back at the text for evidence | Reading | Khan Academy

Sun, 04 Oct 2026 08:06:00 -0000

Evidence is factual information that helps you know if something's true. It's proof! Learn how to back up your claims, whether you're talking about cookies, laws, or Voltron.

Uploaded 27-03-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Credits:

Courthouse Lobby Ambience licensed under a Creative Commons Attribution License: https://freesound.org/people/Tomlija/sounds/101237/

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Basic Language and Notation of Geometry

Sun, 04 Oct 2026 06:06:00 -0000

Lines, line segments, rays and points. A little bit about dimensions

Uploaded 20-09-11

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Interpreting text features | Reading | Khan Academy

Sun, 04 Oct 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-the-moon/xfb4fc0bf01437792:close-reading-informational-text/v/finding-connections-between-ideas-reading

Uploaded 27-03-20

Let's talk about charts, maps, images, timelines, and other features of a passage that aren't just the words! They're just as important to comprehending a text as the words themselves.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Language and notation of the circle | Introduction to Euclidean geometry | Geometry | Khan Academy

Sun, 04 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-circle-basics/v/language-and-notation-of-the-circle

Uploaded 20-09-11

Formal definition of a circle. Tangent and secant lines. Diameters and radii. major and minor arcs

Watch the next lesson: https://www.khanacademy.org/math/geometry/intro_euclid/v/the-golden-ratio?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/intro_euclid/v/geometric-precision-practice?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Summarizing stories | Reading | Khan Academy

Sun, 04 Oct 2026 00:06:00 -0000

Using the example of the Three Little Pigs, let's explore how to summarize stories!

Uploaded 27-03-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Angle basics | Angles and intersecting lines | Geometry | Khan Academy

Sat, 03 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-angles/v/angle-basics

Uploaded 21-09-11

The naming of an angle is related to the line segments that create it. We'll also learn about the angle's vertex. Come on. Let's do this.

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/measuring-angles-in-degrees?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/intro_euclid/v/identifying-ray?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Finding connections between ideas within a passage | Reading | Khan Academy

Sat, 03 Oct 2026 20:06:00 -0000

How are ideas connected to each other in a text? What do sentences in a paragraph have in common with one another? Let's learn together.

Uploaded 27-03-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Measuring angles using a protractor | Angles and intersecting lines | Geometry | Khan Academy

Sat, 03 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-fourth-grade-math/imp-geometry-2/imp-measuring-angles/v/using-a-protractor

Uploaded 21-09-11

Let's use our virtual protractor to measure some angles together, shall we?

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/measuring-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/measuring-angles-in-degrees?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Making inferences in literary texts | Reading | Khan Academy

Sat, 03 Oct 2026 16:06:00 -0000

What does it look like to make inferences from a story? Sherlock Bones, the legendary dogtective, will show us!

Uploaded 27-03-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Credits:
"Bach - Brandenburg Concerto no3 mvt3 allegro" licensed under a Creative Commons ShareAlike license:
https://freemusicarchive.org/music/Advent_Chamber_Orchestra/Selections_from_the_2005-2006_Season

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Measuring angles in degrees | Angles and intersecting lines | Geometry | Khan Academy

Sat, 03 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-fourth-grade-math/imp-geometry-2/imp-measuring-angles/v/measuring-angles-in-degrees

Uploaded 21-09-11

Let's come up with an exact way to measure an angle using a protractor. We'll also learn about acute angles. Not to be confused with augly angles :)

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/using-a-protractor?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/angle-basics?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Using context clues to figure out new words | Reading | Khan Academy

Sat, 03 Oct 2026 12:06:00 -0000

When you're reading, it can be frustrating to encounter words you don't know! Try out these strategies, and use the word's context to figure out the word's meaning.

Uploaded 27-03-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Complementary and supplementary angles | Angles and intersecting lines | Geometry | Khan Academy

Sat, 03 Oct 2026 10:06:00 -0000

Let's add some tools to our geometry tool belt. Here's a thorough explanation of complementary and supplementary angles, as well as definitions of adjacent and straight angles.

Uploaded 21-09-11

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/complementary-supplementary-angl/e/complementary_and_supplementary_angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/complementary-supplementary-angl/v/example-using-algebra-to-find-measure-of-complementary-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/old_angles/v/acute-right-and-obtuse-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Making inferences in informational texts | Reading | Khan Academy

Sat, 03 Oct 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/ela/cc-2nd-reading-vocab/xfb4fc0bf01437792:cc-2nd-rural-suburban-urban/xfb4fc0bf01437792:rural-suburban-urban-reading-for-understanding-informational/v/finding-connections-between-ideas-reading

Uploaded 27-03-20

Inferences: they're not guesses. They're conclusions that you draw from the text. What predictions or connections can you make, based on what's in front of you?

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Credits:

Music: "Horrible" by Mela off the album Mela Two is licensed under an attribution-sharealike license: https://freemusicarchive.org/music/Mela/Mela_two/MELA_-_Mela_Two_-_03_Horrible

Sound effects:

"Rain, Moderate, C.wav" by InspectorJ (www.jshaw.co.uk) of Freesound.org
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Some sound effects used under a Creative Commons 0 License

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Introduction to vertical angles | Angles and intersecting lines | Geometry | Khan Academy

Sat, 03 Oct 2026 06:06:00 -0000

By using our knowledge of supplementary, adjacent, and vertical angles, we can solve problems involving the intersection of two lines, including this one!

Uploaded 21-09-11

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/e/vertical_angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/using-algebra-to-find-the-measures-of-vertical-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/angle-measurement-and-circle-arcs?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Groups influencing policy outcomes | AP US Government and Politics | Khan Academy

Sat, 03 Oct 2026 04:06:00 -0000

How do political actors influence outcomes? In this video, Kim Kutz Elliott discusses when and how political parties, interest groups, bureaucratic agencies, and social movements may attempt to influence the policy process.

Uploaded 26-03-20

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Proof: Vertical angles are equal | Angles and intersecting lines | Geometry | Khan Academy

Sat, 03 Oct 2026 02:06:00 -0000

Proving that vertical angles are equal

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/e/congruent_angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/angles-formed-by-parallel-lines-and-transversals?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/using-algebra-to-find-the-measures-of-vertical-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

Uploaded 21-09-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Getting started with Khan Academy Kids

Sat, 03 Oct 2026 00:06:00 -0000

Khan Academy Kids is an award-winning educational app for young learners ages two to seven. Watch this video to learn how to set up an account for your child and have them start learning. It’s quick and easy, and will take no more than a few minutes.

Uploaded 20-03-20

Head over to our newly created Khan Kids channel on YouTube at
https://www.youtube.com/channel/UC2ri4rEb8abnNwXvTjg5ARw

Khan Academy Kids is available on iPhone, iPad, Google Play, and Amazon. It’s 100% free—no ads, no subscriptions.

Download now!
http://khan.co/YTKhanKids-AppleStore
http://khan.co/YTKhanKids-GooglePlay
http://khan.co/YTKhanKids-Amazon

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Angles formed by parallel lines and transversals | Geometry | Khan Academy

Fri, 02 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/v/angles-formed-by-parallel-lines-and-transversals

Uploaded 21-09-11

Parallel lines, transversal lines, corresponding angles

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/e/congruent_angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/identifying-parallel-and-perpendicular-lines?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/ang_intro/v/proof-vertical-angles-are-equal?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Getting Started with Khan Academy and Khan Academy Kids for Remote Learning

Fri, 02 Oct 2026 20:06:00 -0000

Parents, are you curious about how to use Khan Academy and Khan Academy Kids for remote learning?

Uploaded 18-03-20

Join us as we'll walk you through:
- Setting your kids set up for learning with Khan Academy and Khan Academy Kids
- Finding relevant content for them to learn

You can view the slide deck here:
http://khan.co/parent-quick-start-slides

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Proof - Sum of Measures of Angles in a Triangle are 180

Fri, 02 Oct 2026 18:06:00 -0000

Proof that the sum of the measures of the angles in a triangle are 180

Uploaded 22-09-11

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A message from Sal on school closures and remote learning on Khan Academy.

Fri, 02 Oct 2026 16:06:00 -0000

For more information visit: http://khan.co/KA-remote

Join Sal daily on YouTube Live at 9 am PT, where he will answer questions from teachers, parents, and students.

Uploaded 18-03-20

Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. If you’d like to contribute, please visit: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=live&utm_campaign=schoolclosers

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Triangle angle example 1 | Angles and intersecting lines | Geometry | Khan Academy

Fri, 02 Oct 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/triangle-angle-example-1

Uploaded 22-09-11

Figuring out angles in a triangle. A little about exterior angles being the sum of the remote interior angles

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/triangle-angle-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/proof-sum-of-measures-of-angles-in-a-triangle-are-180?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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How Khan Academy is Here to Help During COVID-19

Fri, 02 Oct 2026 12:06:00 -0000

Our latest resources for parents, teachers, and students about remote learning during school closures: http://khan.co/KA-remote
🌎 If YouTube does not allow donations from your country, please go to: https://www.khanacademy.org/donate

Uploaded 15-03-20

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Triangle angle example 2 | Angles and intersecting lines | Geometry | Khan Academy

Fri, 02 Oct 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/triangle-angle-example-1

Uploaded 22-09-11

Another example finding angles in triangles

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/triangle-angle-example-3?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/triangle-angle-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Estimating actual COVID 19 cases (novel corona virus infections) in an area based on deaths

Fri, 02 Oct 2026 08:06:00 -0000

Estimating actual COVID 19 cases (novel corona virus infections) in an area based on deaths. Based on work by Tomas Pueyo at:

Uploaded 14-03-20

https://medium.com/@tomaspueyo/coronavirus-act-today-or-people-will-die-f4d3d9cd99ca

Data from:
https://github.com/midas-network/COVID-19/tree/master/parameter_estimates/2019_novel_coronavirus

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Proof: Corresponding angle equivalence implies parallel lines | Geometry | Khan Academy

Fri, 02 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-angles/geometry-angles-between-lines/v/proof-corresponding-angle-equivalence-implies-parallel-lines

Uploaded 22-09-11

Proof by contradiction that corresponding angle equivalence implies parallel lines

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/finding-more-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/challenging-triangle-angle-problem?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Policy and the branches of government | AP US Government and Politics | Khan Academy

Fri, 02 Oct 2026 04:06:00 -0000

How can the other branches of government hold the bureaucracy accountable? In this video, Kim Kutz Elliott uses the response to the 2014 VA scandal as a case study.

Uploaded 13-03-20

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Finding more angles | Angles and intersecting lines | Geometry | Khan Academy

Fri, 02 Oct 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-triangle-angles/v/finding-more-angles

Uploaded 22-09-11

Example of angle hunting!

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/e/angles_1?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/sum-of-interior-angles-of-a-polygon?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/proof-corresponding-angle-equivalence-implies-parallel-lines?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Ideology and policymaking | AP US Government and Politics | Khan Academy

Fri, 02 Oct 2026 00:06:00 -0000

Why does public policy change over time? In this video, Kim Kutz Elliott discusses how public policies generated at any given
time reflect the attitudes and beliefs of citizens
who choose to participate in politics at that time.

Uploaded 12-03-20

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Triangle angle example 3 | Angles and intersecting lines | Geometry | Khan Academy

Thu, 01 Oct 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-triangle-angles/v/triangle-angle-example-3

Uploaded 22-09-11

Multiple ways to solve for the angles of multiple triangles

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/challenging-triangle-angle-problem?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/triangle-angle-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Metallic solids | Intermolecular forces and properties | AP Chemistry | Khan Academy

Thu, 01 Oct 2026 20:06:00 -0000

Metallic solids are composed of metal cations held together by a delocalized "sea" of valence electrons. Because their electrons are mobile, metallic solids are good conductors of heat and electricity. Metallic solids also tend to be malleable and ductile due to the ability of the metal nuclei to move past each other without disrupting the bonding. View more lessons or practice this subject at https://www.khanacademy.org/science/chemistry/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:properties-of-solids/v/metallic-solids

Uploaded 11-03-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Challenging triangle angle problem | Angles and intersecting lines | Geometry | Khan Academy

Thu, 01 Oct 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-triangle-angles/v/challenging-triangle-angle-problem

Uploaded 22-09-11

Interesting problem finding the sums of particular exterior angles of an irregular pentagon

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/proof-corresponding-angle-equivalence-implies-parallel-lines?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/triangle-angle-example-3?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Ionic solids | Intermolecular forces and properties | AP Chemistry | Khan Academy

Thu, 01 Oct 2026 16:06:00 -0000

Ionic solids are composed of cations and anions held together by electrostatic forces. Due to the strength of these interactions, ionic solids tend to be hard, brittle and have high melting points. Ionic solids are poor conductors of electricity except when their ions are mobile, such as when a solid is melted or dissolved in solution. View more lessons or practice this subject at https://www.khanacademy.org/science/chemistry/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:properties-of-solids/v/ionic-solids

Uploaded 09-03-20

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Sum of Interior Angles of Any Polygon

Thu, 01 Oct 2026 14:06:00 -0000

Showing a generalized way to find the sum of the interior angles of any polygon

Uploaded 22-09-11

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Information for congruency

Thu, 01 Oct 2026 12:06:00 -0000

Information for congruency

Uploaded 06-03-20

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Congruent triangles and SSS | Congruence | Geometry | Khan Academy

Thu, 01 Oct 2026 10:06:00 -0000

What it means for triangles to be congruent

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/sss-to-show-a-radius-is-perpendicular-to-a-chord-that-it-bisects?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/transformations-congruence/v/another-example-of-rigid-transformations-for-congruence?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

Uploaded 23-09-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Non-congruent shapes and transformations

Thu, 01 Oct 2026 08:06:00 -0000

A student reasons about whether a pair of circles are congruent by trying to map one onto the other using rigid transformations.

Uploaded 06-03-20

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SSS to show a radius is perpendicular to a chord that it bisects | Geometry | Khan Academy

Thu, 01 Oct 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-circles/xff63fac4:hs-geo-proofs-with-inscribed-shapes/v/sss-to-show-a-radius-is-perpendicular-to-a-chord-that-it-bisects

Uploaded 23-09-11

More on the difference between a theorem and axiom. Proving a cool result using SSS

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/other-triangle-congruence-postulates?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/congruent-triangles-and-sss?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Dilating triangles: find the error | Performing transformations | Geometry | Khan Academy

Thu, 01 Oct 2026 04:06:00 -0000

Dilating doesn't just shrink or grow a figure. The scale factor also changes the distance from each point to the center of dilation.

Uploaded 05-03-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Proving the ASA and AAS triangle congruence criteria using transformations | Geometry | Khan Academy

Thu, 01 Oct 2026 00:06:00 -0000

We can prove the angle-side-angle (ASA) and angle-angle-side (AAS) triangle congruence criteria using the rigid transformation definition of congruence.

Uploaded 05-03-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Two column proof showing segments are perpendicular | Congruence | Geometry | Khan Academy

Wed, 30 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-quadrilaterals-theorems/v/two-column-proof-showing-segments-are-perpendicular

Uploaded 23-09-11

Using triangle congruency postulates to show that two intersecting segments are perpendicular

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/finding-congruent-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/other-triangle-congruence-postulates?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Proving the SAS triangle congruence criterion using transformations | Geometry | Khan Academy

Wed, 30 Sep 2026 20:06:00 -0000

We can prove the side-angle-side (SAS) triangle congruence criterion using the rigid transformation definition of congruence.

Uploaded 05-03-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Sum of interior angles of a polygon | Angles and intersecting lines | Geometry | Khan Academy

Wed, 30 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-shapes/angles-with-polygons/v/sum-of-interior-angles-of-a-polygon

Uploaded 23-09-11

Showing a generalized way to find the sum of the interior angles of any polygon

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/e/angles_of_a_polygon?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/sum-of-the-exterior-angles-of-convex-polygon?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/finding-more-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Proving the SSS triangle congruence criterion using transformations | Geometry | Khan Academy

Wed, 30 Sep 2026 16:06:00 -0000

We can prove the side-side-side (SSS) triangle congruence criterion using the rigid transformation definition of congruence.

Uploaded 05-03-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Sum of the exterior angles of convex polygon | Geometry | Khan Academy

Wed, 30 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-shapes/angles-with-polygons/v/sum-of-the-exterior-angles-of-convex-polygon

Uploaded 25-09-11

More elegant way to find the sum of the exterior angles of a convex polygon

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/old_angles/v/introduction-to-angles-old?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/sum-of-interior-angles-of-a-polygon?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Geometric constructions: perpendicular line through a point off the line | Geometry | Khan Academy

Wed, 30 Sep 2026 12:06:00 -0000

We can construct a perpendicular line through a point off the line. The lines must be perpendicular because a rhombus's diagonals are perpendicular.

Uploaded 04-03-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-bisectors .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Finding congruent triangles | Congruence | Geometry | Khan Academy

Wed, 30 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/xff63fac4:hs-geo-congruent-triangles/v/finding-congruent-triangles

Uploaded 26-09-11

Using the SSS, ASA, SAS, and AAS postulates to find congruent triangles

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruency_postulates?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/more-on-why-ssa-is-not-a-postulate?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/two-column-proof-showing-segments-are-perpendicular?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Geometric constructions: congruent angles | Congruence | High school geometry | Khan Academy

Wed, 30 Sep 2026 08:06:00 -0000

We can construct congruent angles with a compass and straight edge. They're congruent corresponding angles of congruent triangles.

Uploaded 04-03-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-bisectors .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Learn more about your ad choices. Visit megaphone.fm/adchoices

More on why SSA is not a postulate | Congruence | Geometry | Khan Academy

Wed, 30 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence/v/more-on-why-ssa-is-not-a-postulate

Uploaded 26-09-11

SSA special cases including RSH

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/perpendicular-radius-bisects-chord?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/finding-congruent-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Geometric constructions: parallel line | Congruence | High school geometry | Khan Academy

Wed, 30 Sep 2026 04:06:00 -0000

We can parallel lines with compass and straightedge by creating a pair of congruent corresponding angles on a transversal.

Uploaded 04-03-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-bisectors .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Congruent triangle proof example | Congruence | Geometry | Khan Academy

Wed, 30 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-theorems/v/congruent-triangle-proof-example

Uploaded 26-09-11

Proving that a point is the midpoint via triangle congruency

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/congruent-triangle-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/perpendicular-radius-bisects-chord?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Angle congruence equivalent to having same measure | Congruence | Geometry | Khan Academy

Wed, 30 Sep 2026 00:06:00 -0000

Two angles are congruent if and only if they have the same measure.

Uploaded 04-03-20

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-trans-and-congruence .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Learn more about your ad choices. Visit megaphone.fm/adchoices

Congruent triangle example 2 | Congruence | Geometry | Khan Academy

Tue, 29 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-theorems/v/congruent-triangle-example-2

Uploaded 26-09-11

Showing that segments have the same length

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/figuring-out-all-the-angles-for-congruent-triangles-example?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/congruent-triangle-proof-example?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Guided visualization to calm your mind

Tue, 29 Sep 2026 20:06:00 -0000

In this short meditation session, Sal introduces a simple visualization technique to help you separate yourself from your thoughts and quiet them.

Uploaded 28-02-20

What did you think of this meditation? Let us know in the comments below!

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Congruent legs and base angles of isosceles triangles | Congruence | Geometry | Khan Academy

Tue, 29 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/congruent-legs-and-base-angles-of-isosceles-triangles

Uploaded 29-09-11

Showing that congruent legs imply equal base angles and vice versa

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/e/recognizing-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/v/equilateral-triangle-sides-and-angles-congruent?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/problem-involving-angle-derived-from-square-and-circle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Guided meditation to help with test anxiety

Tue, 29 Sep 2026 16:06:00 -0000

Are you feeling nervous or stressed out about a big test that’s coming up? Take a few moments to relax and refocus with this guided meditation from Sal. And good luck on your upcoming test - you’ve got this!

Uploaded 28-02-20

What did you think of this meditation? Let us know in the comments below!

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Equilateral triangle sides and angles congruent | Congruence | Geometry | Khan Academy

Tue, 29 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/equilateral-triangle-sides-and-angles-congruent

Uploaded 29-09-11

Showing that all of the angles of an equilateral triangle are 60 degrees

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/e/recognizing-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/v/equilateral-and-isosceles-example-problems?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/v/congruent-legs-and-base-angles-of-isosceles-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Guided meditation to help you stop procrastinating

Tue, 29 Sep 2026 12:06:00 -0000

Procrastination is something we all deal with. Sal procrastinated on making this video. You’re probably going to watch it to procrastinate instead of doing something else. ;) In this short video, Sal shares tips to help motivate you to move forward when you’re procrastinating.

Uploaded 28-02-20

What did you think of this meditation? Let us know in the comments below!

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Equilateral and isosceles example problems | Congruence | Geometry | Khan Academy

Tue, 29 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-working-with-triangles/v/equilateral-and-isosceles-example-problems

Uploaded 29-09-11

Three example problems involving isosceles and equilateral triangles. 2 from Art of Problem Solving (by Richard Rusczyk) book

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/e/recognizing-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/v/another-isosceles-example-problem?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/v/equilateral-triangle-sides-and-angles-congruent?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Learn more about your ad choices. Visit megaphone.fm/adchoices

Guided meditation for students

Tue, 29 Sep 2026 08:06:00 -0000

Many students have asked Sal how to cope with stress. In his personal life, Sal finds meditation invaluable for not only reducing stress and anxiety, but also for enjoying the fullness of life. In this short video, Sal introduces you to simple meditation techniques to help you calm your mind, relax, and focus.

Uploaded 28-02-20

What did you think of this meditation? Are there specific topics that you’d like meditations for? Let us know in the comments below! And subscribe to our channel to stay updated about future meditation videos.

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Another isosceles example problem | Congruence | Geometry | Khan Academy

Tue, 29 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-working-with-triangles/v/another-isosceles-example-problem

Uploaded 29-09-11

Possible angles for an isosceles triangle

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/v/example-involving-an-isosceles-triangle-and-parallel-lines?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/v/equilateral-and-isosceles-example-problems?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Influence of political events on ideology | AP US Government and Politics | Khan Academy

Tue, 29 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/humanities/ap-us-government-and-politics/american-political-ideologies-and-beliefs/influence-of-political-events-on-ideology/a/influence-of-political-events-on-ideology

Uploaded 26-02-20

How do political events affect a person's ideology? In this video, Kim Kutz Elliott discusses how external events can shift a person's beliefs in the short and long term.

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Example involving an isosceles triangle and parallel lines | Congruence | Geometry | Khan Academy

Tue, 29 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-working-with-triangles/v/another-isosceles-example-problem

Uploaded 29-09-11

Integrating what we know about isosceles triangles and parallel lines

Watch the next lesson: https://www.khanacademy.org/math/geometry/similarity/similarity-and-transformations/v/testing-similarity-through-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/v/another-isosceles-example-problem?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Segment congruence equivalent to having same length | Congruence | Geometry | Khan Academy

Tue, 29 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-trans-and-congruence/v/angle-congruence-equivalent-to-having-same-measure

Uploaded 12-02-20

Two line segments are congruent if and only if they have equal lengths

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-trans-and-congruence .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Learn more about your ad choices. Visit megaphone.fm/adchoices

Figuring out all the angles for congruent triangles example | Congruence | Geometry | Khan Academy

Mon, 28 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-working-with-triangles/v/figuring-out-all-the-angles-for-congruent-triangles-example

Uploaded 29-09-11

Another example of using congruency to figure out a bunch of angles

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/problem-involving-angle-derived-from-square-and-circle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/congruent-triangle-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Area model for multiplying polynomials with negative terms

Mon, 28 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/e/multiply-monomials-by-polynomials-intuition

Uploaded 10-02-20

Multiplying polynomials with negative terms may feel weird, but it's actually very useful and works out as well as when you only have positive terms.

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Perimeter and area: the basics | Perimeter, area, and volume | Geometry | Khan Academy

Mon, 28 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-area-perimeter/geometry-perimeter/v/perimeter-and-area-basics

Uploaded 30-09-11

Great geometry primer on perimeter and area. Listen carefully. Sal explains the concepts so you'll understand them.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/e/area_of_triangles_1?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/v/triangle-area-proofs?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/right_triangles_topic/cc-geometry-trig-similarity/v/example-relating-trig-function-to-side-ratios?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Hydrogen bonding | AP Chemistry | Khan Academy

Mon, 28 Sep 2026 16:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:intermolecular-forces/v/hydrogen-bonding

Uploaded 10-02-20

Want to explore more? Check out the full States of matter playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAcadC8xfE0VtGhfHdrECNO&si=aLyVfcDx3Xp257S6

Hydrogen bonding is a special type of dipole-dipole interaction that occurs between the lone pair of a highly electronegative atom (typically N, O, or F) and the hydrogen atom in a N–H, O–H, or F–H bond. Hydrogen bonds can form between different molecules (intermolecular hydrogen bonding) or between different parts of the same molecule (intramolecular hydrogen bonding).

Sections:
00:00 - Introduction to hydrogen bonds
00:35 - Polar bonds and partial charges
01:55 - Intermolecular hydrogen bonding
02:44 - Hydrogen bonds vs. London dispersion forces
03:55 - Boiling point comparison among similar molecules
04:46 - Hydrogen bonds as strong dipole-dipole forces
05:23 - Hydrogen bonding between different molecules
05:36 - Role of hydrogen bonds in biology
06:24 - Importance of hydrogen bonds in life and water

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Triangle area proofs | Perimeter, area, and volume | Geometry | Khan Academy

Mon, 28 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-area-perimeter/geometry-area-triangle/v/triangle-area-proofs

Uploaded 30-09-11

Proving that the area of any triangle is 1/2 b x h

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/e/area_of_triangles_1?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/v/interesting-perimeter-and-area-problems?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/v/perimeter-and-area-basics?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Intermolecular forces and vapor pressure | AP Chemistry | Khan Academy

Mon, 28 Sep 2026 12:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:intermolecular-forces/v/intermolecular-forces-and-vapor-pressure

Uploaded 07-02-20

Want to explore more? Check out the full States of matter playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAcadC8xfE0VtGhfHdrECNO&si=aLyVfcDx3Xp257S6

Some properties of liquids, such as boiling point and vapor pressure, are directly related to the intermolecular forces present between its molecules. The stronger these forces, the lower the rate of evaporation and the lower the vapor pressure. This connection between the strength of the attractive
forces and physical properties also applies to solids and gases.

Sections:
00:00 - Ranking molecules by boiling point
00:34 - Intermolecular forces and boiling points
00:50 - Hydrogen bonding analysis
01:47 - Using London dispersion as tiebreaker
02:46 - Final boiling point ranking
03:21 - Introduction to vapor pressure
03:51 - Behavior of molecules at 20°C
04:40 - Equilibrium between liquid and vapor
05:28 - Vapor pressure vs intermolecular forces
06:01 - Summary: boiling point, vapor pressure, and IMFs

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Interesting perimeter and area problems | Perimeter, area, and volume | Geometry | Khan Academy

Mon, 28 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-area-perimeter/geometry-area-trap-composite/v/interesting-perimeter-and-area-problems

Uploaded 30-09-11

Three example problems involving perimeter and area

Watch the next lesson: https://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/v/area-of-diagonal-generated-triangles-of-rectangle-are-equal?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/v/triangle-area-proofs?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Ion–dipole forces | Intermolecular forces and properties | AP Chemistry | Khan Academy

Mon, 28 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:intermolecular-forces/v/intermolecular-forces-and-vapor-pressure

Uploaded 06-02-20

Ion–dipole forces occur between ions and polar molecules. The relative strength of these forces can be understood in terms of Coulomb's law, which tells us that the electrostatic attraction between ion and dipole is directly related to the magnitudes of the ion charge and the dipole and inversely related to the distance between them. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:intermolecular-forces/v/ion-dipole-forces

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Koch snowflake fractal | Perimeter, area, and volume | Geometry | Khan Academy

Mon, 28 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-volume-surface-area/koch-snowflake/v/koch-snowflake-fractal

Uploaded 30-09-11

A shape that has an infinite perimeter but finite area

Watch the next lesson: https://www.khanacademy.org/math/geometry/basic-geometry/koch_snowflake/v/area-of-an-equilateral-triangle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/v/triangle-inqequality-theorem?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Dipole–dipole forces | AP Chemistry | Khan Academy

Mon, 28 Sep 2026 04:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:intermolecular-forces-and-properties/x2eef969c74e0d802:intermolecular-forces/v/dipole-dipole-forces

Uploaded 03-02-20

Want to explore more? Check out the full States of matter playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAcadC8xfE0VtGhfHdrECNO&si=aLyVfcDx3Xp257S6

Dipole–dipole forces occur between molecules with permanent dipoles (i.e., polar molecules). For molecules of similar size and mass, the strength of these forces increases with increasing polarity. Polar molecules can also induce dipoles in nonpolar molecules, resulting in dipole–induced dipole forces.

Sections:
00:00 - Comparing propane and acetaldehyde
00:34 - Role of intermolecular forces in boiling point
01:14 - London dispersion forces and molar mass
02:15 - Introduction to dipole-dipole forces
03:03 - Molecular dipole moments and symmetry
04:11 - Dipole in acetaldehyde molecule
05:01 - Dipole-dipole interactions explained
05:57 - Can dipoles induce dipoles?
06:25 - Summary of intermolecular interactions

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Challenging perimeter problem | Perimeter, area, and volume | Geometry | Khan Academy

Mon, 28 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-miscellaneous/geometry-worked-examples/v/challenging-perimeter-problem

Uploaded 30-09-11

Perimeter of rectangle covered by 9 non-overlapping squares. From 2000 American Invitational Math Exam

Watch the next lesson: https://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/v/triangle-inqequality-theorem?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/v/area-of-shaded-region-made-from-equilateral-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Guided meditation for procrastination

Mon, 28 Sep 2026 00:06:00 -0000

Don't worry. I'm going to get back to making academic videos soon, but I still have several of these meditation videos I want to get out since I think they can help you learn and deal with anything :) Procrastination in particular is something we all deal with. I've been procrastinating making this video. You are probably going to watch it to procrastinate doing something else :) Hopefully, you'll get right back to it after the meditation :)

Uploaded 03-02-20

Inwards!
-Sal

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Similar triangle basics | Similarity | Geometry | Khan Academy

Sun, 27 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-triangle-similarity-intro/v/similar-triangle-basics

Uploaded 01-10-11

Introduction to what it means for triangles to be similar

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/e/similar_triangles_1?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/v/similarity-postulates?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/similarity/similarity-and-transformations/v/quadrilateral-similarity-by-showing-congruent-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Guided meditation visualizing thoughts as the surface of an ocean

Sun, 27 Sep 2026 20:06:00 -0000

Folks seemed to appreciate the first guided meditation for students and asked for more. This is a slightly shorter meditation introducing a visualization for separating yourself from your thoughts and quieting them.

Uploaded 03-02-20

Inwards!
-Sal

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KA on John Stossel Documentary

Sun, 27 Sep 2026 18:06:00 -0000

Khan Academy on Jon Stossel Documentary in September 2011

Uploaded 01-10-11

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Guided meditation for high school students

Sun, 27 Sep 2026 16:06:00 -0000

Many students have asked me for advice about coping with stress. In my personal life, I have found meditation invaluable for not only reducing stress and anxiety, but for enjoying the fullness of life. This is the first recording I've ever made like this, so I'd love your feedback. Also let me know if there are specific things you're dealing with that you'd love meditations for.

Uploaded 30-01-20

Inwards!
-Sal

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Khan Academy on 20 20 (Sep 2011)

Sun, 27 Sep 2026 14:06:00 -0000

Snippet from Khan Academy's appearance on 20 20 story about YouTube

Uploaded 01-10-11

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The development of an American culture | AP US History | Khan Academy

Sun, 27 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/humanities/us-history/the-early-republic/culture-and-reform/a/antebellum-communal-experiments-cnx

Uploaded 22-01-20

In the early 1800s, American artists, architects, and writers began to create uniquely American styles. In this video, Kim Kutz Elliott discusses the quest to create architecture suitable to a republic and the influence of Romantic ideals on American artists and writers, including the Hudson River School and the Transcendentalists.

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Sal during Education Week (Sep 2011) 1

Sun, 27 Sep 2026 10:06:00 -0000

Sal on CNBC during Education Nation (Sep 2011)

Uploaded 01-10-11

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Showing segment congruence equivalent to having same length

Sun, 27 Sep 2026 08:06:00 -0000

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Similarity postulates | Similarity | Geometry | Khan Academy

Sun, 27 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-triangle-similarity-intro/v/similar-triangle-basics

Uploaded 01-10-11

Thinking about what we need to know to determine whether two triangles are similar

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/e/similar_triangles_1?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/v/similar-triangle-example-problems?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/v/similar-triangle-basics?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Idea behind hypothesis testing

Sun, 27 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/idea-significance-tests/v/examples-of-null-and-alternative-hypotheses

Uploaded 17-01-20

Idea behind hypothesis testing. Null and alternative hypotheses.

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Similarity example problems | Similarity | Geometry | Khan Academy

Sun, 27 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-solving-similar-triangles/v/similarity-example-problems

Uploaded 01-10-11

Two example problems involving similarity

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/e/solving_similar_triangles_1?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/v/similarity-example-where-same-side-plays-different-roles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/v/similar-triangle-example-problems?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Conclusion for a two sample t test using a P value

Sun, 27 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/two-sample-t-test-means/v/conclusion-for-2-sample-t-test-from-confidence-interval

Uploaded 13-01-20

Conclusion for a two sample t test using a P value

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Tom Brokaw interviews Sal at Education Nation 2011

Sat, 26 Sep 2026 22:06:00 -0000

Rough footage of Tom Brokaw interviewing Sal at Education Nation

Uploaded 02-10-11

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Dilating shapes: shrinking | Performing transformations | High school geometry | Khan Academy

Sat, 26 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/v/dilating-triangles-find-the-error

Uploaded 08-01-20

Draw the image of the triangle under a dilation with scale factor 1/4 about the center of dilation on the coordinate plane.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/e/dilations

Watch the next lesson:
https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/v/dilations-and-properties

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/v/thinking-about-dilations

High school geometry on Khan Academy: Learn high school geometry—transformations, congruence, similarity, trigonometry, analytic geometry, and more. (aligned with Common Core standards)

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Challenging similarity problem | Similarity | Geometry | Khan Academy

Sat, 26 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-similar-and-congruent-triangles/v/challenging-similarity-problem

Uploaded 03-10-11

Interesting similarity problem where we don't have a lot of information to work with

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/similarity/cc-solving-prob-similar-tri/e/solving-problems-with-similar-and-congruent-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/similarity/old_school_similarity/v/similar-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/similarity/cc-solving-prob-similar-tri/v/golden-ratio-to-find-radius-of-moon?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Health insurance primer

Sat, 26 Sep 2026 16:06:00 -0000

Introduction to premiums, deductibles, co-pays and co-insurance.

Uploaded 07-01-20

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Similarity example where same side plays different roles | Similarity | Geometry | Khan Academy

Sat, 26 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-solving-similar-triangles/v/similarity-example-where-same-side-plays-different-roles

Uploaded 03-10-11

The same side not corresponding to itself in two similar triangles

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/e/solving_similar_triangles_2?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/similarity/cc-solving-prob-similar-tri/v/finding-area-using-similarity-and-congruence?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/v/similarity-example-problems?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Mapping shapes | Performing transformations | High school geometry | Khan Academy

Sat, 26 Sep 2026 12:06:00 -0000

Finding sequences of rigid transformations that map one shape onto another shape.

Uploaded 07-01-20

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/e/mapping-shapes

Watch the next lesson:
https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-transformations-definitions/v/sequences-of-transformations

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-rigid-transformations-overview/v/rigid-transformations-preserved-properties

High school geometry on Khan Academy: Learn high school geometry—transformations, congruence, similarity, trigonometry, analytic geometry, and more. (aligned with Common Core standards)

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Systemic thinking about cancer | Miscellaneous | Heatlh and Medicine | Khan Academy

Sat, 26 Sep 2026 10:06:00 -0000

Dr. David Agus discusses thinking systemically about cancer and other things. Created by Sal Khan.

Uploaded 03-10-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/inflammation?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/healthcare-misc/v/ritual-of-the-bedside-exam?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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The Court in Action | AP US Government and Politics | Khan Academy

Sat, 26 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/humanities/ap-us-government-and-politics/interactions-among-branches-of-government/the-court-in-action/a/the-court-in-action-lesson-overview

Uploaded 06-01-20

What happens when the Supreme Court's decisions are controversial or unpopular? In this video, Kim Kutz Elliott discusses the ways that Congress and the president can challenge the Supreme Court.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Vitamin C and the Limeys

Sat, 26 Sep 2026 06:06:00 -0000

Sal and Dr. David Agus talk about the history of Scurvy and Vitamin C

Uploaded 03-10-11

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Formal charge | Molecular and ionic compound structure and properties | AP Chemistry | Khan Academy

Sat, 26 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:resonance-and-formal-charge/v/worked-example-using-formal-charges-to-evaluate-nonequivalent-resonance-structures

Uploaded 17-12-19

The formal charge of an atom in a molecule is the charge that would reside on the atom if all of the bonding electrons were shared equally. We can calculate an atom's formal charge using the equation FC = VE - [LPE - ½(BE)], where VE = the number of valence electrons on the free atom, LPE = the number of lone pair electrons on the atom in the molecule, and BE = the number of bonding (shared) electrons around the atom in the molecule. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:resonance-and-formal-charge/v/formal-charge

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Inflammation | Miscellaneous | Heatlh and Medicine | Khan Academy

Sat, 26 Sep 2026 02:06:00 -0000

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Resonance | Molecular and ionic compound structure and properties | AP Chemistry | Khan Academy

Sat, 26 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:resonance-and-formal-charge/v/formal-charge

Uploaded 13-12-19

Resonance arises when more than one valid Lewis structure can be drawn for a molecule or ion. The overall electronic structure of the molecule or ion is given by the weighted average of these resonance structures and is referred to as the "resonance hybrid." View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:resonance-and-formal-charge/v/introduction-to-resonance

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Blue Cross and Blue Shield | Health care system | Heatlh and Medicine | Khan Academy

Fri, 25 Sep 2026 22:06:00 -0000

Sal and Dr. Baker talk a bit about Blue Cross and Blue Shield. Created by Sal Khan.

Uploaded 03-10-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/health-care-system/v/conversation-about-drug-pricing?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/current-issues-in-health-and-medicine/ebola-outbreak/v/r-nought-and-vaccine-coverage?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
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Exceptions to the octet rule | AP Chemistry | Khan Academy

Fri, 25 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:lewis-diagrams/v/worked-example-lewis-diagram-of-xenon-difluoride

Uploaded 13-12-19

While most atoms obey the duet and octet rules, there are some exceptions. For example, elements such as boron or beryllium often form compounds in which the central atom is surrounded by fewer than eight electrons (e.g., BF₃ or BeH₂). In contrast, many elements in the third-row and beyond have been observed to exceed the octet rule, forming compounds in which the central atom is surrounded by more than eight electrons (e.g. ICl₄⁻ or PF₅). View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:lewis-diagrams/v/exceptions-to-the-octet-rule

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Conversation about drug pricing | Health care system | Heatlh and Medicine | Khan Academy

Fri, 25 Sep 2026 18:06:00 -0000

Dr. Laurence Baker talks to Sal about how drug prices are set. Created by Sal Khan.

Uploaded 03-10-11

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/health-care-system/v/health-care-costs-in-us-vs-europe?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/health-care-system/v/blue-cross-and-blue-shield?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health and Medicine channel: https://www.youtube.com/channel/UC1RAowgA3q8Gl7exSWJuDEw?sub_confirmation=1
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Worked example: Lewis diagram of xenon difluoride (XeF₂) | AP Chemistry | Khan Academy

Fri, 25 Sep 2026 16:06:00 -0000

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https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:lewis-diagrams/e/lewis-diagrams

Uploaded 13-12-19

In some molecules, the central atom exceeds the octet rule (is surrounded by more than eight electrons). See an example of a molecule that violates the octet rule (XeF₂) and learn how to draw its Lewis diagram in this video. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:lewis-diagrams/v/worked-example-lewis-diagram-of-xenon-difluoride

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Health care costs in US vs Europe | Health care system | Heatlh and Medicine | Khan Academy

Fri, 25 Sep 2026 14:06:00 -0000

A discussion about US health care costs. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/health-care-system/v/healthcare-system-overview?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/health-care-system/v/conversation-about-drug-pricing?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health and Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

Uploaded 03-10-11

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

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Worked example: Lewis diagram of the cyanide ion (CN⁻) | AP Chemistry | Khan Academy

Fri, 25 Sep 2026 12:06:00 -0000

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https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:lewis-diagrams/v/exceptions-to-the-octet-rule

Uploaded 12-12-19

We can draw Lewis structures for polyatomic ions (ions containing multiple atoms) using the same stepwise procedure as for neutral molecules. In this video, we'll see how to construct the Lewis diagram of the cyanide ion (CN⁻). View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:lewis-diagrams/v/worked-example-lewis-diagram-of-cyanide-ion

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Drawing Lewis diagrams | AP Chemistry | Khan Academy

Fri, 25 Sep 2026 08:06:00 -0000

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https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:lewis-diagrams/v/worked-example-lewis-diagram-of-formaldehyde

Uploaded 12-12-19

A Lewis diagram shows how the valence electrons are distributed around the atoms in a molecule. Shared pairs of electrons are drawn as lines between atoms, while lone pairs of electrons are drawn as dots next to atoms. When constructing a Lewis diagram, keep in mind the octet rule, which refers to the tendency of atoms to gain, lose, or share electrons until they are surrounded by eight valence electrons (an "octet"). View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:lewis-diagrams/v/drawing-lewis-diagrams

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Finding area using similarity and congruence | Similarity | Geometry | Khan Academy

Fri, 25 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-similar-and-congruent-triangles/v/finding-area-using-similarity-and-congruence

Uploaded 04-10-11

Example of using similarity and congruence to find the area of a triangle

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/similarity/cc-solving-prob-similar-tri/e/solving-problems-with-similar-and-congruent-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Worked example: Lewis diagram of formaldehyde (CH₂O) | AP Chemistry | Khan Academy

Fri, 25 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:lewis-diagrams/v/worked-example-lewis-diagram-of-cyanide-ion

Uploaded 12-12-19

The Lewis diagram of a molecule can be constructed using the following stepwise procedure: (1) Find the number of valence electrons in the molecule. (2) Draw single bonds between bonded atoms. (3) Distribute the remaining electrons throughout the molecule, keeping in mind the duet and octet rules. In this video, we'll use these steps to construct the Lewis diagram of formaldehyde (CH₂O). View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:lewis-diagrams/v/worked-example-lewis-diagram-of-formaldehyde

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Pythagorean theorem proof using similarity | Geometry | Khan Academy

Fri, 25 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-pythagorean-proofs/v/pythagorean-theorem-proof-using-similarity

Uploaded 04-10-11

Proof of the Pythagorean Theorem using similarity

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/right_triangles_topic/pythagorean_proofs/e/pythagorean-theorem-proofs?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/right_triangles_topic/pythagorean_proofs/v/another-pythagorean-theorem-proof?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Causation from 1980-2020

Fri, 25 Sep 2026 00:06:00 -0000

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https://www.khanacademy.org/humanities/us-history/modern-us/us-after-2000/e/the-united-states-after-2000

Uploaded 06-12-19

How did events in the years after 1980 affect national identity in the United States? In this video, Kim Kutz Elliott discusses changes in US foreign policy, economics, and politics, attempting to place the developments of this era into a broader historical context.

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Examples using Pythagorean Theorem

Thu, 24 Sep 2026 22:06:00 -0000

Uploaded 04-10-11

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Worked example: Using formal charges to evaluate nonequivalent resonance structures | Khan Academy

Thu, 24 Sep 2026 20:06:00 -0000

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https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:resonance-and-formal-charge/e/resonance-and-formal-charge

Uploaded 05-12-19

When a molecule has nonequivalent resonance structures, one structure may contribute more to the resonance hybrid than another. In terms of formal charge, a structure generally contributes more when (1) the formal charges on the atoms are minimized and (2) any negative formal charges are on more electronegative atoms and any positive charges are on more electropositive atoms. In this video, we use these guidelines to evaluate the nonequivalent resonance structures of SCN⁻. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:resonance-and-formal-charge/v/worked-example-using-formal-charges-to-evaluate-nonequivalent-resonance-structures

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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30-60-90 triangle side ratios proof | Right triangles and trigonometry | Geometry | Khan Academy

Thu, 24 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-triangles/v/30-60-90-triangle-side-ratios-proof

Uploaded 04-10-11

Proving the ratios between the sides of a 30-60-90 triangle

Watch the next lesson: https://www.khanacademy.org/math/geometry/right_triangles_topic/special_right_triangles/v/45-45-90-triangle-side-ratios?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Representing alloys using particulate models | AP Chemistry | Khan Academy

Thu, 24 Sep 2026 16:06:00 -0000

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https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:structure-of-metals-and-alloys/e/structure-of-metals-and-alloys

Uploaded 04-12-19

An alloy is a mixture of two or more elements, of which at least one is a metal. There are two main types of alloys: interstitial alloys, which form between atoms of different radii, and substitutional alloys, which form between atoms of similar radii. In this video, we'll learn how to represent the different types of alloys using particulate models. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:structure-of-metals-and-alloys/v/representing-alloys-using-particulate-models

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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45-45-90 triangle side ratios | Right triangles and trigonometry | Geometry | Khan Academy

Thu, 24 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-triangles/v/45-45-90-triangle-side-ratios

Uploaded 04-10-11

Showing the ratios of the sides of a 45-45-90 triangle are 1:1:sqrt(2)

Watch the next lesson: https://www.khanacademy.org/math/geometry/right_triangles_topic/special_right_triangles/v/30-60-90-triangle-example-problem?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/right_triangles_topic/special_right_triangles/v/30-60-90-triangle-side-ratios-proof?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Representing ionic solids using particulate models | AP Chemistry | Khan Academy

Thu, 24 Sep 2026 12:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:structure-of-ionic-solids/v/representing-ionic-solids-using-particulate-models

Uploaded 03-12-19

Want to explore more? Check out the full Atomic models and periodicity playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAYCvTHhMGsNvLS-btVPXRw&si=ewZ4I_TtM8MDBokW

The cations and anions in an ionic solid are arranged in a lattice structure that maximizes the attractive forces between opposite charges and minimizes the repulsive forces between like charges. In this video, we'll learn how to represent the structure of an ionic solid using a particulate model.

Sections:
00:00 - How ions form crystals
00:30 - Visualizing ionic arrangements
01:27 - Forces driving ion arrangement
02:07 - Checkerboard lattice structure
02:54 - Introducing rubidium bromide
03:32 - Electron configuration of ions
04:20 - Comparing ion sizes
05:02 - Drawing a particulate model

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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The golden ratio | Introduction to Euclidean geometry | Geometry | Khan Academy

Thu, 24 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-lines/the-golden-ratio/v/the-golden-ratio

Uploaded 05-10-11

An introduction to one of the most amazing ideas/numbers in mathematics

Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/Angle_basics/v/angle-basics?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/intro_euclid/v/language-and-notation-of-the-circle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
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Lattice energy | Molecular and ionic compound structure and properties | AP Chemistry | Khan Academy

Thu, 24 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:intramolecular-force-and-potential-energy/e/intramolecular-force-and-potential-energy

Uploaded 03-12-19

The energy required to separate the ions in a crystal lattice into individual gaseous ions is known as lattice energy. Lattice energy depends on the strength of interactions between cations and anions in the lattice, which we can estimate using Coulomb's law: Fₑ = (q₁q₂)/r². According to this equation, stronger interactions occur between ions with larger charges and smaller radii. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:intramolecular-force-and-potential-energy/v/lattice-energy

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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30-60-90 triangle example problem | Right triangles and trigonometry | Geometry | Khan Academy

Thu, 24 Sep 2026 06:06:00 -0000

Using what we know about 30-60-90 triangles to solve what at first seems to be a challenging problem

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/right_triangles_topic/special_right_triangles/e/pythagorean_theorem_2?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/right_triangles_topic/special_right_triangles/v/area-of-a-regular-hexagon?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/right_triangles_topic/special_right_triangles/v/45-45-90-triangle-side-ratios?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

Uploaded 05-10-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Worked example: Interpreting potential energy curves of diatomic molecules | Khan Academy

Thu, 24 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:intramolecular-force-and-potential-energy/v/lattice-energy

Uploaded 02-12-19

The length and energy of a bond are influenced by both the bond order and the size of the atoms in the bond. In general, the higher the bond order and the smaller the atoms, the shorter and stronger the bond. As shown in this video, we can use these relationships to match diatomic molecules to their potential energy curves. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:intramolecular-force-and-potential-energy/v/worked-example-interpreting-potential-energy-curves-of-diatomic-molecules

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Area of an equilateral triangle | Perimeter, area, and volume | Geometry | Khan Academy

Thu, 24 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-area-perimeter/advanced-area-with-triangles/v/area-of-an-equilateral-triangle

Uploaded 05-10-11

Finding the formula for the area of an equilateral triangle with side s

Watch the next lesson: https://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/v/area-of-shaded-region-made-from-equilateral-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/v/area-of-diagonal-generated-triangles-of-rectangle-are-equal?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Bond length and bond energy | AP Chemistry | Khan Academy

Thu, 24 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:intramolecular-force-and-potential-energy/v/worked-example-interpreting-potential-energy-curves-of-diatomic-molecules

Uploaded 26-11-19

A diatomic molecule can be represented using a potential energy curve, which graphs potential energy versus the distance between the two atoms (called the internuclear distance). From this graph, we can determine the equilibrium bond length (the internuclear distance at the potential energy minimum) and the bond energy (the energy required to separate the two atoms). View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:intramolecular-force-and-potential-energy/v/bond-length-and-bond-energy

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Area of Koch snowflake (part 1) - advanced | Perimeter, area, and volume | Geometry | Khan Academy

Wed, 23 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-volume-surface-area/koch-snowflake/v/area-of-koch-snowflake-part-1-advanced

Uploaded 05-10-11

Starting to figure out the area of a Koch Snowflake (which has an infinite perimeter)

Watch the next lesson: https://www.khanacademy.org/math/geometry/basic-geometry/koch_snowflake/v/area-of-koch-snowflake-part-2-advanced?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/basic-geometry/koch_snowflake/v/area-of-an-equilateral-triangle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Predicting bond type (electronegativity) | AP Chemistry | Khan Academy

Wed, 23 Sep 2026 20:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:types-of-chemical-bonds/v/predicting-bond-type-electronegativity

Uploaded 25-11-19

Want to explore more? Check out the full States of matter playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAcadC8xfE0VtGhfHdrECNO&si=aLyVfcDx3Xp257S6

One way to predict the type of bond that forms between two elements is to compare the electronegativities of the elements. In general, large differences in electronegativity result in ionic bonds, while smaller differences result in covalent bonds.

Sections:
00:00 - Bond types by element combinations
00:41 - Bonding as a spectrum
01:02 - Role of electronegativity in bonding
01:29 - Electronegativity difference and bond polarity
02:23 - Example: oxygen and hydrogen bond
03:26 - Polar covalent bond explanation
03:59 - Where metallic bonds fit in
04:20 - Properties of metallic bonds

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Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Area of Koch snowflake (part 2) - advanced | Perimeter, area, and volume | Geometry | Khan Academy

Wed, 23 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/geometry-volume-surface-area/koch-snowflake/v/area-of-koch-snowflake-part-2-advanced

Uploaded 05-10-11

Summing an infinite geometric series to finally find the finite area of a Koch Snowflake

Watch the next lesson: https://www.khanacademy.org/math/geometry/basic-geometry/heron_formula_tutorial/v/heron-s-formula?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/basic-geometry/koch_snowflake/v/area-of-koch-snowflake-part-1-advanced?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Predicting bond type (metals vs. nonmetals) | AP Chemistry | Khan Academy

Wed, 23 Sep 2026 16:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:types-of-chemical-bonds/v/predicting-bond-type-metals-nonmetals

Uploaded 25-11-19

Want to explore more? Check out the full Chemical bonding playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAYCvTHhMGsNvLS-btVPXRw&si=IRQTiEfJUfgET1kD

One way to predict the type of bond that forms between two elements is to consider whether each element is a metal or nonmetal. In general, covalent bonds form between nonmetals, ionic bonds form between metals and nonmetals, and metallic bonds form between metals.

Sections:
00:00 - Review of bond types
00:22 - Metals vs nonmetals
00:44 - Properties of metals
01:14 - Properties of nonmetals
01:31 - Periodic table division
02:08 - Noble gases and nonmetals
02:36 - Overview of metals and metalloids
03:20 - Predicting bond types by element classification
03:59 - Metal + nonmetal = ionic bond
04:14 - Nonmetal + nonmetal = covalent bond
04:45 - Metal + metal = metallic bond

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Perpendicular radius bisects chord | Congruence | Geometry | Khan Academy

Wed, 23 Sep 2026 14:06:00 -0000

Simple proof using RSH postulate to show that a radius perpendicular to a chord bisects it

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/congruent-triangle-proof-example?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/more-on-why-ssa-is-not-a-postulate?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

Uploaded 07-10-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Electron configurations of ions | AP Chemistry | Khan Academy

Wed, 23 Sep 2026 12:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:atomic-structure-and-properties/x2eef969c74e0d802:atomic-structure-and-electron-configuration/v/electron-configurations-of-ions

Uploaded 22-11-19

Want to explore more? Check out the full Atomic models and periodicity playlist here: https://www.youtube.com/playlist?list=PLSQl0a2vh4HD2AZcy7Pe8mHAiO5UG2WKt

To find the electron configuration for an ion, first identify the configuration for the neutral atom. Then, add or remove electrons depending on the ion's charge. For example, to find the configuration for the lithium ion (Li⁺), start with neutral lithium (1s²2s¹). Then, since the lithium ion has one less electron, remove an electron from the 2s subshell to get 1s².

Sections:
00:00 - Introduction to electron configurations of ions
00:19 - Electron configuration of neutral fluorine
01:16 - Fluoride ion configuration (F⁻)
02:07 - Electron configuration of calcium ion (Ca²⁺)
02:51 - Using noble gas notation for calcium
03:36 - Ca²⁺ has same configuration as argon
03:44 - Encouragement to explore more ion configurations

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Circumcenter of a triangle | Special properties and parts of triangles | Geometry | Khan Academy

Wed, 23 Sep 2026 10:06:00 -0000

Multiple proofs showing that a point is on a perpendicular bisector of a segment if and only if it is equidistant from the endpoints. Using this to establish the circumcenter, circumradius, and circumcircle for a triangle

Uploaded 07-10-11

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/perpendicular_bisectors/v/circumcenter-of-a-right-triangle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/cc-geometry-circles/area-inscribed-triangle/v/area-of-inscribed-equilateral-triangle-some-basic-trig-used?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Stories: Jason Spyres

Wed, 23 Sep 2026 08:06:00 -0000

Video that Sal took of an incredible student who attended one of his lectures. Jason learned from Khan Academy while in prison for 15 years and is off to accomplish great things.

Uploaded 12-11-19

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Circumcenter of a right triangle | Geometry | Khan Academy

Wed, 23 Sep 2026 06:06:00 -0000

Showing that the midpoint of the hypotenuse is the circumcenter

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/perpendicular_bisectors/v/three-points-defining-a-circle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/perpendicular_bisectors/v/circumcenter-of-a-triangle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

Uploaded 07-10-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Ionic bonds | AP Chemistry | Khan Academy

Wed, 23 Sep 2026 04:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:types-of-chemical-bonds/v/ionic-bonds

Uploaded 30-10-19

Want to explore more? Check out the full Chemical bonding playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAYCvTHhMGsNvLS-btVPXRw&si=vZ4FA1B53s-e3sq9

Ionic bonds result from the electrostatic attraction between oppositely charged ions, which form when valence electrons are transferred from one atom to another.

Sections:
00:00 - Atoms don't act alone
00:27 - Introduction to atomic bonding
00:51 - Group 1 and Lewis dot structure
01:33 - Halogens and their valence electrons
02:22 - Sodium and chlorine interaction
03:00 - Formation of ions
03:29 - Ionic attraction and bonding
04:03 - What is an ionic bond?

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Three points defining a circle | Special properties and parts of triangles | Geometry | Khan Academy

Wed, 23 Sep 2026 02:06:00 -0000

Three points uniquely define a circle. The center of a circle is the circumcenter of any triangle the circle is circumscribed about.

Uploaded 12-10-11

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/perpendicular_bisectors/v/area-circumradius-formula-proof?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/perpendicular_bisectors/v/circumcenter-of-a-right-triangle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Covalent bonds | AP Chemistry | Khan Academy

Wed, 23 Sep 2026 00:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:types-of-chemical-bonds/v/covalent-bonds

Uploaded 30-10-19

Want to explore more? Check out the full Chemical bonding playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAYCvTHhMGsNvLS-btVPXRw&si=kYyGJH85xGqjzLBC

Covalent bonds involve the sharing of electron pairs between atoms. Electron pairs shared between atoms of equal or very similar electronegativity constitute a nonpolar covalent bond (e.g., H–H or C–H), while electrons shared between atoms of unequal electronegativity constitute a polar covalent bond (e.g., H–O).

Sections:
00:00 - From ionic to covalent bonding
00:24 - Valence electrons in oxygen
00:56 - Sharing electrons to form bonds
01:45 - Double covalent bond in O₂
02:38 - Covalent bonds bring stability
03:15 - Water molecule and covalent bonding
04:27 - Electronegativity and partial charges
05:30 - What is a polar covalent bond?

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Point-line distance and angle bisectors | Geometry | Khan Academy

Tue, 22 Sep 2026 22:06:00 -0000

Thinking about the distance between a point and a line. Proof that a point on an angle bisector is equidistant to the sides of the angle and a point equidistant to the sides is on an angle bisector

Uploaded 12-10-11

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/incenter-and-incircles-of-a-triangle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/perpendicular_bisectors/v/2003-aime-ii-problem-7?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Metallic bonds | AP Chemistry | Khan Academy

Tue, 22 Sep 2026 20:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:types-of-chemical-bonds/v/metallic-bonds

Uploaded 30-10-19

Want to explore more? Check out the full Chemical bonding playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HAYCvTHhMGsNvLS-btVPXRw&si=98ncVOtXhe4kZibm

Metallic bonds result from the electrostatic attraction between metal cations and delocalized electrons. The nature of metallic bonding accounts for many of the physical properties of metals, such as conductivity and malleability.

Sections:
00:00 - Introduction to metallic bonds
00:20 - Iron atoms and metallic structure
00:46 - Sea of electrons model
01:44 - Delocalized valence electrons
02:00 - Properties of metals from bonding
02:23 - Recap of bonding types and spectrum

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Incenter and incircles of a triangle | Geometry | Khan Academy

Tue, 22 Sep 2026 18:06:00 -0000

Using angle bisectors to find the incenter and incircle of a triangle

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/inradius-perimeter-and-area?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/point-line-distance-and-angle-bisectors?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

Uploaded 12-10-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Isotopes | Atomic structure and properties | AP Chemistry | Khan Academy

Tue, 22 Sep 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:atomic-structure-and-properties/x2eef969c74e0d802:mass-spectrometry-of-elements/v/mass-spectrometry

Uploaded 29-10-19

Isotopes are atoms of the same element with different numbers of neutrons. Because they contain different numbers of neutrons, isotopes have different atomic masses. The average atomic mass of an element is calculated by taking the weighted average mass of the element's naturally occurring isotopes. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:atomic-structure-and-properties/x2eef969c74e0d802:mass-spectrometry-of-elements/v/isotopes

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Angle bisector theorem proof | Special properties and parts of triangles | Geometry | Khan Academy

Tue, 22 Sep 2026 14:06:00 -0000

What the angle bisector theorem is and its proof

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/angle-bisector-theorem-examples?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/inradius-perimeter-and-area?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

Uploaded 12-10-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Mass spectrometry | Atomic structure and properties | AP Chemistry | Khan Academy

Tue, 22 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:atomic-structure-and-properties/x2eef969c74e0d802:mass-spectrometry-of-elements/a/isotopes-and-mass-spectrometry

Uploaded 29-10-19

In the analytical technique of mass spectrometry, atoms or molecules are ionized using a high-energy electron beam and then separated based on their mass-to-charge ratios (m/z). The results are presented as a mass spectrum, which shows the relative abundances of the ions on the y-axis and their m/z ratios on the x-axis. This data can be used to calculate the exact masses of the atoms or molecules in the sample. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:atomic-structure-and-properties/x2eef969c74e0d802:mass-spectrometry-of-elements/v/mass-spectrometry

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Inradius, perimeter, and area | Special properties and parts of triangles | Geometry | Khan Academy

Tue, 22 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/angle-bisectors/v/inradius-perimeter-and-area

Uploaded 13-10-11

Showing that area is equal to inradius times semiperimeter

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/angle-bisector-theorem-proof?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/incenter-and-incircles-of-a-triangle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Making line plots with fractional data

Tue, 22 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-fourth-grade-math/imp-fractions-2/imp-line-plots-with-fractions/e/graph-data-on-line-plots--through-1-8-of-a-unit-

Uploaded 25-10-19

Making line plots with fractional data

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Angle bisector theorem examples | Geometry | Khan Academy

Tue, 22 Sep 2026 06:06:00 -0000

Using the angle bisector theorem to solve for sides of a triangle

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/e/angle_bisector_theorem?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/medians_centroids/v/triangle-medians-and-centroids?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/angle-bisector-theorem-proof?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

Uploaded 13-10-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Interpreting line plots

Tue, 22 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-third-grade-math/represent-and-interpret-data/imp-line-plots/e/read-line-plots

Uploaded 25-10-19

Interpreting line plots

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Medians divide into smaller triangles of equal area | Geometry | Khan Academy

Tue, 22 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/medians-centroids/v/medians-divide-into-smaller-triangles-of-equal-area

Uploaded 13-10-11

Showing that the three medians of a triangle divide it into six smaller triangles of equal area. Brief discussion of the centroid as well

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/medians_centroids/v/exploring-medial-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/medians_centroids/v/triangle-medians-and-centroids-2d-proof?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Line plots with fractions

Tue, 22 Sep 2026 00:06:00 -0000

Line plots with fractions

Uploaded 25-10-19

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At Words 1

Mon, 21 Sep 2026 22:06:00 -0000

Experimenting with basic reading videos (especially because my son is just learning to read!)

Uploaded 13-10-11

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Measure lengths to nearest 1/4

Mon, 21 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-third-grade-math/represent-and-interpret-data/imp-line-plots/e/measure-lengths-to-nearest-1-4-unit

Uploaded 25-10-19

Measure lengths to nearest 1/4

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Exploring medial triangles | Special properties and parts of triangles | Geometry | Khan Academy

Mon, 21 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/hs-geo-similarity/xff63fac4:hs-geo-proving-relationships-using-similarity/v/exploring-medial-triangles

Uploaded 13-10-11

The three midsegments (segments joining the midpoints of the sides) of a triangle form a medial triangle. Find out the properties of the midsegments, the medial triangle and the other 3 triangles formed in this way.

View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-proving-relationships-using-similarity .

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Multiplication and division relationship for fractions

Mon, 21 Sep 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-fifth-grade-math/divide-fractions/relate-fraction-division-to-fraction-multiplication/e/relate-fraction-division-to-fraction-multiplication

Uploaded 25-10-19

Multiplication and division relationship for fractions

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Proving that the centroid is 2-3rds along the median | Geometry | Khan Academy

Mon, 21 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/medians-centroids/v/proving-that-the-centroid-is-2-3rds-along-the-median

Uploaded 17-10-11

Showing that the centroid divides each median into segments with a 2:1 ratio (or that the centroid is 2/3 along the median)

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/medians_centroids/v/median-centroid-right-triangle-example?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/medians_centroids/v/exploring-medial-triangles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Fraction division in context

Mon, 21 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-fifth-grade-math/divide-fractions/imp-dividing-fractions-and-whole-numbers-word-problems/e/fraction-and-whole-number-division-in-contexts
Fraction division in context

Uploaded 25-10-19

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Median centroid right triangle example | Geometry | Khan Academy

Mon, 21 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/medians-centroids/v/median-centroid-right-triangle-example

Uploaded 17-10-11

Example involving properties of medians

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/altitudes/v/proof-triangle-altitudes-are-concurrent-orthocenter?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/medians_centroids/v/proving-that-the-centroid-is-2-3rds-along-the-median?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Dividing fractions and whole number word problems

Mon, 21 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/cc-fifth-grade-math/divide-fractions/imp-dividing-fractions-and-whole-numbers-word-problems/e/division-with-fractions-and-whole-numbers

Uploaded 25-10-19

Dividing fractions and whole number word problems

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Proof: Triangle altitudes are concurrent (orthocenter) | Geometry | Khan Academy

Mon, 21 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/altitudes/v/proof-triangle-altitudes-are-concurrent-orthocenter

Uploaded 17-10-11

Showing that any triangle can be the medial triangle for some larger triangle. Using this to show that the altitudes of a triangle are concurrent (at the orthocenter).

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/altitudes/v/common-orthocenter-and-centroid?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/medians_centroids/v/median-centroid-right-triangle-example?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Worked example: Identifying an element from its mass spectrum | AP Chemistry | Khan Academy

Mon, 21 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:atomic-structure-and-properties/x2eef969c74e0d802:mass-spectrometry-of-elements/e/mass-spectrometry-of-elements

Uploaded 24-10-19

Using mass spectrometry data, we can estimate an element's average atomic mass and determine its identity. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:atomic-structure-and-properties/x2eef969c74e0d802:mass-spectrometry-of-elements/v/worked-example-identifying-element-from-mass-spectrum

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Derivative intuition module | Taking derivatives | Differential Calculus | Khan Academy

Mon, 21 Sep 2026 02:06:00 -0000

Sal walking through the derivative intuition module made by Ben Eater

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/visualizing-derivatives-tutorial/e/derivative_intuition?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/visualizing-derivatives-tutorial/v/interpreting-slope-of-a-curve-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/calculus-derivatives-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

Uploaded 20-10-11

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Worked example: Calculating mass percent | AP Chemistry | Khan Academy

Mon, 21 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:atomic-structure-and-properties/x2eef969c74e0d802:elemental-composition-of-pure-substances/v/formula-mass-composition

Uploaded 24-10-19

Want to explore more? Check out the full Stoichiometry and the mole playlist here: https://youtube.com/playlist?list=PLSQl0a2vh4HDlQzYt6FMr4i4Yf_nyjRN6&si=1hPtTbDzzDQ5JUAw

To calculate the mass percent of an element in a compound, we divide the mass of the element in 1 mole of the compound by the compound's molar mass and multiply the result by 100. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:atomic-structure-and-properties/x2eef969c74e0d802:elemental-composition-of-pure-substances/v/worked-example-calculating-mass-percent

Sections:
00:00 - Calculating percent by mass of carbon in glucose
00:41 - Assuming one mole of glucose
01:32 - Calculating mass of carbon in one mole
02:11 - Total molar mass of glucose
03:26 - Performing the calculation
04:48 - Considering significant figures
05:20 - Final answer: 40.00% carbon by mass

------------------

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Review of triangle properties | Special properties and parts of triangles | Geometry | Khan Academy

Sun, 20 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/triangle-property-review/v/review-of-triangle-properties

Uploaded 20-10-11

Comparing perpendicular bisectors to angle bisectors to medians to altitudes

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/triangle_property_review/v/euler-line?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/altitudes/v/common-orthocenter-and-centroid?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Acid–base indicators | Acids and bases | AP Chemistry | Khan Academy

Sun, 20 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-titrations/e/acid-base-titrations

Uploaded 17-09-21

Acid–base indicators are compounds that change color when they become protonated or deprotonated. Because this color change occurs over a specific pH range, indicators can be used to approximate the equivalence point of an acid–base titration. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-titrations/v/acid-base-indicators

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Euler line | Special properties and parts of triangles | Geometry | Khan Academy

Sun, 20 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/triangle-property-review/v/euler-line

Uploaded 20-10-11

The magic and mystery of the Euler Line

Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/triangle_property_review/v/euler-s-line-proof?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/triangle-properties/triangle_property_review/v/review-of-triangle-properties?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1
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Weak base–strong acid titrations | Acids and bases | AP Chemistry | Khan Academy

Sun, 20 Sep 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-titrations/v/titrations-of-polyprotic-acids

Uploaded 17-09-21

For the titration of a weak base with a strong acid, the pH curve is initially basic and has an acidic equivalence point (pH is less than 7). The section of curve between the initial point and the equivalence point is known as the buffer region. At the half-equivalence point, the concentrations of the buffer components are equal, resulting in pH = pKₐ (where pKₐ refers to the conjugate acid of the weak base). View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-titrations/v/weak-base-strong-acid-titrations

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Financial Times October 2011

Sun, 20 Sep 2026 14:06:00 -0000

Sal answers questions for the Financial Times

Uploaded 20-10-11

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Weak acid–strong base titrations | Acids and bases | AP Chemistry | Khan Academy

Sun, 20 Sep 2026 12:06:00 -0000

For the titration of a weak acid with a strong base, the pH curve is initially acidic and has a basic equivalence point (pH is greater than 7). The section of curve between the initial point and the equivalence point is known as the buffer region. At the half-equivalence point, the concentrations of the buffer components are equal, resulting in pH = pKₐ. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-titrations/v/weak-acid-strong-base-titrations

Uploaded 17-09-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Potassium-argon (K-Ar) dating | Cosmology and Astronomy | Khan Academy

Sun, 20 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/biology/history-of-life-on-earth/radiometric-dating/v/potassium-argon-k-ar-dating

Uploaded 21-10-11

How K-Ar dating can be used to date very old volcanic rock and the things that might be buried in between. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/measuring-age-tutorial/v/k-ar-dating-calculation?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/measuring-age-tutorial/v/carbon-14-dating-2?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Cosmology and Astronomy channel: https://www.youtube.com/channel/UChNPnEkW8LYZ5Rwi8_A2-DA?sub_confirmation=1
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Strong acid–strong base titrations | Acids and bases | AP Chemistry | Khan Academy

Sun, 20 Sep 2026 08:06:00 -0000

The results of an acid–base titration can be summarized using a titration curve, which plots pH vs. volume of titrant added. For the titration of a strong acid with a strong base, the curve begins acidic and then turns basic after the equivalence point, which occurs at pH = 7. For the titration of a strong base with a strong acid, the curve is similar except that it begins basic and turns acidic. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-titrations/v/strong-acid-strong-base-titrations

Uploaded 17-09-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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K-Ar dating calculation | Life on earth and in the universe | Cosmology and Astronomy | Khan Academy

Sun, 20 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/biology/history-of-life-on-earth/radiometric-dating/v/k-ar-dating-calculation

Uploaded 21-10-11

Working through a calculation for K-Ar dating (good to have some prior experience with e and logarithms). Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/life-in-universe-topic/v/detectable-civilizations-in-our-galaxy-1?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/measuring-age-tutorial/v/potassium-argon-k-ar-dating?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Opportunities for high school and college tutors

Sun, 20 Sep 2026 04:06:00 -0000

Excited that now both MIT and UChicago are considering Schoolhouse.world tutor transcripts for college admissions. More universities (and employers) coming soon...
https://youtu.be/5CdSLyACbUE
If you are interested in admitting or giving internships to some of the most amazing young people in the world, you can fill out an interest form here:
https://forms.gle/nJPhees1jtxV7ZeH8#collegeadmissions #internships #universities #recentgrads

Uploaded 14-09-21

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Sums and scalar multiples of linear transformations | Linear Algebra | Khan Academy

Sun, 20 Sep 2026 02:06:00 -0000

Sums and Scalar Multiples of Linear Transformations. Definitions of matrix addition and scalar multiplication.

Uploaded 23-10-09

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/more-on-matrix-addition-and-scalar-multiplication?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/preimage-and-kernel-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Buffer capacity | Acids and bases | AP Chemistry | Khan Academy

Sun, 20 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:buffers/e/buffers

Uploaded 02-09-21

The capacity of a buffer to neutralize added acid or base depends on the concentrations of HA and A⁻ in solution. For a given ratio of [HA] to [A⁻], the greater the concentrations, the higher the overall buffer capacity. When [HA] is greater than [A⁻], the capacity is higher for added base than acid. When [A⁻] is greater than [HA], the capacity is higher for added acid than base. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:buffers/v/buffer-capacity-ap

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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More on matrix addition and scalar multiplication | Linear Algebra | Khan Academy

Sat, 19 Sep 2026 22:06:00 -0000

More on Matrix Addition and Scalar Multiplication

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/linear-transformation-examples-scaling-and-reflections?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/sums-and-scalar-multiples-of-linear-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

Uploaded 23-10-09

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Sal answers questions from attendees at his Schoolhouse.world series

Sat, 19 Sep 2026 20:06:00 -0000

Sal answers questions from attendees at his Schoolhouse.world series. Not too late to join the second session at https://schoolhouse.world/series/309?celebrate

Uploaded 27-08-21

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Linear transformation examples: Scaling and reflections | Linear Algebra | Khan Academy

Sat, 19 Sep 2026 18:06:00 -0000

Creating scaling and reflection transformation matrices (which are diagonal)

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/linear-transformation-examples-rotations-in-r2?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

Uploaded 23-10-09

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Buffer range | Acids and bases | AP Chemistry | Khan Academy

Sat, 19 Sep 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:buffers/v/buffer-capacity-ap

Uploaded 24-08-21

A buffer has an effective pH range of one pH unit on either side of the pKₐ value for the weak acid. If the pH of a buffer goes out of this range, the buffer will no longer be effective at resisting large changes in pH. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:buffers/v/buffer-range

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Linear transformation examples: Rotations in R2 | Linear Algebra | Khan Academy

Sat, 19 Sep 2026 14:06:00 -0000

Linear Transformation Examples: Rotations in R2

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/rotation-in-r3-around-the-x-axis?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/linear-transformation-examples-scaling-and-reflections?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

Uploaded 23-10-09

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Methods for preparing buffers | Acids and bases | AP Chemistry | Khan Academy

Sat, 19 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:buffers/v/buffer-range

Uploaded 24-08-21

In this video, we'll explore two common methods for preparing buffer solutions. In the first approach, a certain amount of a weak acid (or weak base) is neutralized with a strong base (or strong acid), forming a conjugate acid–base pair in solution. In the second approach, a weak acid (or weak base) is combined with a salt containing its conjugate base (or conjugate acid). View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:buffers/v/methods-for-preparing-buffers

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Rotation in R3 around the x-axis | Matrix transformations | Linear Algebra | Khan Academy

Sat, 19 Sep 2026 10:06:00 -0000

Construction a rotation transformation in R3

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/unit-vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/linear-transformation-examples-rotations-in-r2?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

Uploaded 25-10-09

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Henderson–Hasselbalch equation | Acids and bases | AP Chemistry | Khan Academy

Sat, 19 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:buffers/v/methods-for-preparing-buffers

Uploaded 24-08-21

One way to determine the pH of a buffer is by using the Henderson–Hasselbalch equation, which is pH = pKₐ + log([A⁻]/[HA]). In this equation, [HA] and [A⁻] refer to the equilibrium concentrations of the conjugate acid–base pair used to create the buffer solution. When [HA] = [A⁻], the solution pH is equal to the pKₐ of the acid. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:buffers/v/hendersonhasselbalch-equation

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Unit vectors | Matrix transformations | Linear Algebra | Khan Academy

Sat, 19 Sep 2026 06:06:00 -0000

What unit vectors are and how to construct them

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/introduction-to-projections?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/rotation-in-r3-around-the-x-axis?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

Uploaded 26-10-09

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Properties of buffers | Acids and bases | AP Chemistry | Khan Academy

Sat, 19 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:buffers/v/hendersonhasselbalch-equation

Uploaded 24-08-21

Buffer solutions contain high concentrations of both a weak acid and its conjugate base (or a weak base and its conjugate acid). Because these components can neutralize added H⁺ or OH⁻, buffers are highly resistant to changes in pH. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:buffers/v/properties-of-buffers

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Introduction to projections | Matrix transformations | Linear Algebra | Khan Academy

Sat, 19 Sep 2026 02:06:00 -0000

Determining the projection of a vector on s line

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/expressing-a-projection-on-to-a-line-as-a-matrix-vector-prod?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/unit-vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

Uploaded 26-10-09

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Cellular respiration | Energy and matter in biological systems | High school biology | Khan Academy

Sat, 19 Sep 2026 00:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:energy-and-matter-in-biological-systems/x230b3ff252126bb6:cellular-respiration/v/cellular-respiration

Uploaded 24-08-21

Cellular respiration is a chemical process in which the bonds of food molecules and oxygen molecules are broken and new compounds are formed that can transport energy to muscles. Cellular respiration also releases the energy needed to maintain body temperature despite ongoing energy transfer to the surrounding environment.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Expressing a projection on to a line as a matrix vector prod | Linear Algebra | Khan Academy

Fri, 18 Sep 2026 22:06:00 -0000

Expressing a Projection on to a line as a Matrix Vector prod

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

Uploaded 26-10-09

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Cell division and organism growth | High school biology | Khan Academy

Fri, 18 Sep 2026 20:06:00 -0000

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https://www.khanacademy.org/science/hs-biology/x4c673362230887ef:growth-and-feedback-in-organisms/x4c673362230887ef:cell-division-and-organism-growth/v/creativity-break-how-do-you-apply-creativity-to-biology

Uploaded 17-08-21

In multicellular organisms individual cells grow and then divide via a process called mitosis, thereby allowing the organism to grow. The organism begins as a single cell (fertilized egg) that divides successively to produce many cells, with each parent cell passing identical genetic material (two variants of each chromosome pair) to both daughter cells. Cellular division and differentiation produce and maintain a complex organism, composed of systems of tissues and organs that work together to meet the needs of the whole organism.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Fractional Reserve Banking Commentary 1

Fri, 18 Sep 2026 18:06:00 -0000

Understanding the weak points of Fractional Reserve Banking
More free lessons at: http://www.khanacademy.org/video?v=ZyyaE3DIxhc

Uploaded 26-10-09

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Natural selection and evolution | Mechanisms of evolution | High school biology | Khan Academy

Fri, 18 Sep 2026 16:06:00 -0000

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FRB Commentary 2: Deposit Insurance

Fri, 18 Sep 2026 14:06:00 -0000

More on the weaknesses of fractional reserve banking. The FDIC and deposit insurance and its side effects.
More free lessons at: http://www.khanacademy.org/video?v=otstXFxMkl4

Uploaded 26-10-09

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Genes, traits, and the environment | Inheritance and variation | High school biology | Khan Academy

Fri, 18 Sep 2026 12:06:00 -0000

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https://www.khanacademy.org/science/hs-biology/x4c673362230887ef:inheritance-and-variation/x4c673362230887ef:genes-traits-and-the-environment/v/mendelian-inheritance-and-punnett-squares

Uploaded 17-08-21

Environmental factors affect expression of traits, and hence affect the probability of occurrences of traits in a population. The variation and distribution of traits observed depends on both genetic and environmental factors.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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"WinningHimalayan" by Amber, licensed under a Creative Commons Attribution License (CC BY 3.0):
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FRB Commentary 3: Big Picture

Fri, 18 Sep 2026 10:06:00 -0000

Summary of thoughts in last two videos. Discussion of why Fractional Reserve Banking is a subsidy to banks and allows them to arbitrage the yield curve.
More free lessons at: http://www.khanacademy.org/video?v=8SAMey9Gl5I

Uploaded 26-10-09

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Gene expression and regulation | Inheritance and variation | High school biology | Khan Academy

Fri, 18 Sep 2026 08:06:00 -0000

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https://www.khanacademy.org/science/hs-biology/x4c673362230887ef:inheritance-and-variation/x4c673362230887ef:gene-expression-and-regulation/e/understand-gene-expression-and-regulation

Uploaded 17-08-21

Each chromosome consists of a single very long DNA molecule, and each gene on the chromosome is a particular segment of that DNA. The instructions for forming species’ characteristics are carried in DNA. All cells in an organism have the same genetic content, but the genes used (expressed) by the cell may be regulated in different ways. Not all DNA codes for a protein; some segments of DNA are involved in regulatory or structural functions, and some have no as-yet known function.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Compositions of linear transformations 1 | Matrix transformations | Linear Algebra | Khan Academy

Fri, 18 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/composition-of-transformations/v/compositions-of-linear-transformations-1

Uploaded 27-10-09

Introduction to compositions of Linear Transformations

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/composition_of_transformations/v/compositions-of-linear-transformations-2?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Stratospheric Ozone Depletion| Global change| AP Environmental Science| Khan Academy

Fri, 18 Sep 2026 04:06:00 -0000

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https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:global-change/x0b0e430a38ebd23f:ozone/e/ozone

Uploaded 16-08-21

Stratospheric ozone depletion is caused by anthropogenic factors, such as chlorofluorocarbons (CFC's), and natural factors, such as the melting of ice crystals in the atmosphere at the beginning of the Antarctic spring.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Compositions of linear transformations 2 | Matrix transformations | Linear Algebra | Khan Academy

Fri, 18 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/composition-of-transformations/v/compositions-of-linear-transformations-2

Uploaded 27-10-09

Providing the motivation for definition of matrix products

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/composition_of_transformations/v/linear-algebra-matrix-product-examples?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Pathogens and the environment| AP Environmental science| Khan Academy

Fri, 18 Sep 2026 00:06:00 -0000

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https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:aquatic-and-terrestrial-pollution/x0b0e430a38ebd23f:pathogens/e/pathogens

Uploaded 16-08-21

Pathogens, such as the pathogen that causes malaria, adapt to take advantage of new opportunities to infect and spread through human populations. As equatorial-type climate zones spread north and south into what are currently subtropical and temperate climate zones, pathogens, infectious diseases, and any associated vectors are spreading into these areas where the disease has not previously been know to occur.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Matrix product examples | Matrix transformations | Linear Algebra | Khan Academy

Thu, 17 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/composition-of-transformations/v/linear-algebra-matrix-product-examples

Uploaded 28-10-09

Example of taking the product of two matrices

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/composition_of_transformations/v/matrix-product-associativity?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Nonrenewable Energy Resources| AP Environmental science| Khan Academy

Thu, 17 Sep 2026 20:06:00 -0000

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https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:energy-resources-and-consumption/x0b0e430a38ebd23f:intro-to-energy-resources-and-consumption/e/intro-to-energy-resources-and-consumption

Uploaded 16-08-21

Nonrenewable energy sources are those that exist in a fixed amount and involve energy transformation that cannot be easily replaced.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Matrix product associativity | Matrix transformations | Linear Algebra | Khan Academy

Thu, 17 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/composition-of-transformations/v/matrix-product-associativity

Uploaded 28-10-09

Showing that matrix products are associative

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/composition_of_transformations/v/distributive-property-of-matrix-products?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Integrated pest management| Land and Water Use| AP Environmental science| Khan Academy

Thu, 17 Sep 2026 16:06:00 -0000

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https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:land-and-water-use/x0b0e430a38ebd23f:types-of-sustainable-practices/a/sustainable-agriculture

Uploaded 16-08-21

Integrated pest management (IPM) is a combination of methods used to effectively control pest species while minimizing the disruption to the environment. These methods include biological, physical, and limited chemical methods such as biocontrol, intercropping, crop rotation, and natural predators of the pests. Integrated pest management (IPM) minimizes disruptions to the environment and threats to human health but can be complex and expensive.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Distributive property of matrix products | Matrix transformations | Linear Algebra | Khan Academy

Thu, 17 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/composition-of-transformations/v/distributive-property-of-matrix-products

Uploaded 28-10-09

Showing that matrix products are associative

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/linear-algebra-introduction-to-the-inverse-of-a-function?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Demographic transition model| Human populations| AP Environmental science| Khan Academy

Thu, 17 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:populations/x0b0e430a38ebd23f:human-populations/e/human-populations

Uploaded 16-08-21

Learn to apply the demographic transition model to populations.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Introduction to the inverse of a function | Matrix transformations | Linear Algebra | Khan Academy

Thu, 17 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-transformations/v/linear-algebra-introduction-to-the-inverse-of-a-function

Uploaded 28-10-09

Introduction to the inverse of a function

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/proof-invertibility-implies-a-unique-solution-to-f-x-y?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

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https://www.khanacademy.org/math/linear-algebra/matrix_transformations/composition_of_transformations/v/distributive-property-of-matrix-products?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Weak acid–weak base reactions | Acids and bases | AP Chemistry | Khan Academy

Thu, 17 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-reactions/e/acid-base-reactions

Uploaded 10-08-21

When a weak acid and a weak base are mixed, they come to an equilibrium state represented by the following equation: HA(aq) + B(aq) ⇌ A⁻(aq) + HB⁺(aq). The equilibrium position lies on the side of the weaker acid and the weaker base, and we can determine whether the resulting solution is acidic, basic, or neutral by comparing the Ka and Kb values of these species. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-reactions/v/weak-acid-weak-base-reactions

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Proof: Invertibility implies a unique solution to f(x)=y | Linear Algebra | Khan Academy

Thu, 17 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-transformations/v/proof-invertibility-implies-a-unique-solution-to-f-x-y

Uploaded 28-10-09

Proof: Invertibility implies a unique solution to f(x)=y for all y in co-domain of f.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/surjective-onto-and-injective-one-to-one-functions?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/linear-algebra-introduction-to-the-inverse-of-a-function?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Weak base–strong acid reactions | Acids and bases | AP Chemistry | Khan Academy

Thu, 17 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-reactions/v/weak-acid-weak-base-reactions

Uploaded 10-08-21

When a weak base and a strong acid are mixed, they react according to the following net-ionic equation: B(aq) + H₃O⁺(aq) → HB⁺(aq) + H₂O(l). If the acid and base are equimolar, the pH of the resulting solution can be determined by considering the equilibrium reaction of HB⁺ with water. If the base is in excess, the pH can be determined from the concentrations of B and HB⁺ after the reaction. If the acid is in excess, the pH can be determined from the concentration of excess H₃O⁺. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-reactions/v/weak-base-strong-acid-reactions

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Surjective (onto) and injective (one-to-one) functions | Linear Algebra | Khan Academy

Thu, 17 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-transformations/v/surjective-onto-and-injective-one-to-one-functions

Uploaded 29-10-09

Introduction to surjective and injective functions

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/relating-invertibility-to-being-onto-and-one-to-one?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/proof-invertibility-implies-a-unique-solution-to-f-x-y?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Worked example: Calculating the pH after a weak acid–strong base reaction (excess acid)

Thu, 17 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-reactions/v/weak-base-strong-acid-reactions

Uploaded 10-08-21

When a strong base reacts with excess weak acid, the resulting solution contains both HA and A⁻. We can use reaction stoichiometry to determine the concentration of each species and then solve a common-ion equilibrium problem to find [H₃O⁺] and thus the pH. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-reactions/v/worked-example-calculating-the-ph-after-a-weak-acid-strong-base-reaction-excess-acid

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Relating invertibility to being onto and one-to-one | Linear Algebra | Khan Academy

Wed, 16 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-transformations/v/relating-invertibility-to-being-onto-and-one-to-one

Uploaded 29-10-09

Relating invertibility to being onto (surjective) and one-to-one (injective)

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/determining-whether-a-transformation-is-onto?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/surjective-onto-and-injective-one-to-one-functions?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Weak acid–strong base reactions | Acids and bases | AP Chemistry | Khan Academy

Wed, 16 Sep 2026 20:06:00 -0000

When a weak acid and a strong base are mixed, they react according to the following net-ionic equation: HA(aq) + OH⁻(aq) → A⁻(aq) + H₂O(l). If the acid and base are equimolar, the pH of the resulting solution can be determined by considering the equilibrium reaction of A⁻ with water. If the acid is in excess, the pH can be determined from the concentrations of HA and A⁻ after the reaction. If the base is in excess, the pH can be determined from the concentration of excess OH⁻. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-reactions/v/weak-acid-strong-base-reactions

Uploaded 10-08-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Determining whether a transformation is onto | Linear Algebra | Khan Academy

Wed, 16 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-transformations/v/determining-whether-a-transformation-is-onto

Uploaded 29-10-09

Determining whether a transformation is onto

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/linear-algebra-exploring-the-solution-set-of-ax-b?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/relating-invertibility-to-being-onto-and-one-to-one?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Strong acid–strong base reactions | Acids and bases | AP Chemistry | Khan Academy

Wed, 16 Sep 2026 16:06:00 -0000

When a strong acid and a strong base are mixed, they react according to the following net-ionic equation: H₃O⁺(aq) + OH⁻(aq) → 2H₂O(l). If either the acid or the base is in excess, the pH of the resulting solution can be determined from the concentration of excess reactant. If the acid and base are equimolar, the pH of the solution is 7.00 at 25°C. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:acidbase-reactions/v/strong-acid-strong-base-reactions

Uploaded 10-08-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Simple Analysis of Cost per Job Saved from Stimulus

Wed, 16 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/current-economics/unemployment-tutorial/v/simple-analysis-of-cost-per-job-saved-from-stimulus

Uploaded 30-10-09

Simple analysis of cost per job saved from stimulus
More free lessons at: http://www.khanacademy.org/video?v=sSqxVMbml_k

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Sal's back to school 2021 message

Wed, 16 Sep 2026 12:06:00 -0000

As we enter into an unusual back to school, Sal shares some reflections on the past year and what we are hopeful for this year.

Uploaded 10-08-21

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Exploring the solution set of Ax = b | Matrix transformations | Linear Algebra | Khan Academy

Wed, 16 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-transformations/v/linear-algebra-exploring-the-solution-set-of-ax-b

Uploaded 30-10-09

Exploring the solution set of Ax=b (non homogeneous equations)

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/linear-algebra-matrix-condition-for-one-to-one-trans?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/determining-whether-a-transformation-is-onto?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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LearnStorm 2021 - Khan Academy LearnStorm

Wed, 16 Sep 2026 08:06:00 -0000

WELCOME TO LEARNSTORM 2021

LearnStorm brings teachers and students together to build skills and mindsets for a successful school year, for free! As always, the program uses standards-aligned Khan Academy content that supplements your back-to-school instruction. This year, you'll have from 8/9 through 11/21 to enjoy seeing your students motivated to learn by completing assignments, having fun, and earn prizes!

Uploaded 06-08-21

See LearnStorm in action! https://learnstorm.khanacademy.org

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Matrix condition for one-to-one trans | Matrix transformations | Linear Algebra | Khan Academy

Wed, 16 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-transformations/v/linear-algebra-matrix-condition-for-one-to-one-trans

Uploaded 30-10-09

Showing that the rank of the of an mxn transformation matrix has to be an for the transformation to be one-to-one (injective)

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/linear-algebra-simplifying-conditions-for-invertibility?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/linear-algebra-exploring-the-solution-set-of-ax-b?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Adaptation and environmental change | Mechanisms of evolution | High school biology | Khan Academy

Wed, 16 Sep 2026 04:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:mechanisms-of-evolution-hs/x230b3ff252126bb6:natural-selection-and-adaptation/v/adaptation-and-environmental-change

Uploaded 05-08-21

Adaptations in organisms respond to environmental changes through natural selection, which promotes traits enhancing survival and reproduction. There are three selection types: directional, disruptive, and stabilizing. Explore case studies of snow voles and dung beetles to learn how species evolve in response to new environmental conditions.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Simplifying conditions for invertibility | Matrix transformations | Linear Algebra | Khan Academy

Wed, 16 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-transformations/v/linear-algebra-simplifying-conditions-for-invertibility

Uploaded 30-10-09

Showing that a transformation is invertible if and only if rref(A) is equal to the identity matrix

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/linear-algebra-showing-that-inverses-are-linear?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/linear-algebra-matrix-condition-for-one-to-one-trans?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Factors affecting acid strength | Acids and bases | AP Chemistry | Khan Academy

Wed, 16 Sep 2026 00:06:00 -0000

The relative strength of an acid can be predicted based on its chemical structure. In general, an acid is stronger when the H–A bond is more polar. Acidity is also greater when the H–A bond is weaker and when the conjugate base, A⁻, is more stable. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:molecular-structure-of-acids-and-bases/v/factors-affecting-acid-strength

Uploaded 30-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Showing that inverses are linear | Matrix transformations | Linear Algebra | Khan Academy

Tue, 15 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-transformations/v/linear-algebra-showing-that-inverses-are-linear

Uploaded 30-10-09

Showing that inverse transformations are also linear

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-deriving-a-method-for-determining-inverses?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/linear-algebra-simplifying-conditions-for-invertibility?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Acid–base properties of salts | Acids and bases | AP Chemistry | Khan Academy

Tue, 15 Sep 2026 20:06:00 -0000

We can determine whether a salt solution will be acidic, basic, or neutral by considering the reactivity of both the cation and the anion with water. If neither species reacts with water, the solution will be neutral. If only the cation reacts with water, the solution will be acidic. If only the anion reacts with water, the solution will be basic. If both species react with water, the pH of the solution will depend on the relative strengths of the cation and the anion. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:weak-acid-and-base-equilibria/v/acid-base-properties-of-salts

Uploaded 30-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Deriving a method for determining inverses | Matrix transformations | Linear Algebra | Khan Academy

Tue, 15 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-of-matrices/v/linear-algebra-deriving-a-method-for-determining-inverses

Uploaded 31-10-09

Determining a method for constructing inverse transformation matrices

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-example-of-finding-matrix-inverse?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_transformations/v/linear-algebra-showing-that-inverses-are-linear?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Weak base equilibria | Acids and bases | AP Chemistry | Khan Academy

Tue, 15 Sep 2026 16:06:00 -0000

Weak bases partially ionize in water to produce hydroxide ions. Because the ionization is not complete, the concentration of OH⁻ in a weak base solution is typically much less than the initial base concentration. The relative strength of a weak base is described by the base ionization constant, Kb, which is the equilibrium constant for the reaction of the weak base with water. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:weak-acid-and-base-equilibria/v/weak-base-equilibria

Uploaded 30-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Example of finding matrix inverse | Matrix transformations | Linear Algebra | Khan Academy

Tue, 15 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-of-matrices/v/linear-algebra-example-of-finding-matrix-inverse

Uploaded 31-10-09

Example of calculating the inverse of a matrix

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-formula-for-2x2-inverse?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-deriving-a-method-for-determining-inverses?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Worked example: Finding the percent ionization of a weak acid | AP Chemistry | Khan Academy

Tue, 15 Sep 2026 12:06:00 -0000

The percent ionization of a weak acid, HA, is defined as the ratio of the equilibrium H₃O⁺ concentration to the initial HA concentration, multiplied by 100%. In this video, we'll use this relationship to find the percent ionization of acetic acid in a 0.20 M solution. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:weak-acid-and-base-equilibria/v/worked-example-finding-the-percent-ionization-of-a-weak-acid

Uploaded 30-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Calculating slope of tangent line using derivative definition | Differential Calculus | Khan Academy

Tue, 15 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-2/v/calculus-derivatives-2-new-hd-version

Uploaded 02-11-09

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/e/tangent-slope-is-limiting-value-of-secant-slope?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/calculus-derivatives-2-new-hd-version?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/tangent-slope-as-limiting-value-of-secant-slope-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Weak acid equilibria | Acids and bases | AP Chemistry | Khan Academy

Tue, 15 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:weak-acid-and-base-equilibria/v/worked-example-finding-the-percent-ionization-of-a-weak-acid

Uploaded 30-07-21

Unlike strong acids, weak acids only partially ionize in aqueous solution. As a result, the concentration of H₃O⁺ in a weak acid solution is typically much less than the initial acid concentration. The relative strength of a weak acid is described by the acid ionization constant, Kₐ, which is the equilibrium constant for the reaction of the weak acid with water. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:weak-acid-and-base-equilibria/v/weak-acid-equilibria

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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The derivative of f(x)=x^2 for any x | Taking derivatives | Differential Calculus | Khan Academy

Tue, 15 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-2/v/calculus-derivatives-2-5-new-hd-version

Uploaded 02-11-09

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/alternate-form-of-the-derivative?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/calculus-derivatives-2-new-hd-version?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Strong base solutions | Acids and bases | AP Chemistry | Khan Academy

Tue, 15 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:ph-and-poh-of-strong-acids-and-bases/e/ph-and-poh-of-strong-acids-and-bases

Uploaded 30-07-21

Strong bases (such as Group 1 and 2 metal hydroxides) dissociate completely in water to produce hydroxide ions. The concentration of OH⁻ in a strong base solution can therefore be determined from the initial concentration of the base and the stoichiometry of the dissolution. For example, the strong base Ba(OH)₂ dissociates to give two OH⁻ ions per formula unit, so a 0.1 M Ba(OH)₂ solution has an OH⁻ concentration of 0.2 M. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:ph-and-poh-of-strong-acids-and-bases/v/strong-base-solutions

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Derivative as slope of a tangent line | Taking derivatives | Differential Calculus | Khan Academy

Tue, 15 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-2/v/calculus-derivatives-1-new-hd-version

Uploaded 02-11-09

Understanding that the derivative is just the slope of a curve at a point (or the slope of the tangent line)

Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/skill-check--tangent-lines?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/tangent-slope-as-limiting-value-of-secant-slope-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/secant-line-slope-tangent/v/approximating-equation-of-tangent-line-word-problem-1?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Strong acid solutions | Acids and bases | AP Chemistry | Khan Academy

Tue, 15 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:ph-and-poh-of-strong-acids-and-bases/v/strong-base-solutions

Uploaded 30-07-21

Strong acids (such as HCl, HBr, HI, HNO₃, HClO₄, and H₂SO₄) ionize completely in water to produce hydronium ions. The concentration of H₃O⁺ in a strong acid solution is therefore equal to the initial concentration of the acid. For example, a solution of 0.1 M HNO₃ contains 0.1 M H₃O⁺ and has a pH of 1.0. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:ph-and-poh-of-strong-acids-and-bases/v/strong-acid-solutions

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Formula for 2x2 inverse | Matrix transformations | Linear Algebra | Khan Academy

Mon, 14 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-of-matrices/v/linear-algebra-formula-for-2x2-inverse

Uploaded 02-11-09

Figuring out the formula for a 2x2 matrix. Defining the determinant.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-3x3-determinant?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-example-of-finding-matrix-inverse?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Worked examples: Calculating [H₃O⁺] and pH | Acids and bases | AP Chemistry | Khan Academy

Mon, 14 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:introduction-to-acids-and-bases/e/introduction-to-acids-and-bases

Uploaded 30-07-21

In this video, we'll solve for [H₃O⁺] and pH in two different worked examples. First, we'll walk through the possible approaches for calculating [H₃O⁺] from pOH. Then, we'll find the pH of pure water at 50°C from the value of the autoionization constant at 50°C. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:introduction-to-acids-and-bases/v/worked-examples-calculating-hydronium-ion-concentration-and-ph

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Introduction to scientific notation | Pre-Algebra | Khan Academy

Mon, 14 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/in-in-class-7th-math-cbse/x939d838e80cf9307:exponents-and-powers/x939d838e80cf9307:large-numbers-in-standard-form/v/scientific-notation-old

Uploaded 02-11-09

Introduction to scientific notation. An in-depth discussion about why and how scientific notation is used.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/exponents-radicals/scientific-notation/e/scientific_notation_intuition?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/exponents-radicals/scientific-notation/v/scientific-notation?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/negative-exponents-tutorial/v/zero-negative-and-fractional-exponents?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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The pH scale | Acids and bases | AP Chemistry | Khan Academy

Mon, 14 Sep 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:introduction-to-acids-and-bases/v/worked-examples-calculating-hydronium-ion-concentration-and-ph

Uploaded 30-07-21

The pH scale is a convenient way to represent the acidity or basicity of a solution. We can calculate the pH of a solution by taking the negative logarithm of the hydronium ion concentration, or pH = -log[H₃O⁺]. At 25°C, a solution with a pH less than 7 is acidic, a solution with a pH greater than 7 is basic, and a solution with a pH equal to 7 is neutral. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:introduction-to-acids-and-bases/v/the-ph-scale

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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3 x 3 determinant | Matrix transformations | Linear Algebra | Khan Academy

Mon, 14 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-of-matrices/v/linear-algebra-3x3-determinant

Uploaded 02-11-09

Determinants: Finding the determinant of a 3x3 matrix

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-nxn-determinant?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-formula-for-2x2-inverse?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Autoionization of water | Acids and bases | AP Chemistry | Khan Academy

Mon, 14 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:introduction-to-acids-and-bases/v/the-ph-scale

Uploaded 30-07-21

In the autoionization of water, a proton is transferred from one water molecule to another to produce a hydronium ion (H₃O⁺) and a hydroxide ion (OH⁻). The equilibrium expression for this reaction is Kw = [H₃O⁺][OH⁻], where Kw is the autoionization constant for water. At 25°C, the value of Kw is 1.0 x 10⁻¹⁴. In pure water, the concentrations of H₃O⁺ and OH⁻ are equal, and the water is considered to be neutral. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:acids-and-bases/x2eef969c74e0d802:introduction-to-acids-and-bases/v/autoionization-of-water-ap

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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n x n determinant | Matrix transformations | Linear Algebra | Khan Academy

Mon, 14 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-of-matrices/v/linear-algebra-nxn-determinant

Uploaded 02-11-09

Defining the determinant for nxn matrices. An example of a 4x4 determinant.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-determinants-along-other-rows-cols?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-3x3-determinant?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Digital and analog information | Information Technologies | High School Physics | Khan Academy

Mon, 14 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-physics/x215e29cb31244fa1:information-technologies/x215e29cb31244fa1:information-in-waves/e/understand-information-in-waves

Uploaded 29-07-21

Analog information can be digitized and stored reliably in computer memory. This way it can be sent over long distances as a series of wave pulses. Learn about the differences between digital and analog information and how digital information is created.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

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Determinants along other rows/cols | Matrix transformations | Linear Algebra | Khan Academy

Mon, 14 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-of-matrices/v/linear-algebra-determinants-along-other-rows-cols

Uploaded 02-11-09

Finding the determinant by going along other rows or columns

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-rule-of-sarrus-of-determinants?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-nxn-determinant?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Wave properties | Wave properties | High School Physics | Khan Academy

Mon, 14 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-physics/x215e29cb31244fa1:wave-properties/x215e29cb31244fa1:waves/e/understand-mechanical-waves

Uploaded 29-07-21

The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

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Rule of Sarrus of determinants | Matrix transformations | Linear Algebra | Khan Academy

Mon, 14 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-of-matrices/v/linear-algebra-rule-of-sarrus-of-determinants

Uploaded 02-11-09

A alternative "short cut" for calculating 3x3 determinants (Rule of Sarrus)

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-when-row-multiplied-by-scalar?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-determinants-along-other-rows-cols?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Calculating height using energy | Modeling Energy | High School Physics | Khan Academy

Mon, 14 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-physics/x215e29cb31244fa1:modeling-energy/x215e29cb31244fa1:predictions-using-energy/e/understand-predictions-using-energy

Uploaded 29-07-21

Learn how you can calculate the maximum height of a launched object by using the total energy of a system. Energy that is conserved can be transferred within a system from one object to another changing the characteristics of each object, like position.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

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Detectable civilizations in our galaxy 5 | Cosmology and Astronomy | Khan Academy

Sun, 13 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/life-in-universe-topic/v/detectable-civilizations-in-our-galaxy-5

Uploaded 23-05-11

Apsidal Precession (Perihelion Precession). Created by Sal Khan.

This is the last video in our Cosmology and Astronom subject! Now move on to our first video in Computing: https://www.khanacademy.org/computing/computer-programming/programming/intro-to-programming/v/programming-intro=Computing

Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/life-in-universe-topic/v/detectable-civilizations-in-our-galaxy-4?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy

Cosmology and Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Calculating velocity using energy | Modeling Energy | High School Physics | Khan Academy

Sun, 13 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-physics/x215e29cb31244fa1:modeling-energy/x215e29cb31244fa1:predictions-using-energy/v/calculating-height-using-energy

Uploaded 29-07-21

Learn how you can calculate the launch velocity of an object by using the total energy of a system. Energy that is conserved can be transferred within a system from one object to another changing the characteristics of each object, like velocity.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

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Determinant when row multiplied by scalar | Matrix transformations | Linear Algebra | Khan Academy

Sun, 13 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-determinant-when-row-multiplied-by-scalar

Uploaded 03-11-09

The determinant when a row is multiplied by a scalar

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-correction-scalar-muliplication-of-row?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/inverse_of_matrices/v/linear-algebra-rule-of-sarrus-of-determinants?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Natural selection and adaptation | Mechanisms of evolution | High school biology | Khan Academy

Sun, 13 Sep 2026 16:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:mechanisms-of-evolution-hs/x230b3ff252126bb6:natural-selection-and-adaptation/v/natural-selection-and-adaptation

Uploaded 28-07-21

Natural selection leads to adaptation, that is, to a population dominated by organisms that are anatomically, behaviorally, and physiologically well suited to survive and reproduce in a specific environment. That is, the differential survival and reproduction of organisms in a population that have an advantageous heritable trait leads to an increase in the proportion of individuals in future generations that have the trait and to a decrease in the proportion of individuals that do not.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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(correction) scalar multiplication of row | Matrix transformations | Linear Algebra | Khan Academy

Sun, 13 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-correction-scalar-muliplication-of-row

Uploaded 03-11-09

Correction of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-when-row-is-added?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-when-row-multiplied-by-scalar?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Acid Rain| Atmospheric Pollution| AP Environmental science| Khan Academy

Sun, 13 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:atmospheric-pollution/x0b0e430a38ebd23f:other-atmospheric-pollution/e/other-atmospheric-pollution

Uploaded 28-07-21

Acid rain and deposition is due to nitrogen oxides and sulfur oxides from anthropogenic and natural sources in the atmosphere. Nitric oxides that cause acid deposition come from motor vehicles and coal-burning power plants. Sulfur dioxides that cause acid deposition come from coal-burning power plants. Acid deposition mainly affects communities that are downwind from coal-burning power plants. Acid rain and deposition can lead to the acidification of soils and bodies of water and corrosion of human-made structures.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

Credits:

"Acid damaged gargoyle" by Nino Barbieri [Public domain], via Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:-_Acid_rain_damaged_gargoyle_-.jpg

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Determinant when row is added | Matrix transformations | Linear Algebra | Khan Academy

Sun, 13 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-determinant-when-row-is-added

Uploaded 03-11-09

The determinant when one matrix has a row that is the sum of the rows of other matrices (and every other term is identical in the 3 matrices)

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-duplicate-row-determinant?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-correction-scalar-muliplication-of-row?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Evolution of group behavior | Mechanisms of evolution | High school biology | Khan Academy

Sun, 13 Sep 2026 08:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:mechanisms-of-evolution-hs/x230b3ff252126bb6:group-behavior-and-evolution/v/evolution-of-group-behavior

Uploaded 27-07-21

Evolution influences group behaviors that enhance survival and reproduction. Fish school to evade predators, and wildebeest herd to protect their young. These behaviors not only offer protection but also aid in passing on genetic material, highlighting the relationship between individual and group survival strategies.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Credits:
"Large fish school" by OpenStax College, licensed under a Creative Commons Attribution License (CC BY-SA 3.0):
https://commons.wikimedia.org/wiki/File:Large_fish_school.png
https://creativecommons.org/licenses/by-sa/3.0/deed.en

"The leading gnu" by Vincenzo Gianferrari Pini, licensed under a Creative Commons Attribution License (CC BY-SA 2.5 IT):
https://commons.wikimedia.org/wiki/File:The_leading_gnu.JPG
https://creativecommons.org/licenses/by-sa/2.5/it/deed.en

"Elephants are extremely protective of their young. At the sight of our jeep, adults surround the infants. Around 175 jee - Flickr - Al Jazeera English" by Al Jazeera English, licensed under a Creative Commons Attribution License (CC BY-SA 2.0):
https://commons.wikimedia.org/wiki/File:Elephants_are_extremely_protective_of_their_young._At_the_sight_of_our_jeep,_adults_surround_the_infants._Around_175_jee_-_Flickr_-_Al_Jazeera_English.jpg
https://creativecommons.org/licenses/by-sa/2.0/deed.en

"Canis lupus pack surrounding Bison" by Doug Smith [Public domain], via Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:Canis_lupus_pack_surrounding_Bison.jpg

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Duplicate row determinant | Matrix transformations | Linear Algebra | Khan Academy

Sun, 13 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-duplicate-row-determinant

Uploaded 03-11-09

Determinant of a matrix with duplicate rows

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-after-row-operations?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-when-row-is-added?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Ocean acidification | Biodiversity and human impacts | High school biology | Khan Academy

Sun, 13 Sep 2026 04:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:biodiversity-and-human-impacts/x230b3ff252126bb6:global-change-biology/v/ocean-acidification

Uploaded 26-07-21

Ocean acidification, a result of increased atmospheric carbon dioxide, is making our oceans more acidic, disrupting the formation of calcium carbonate in sea life and disturbing their homeostasis. This phenomenon is linked to emissions from human activities, such as the combustion of fossil fuels, driving vehicles, and deforestation.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Determinant after row operations | Matrix transformations | Linear Algebra | Khan Academy

Sun, 13 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-determinant-after-row-operations

Uploaded 03-11-09

What happens to the determinant when we perform a row operation

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-upper-triangular-determinant?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-duplicate-row-determinant?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Science, technology, and the environment | High school biology | Khan Academy

Sun, 13 Sep 2026 00:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:biodiversity-and-human-impacts/x230b3ff252126bb6:sustainability/v/science-technology-and-the-environment

Uploaded 26-07-21

Scientists and engineers are using banana peels and leaves to create biodegradable materials, such as shoe soles and containers, which help to reduce plastic waste and promote sustainability. Other green technologies include solar panels and windmills, which harness renewable energy sources to reduce reliance on fossil fuels and decrease greenhouse gas emissions. However, there are challenges and drawbacks of implementing these technologies, such as initial high costs and potential job losses in conventional industries.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Credits:
"Bananas" by Elembis [Public domain], via Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:Bananas.svg

"Gobabeb solar panels" by GbbIT, licensed under a Creative Commons Attribution License (CC BY-SA 3.0):
https://commons.wikimedia.org/wiki/File:Gobabeb_solar_panels.jpg
https://creativecommons.org/licenses/by-sa/3.0/deed.en

"Wind Mill of Bangui, Ilocos Norte" by JufelBaldado, licensed under a Creative Commons Attribution License (CC BY-SA 3.0):
https://commons.wikimedia.org/wiki/File:Wind_Mill_of_Bangui,_Ilocos_Norte.jpg
https://creativecommons.org/licenses/by-sa/3.0/deed.en

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Upper triangular determinant | Matrix transformations | Linear Algebra | Khan Academy

Sat, 12 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-upper-triangular-determinant

Uploaded 03-11-09

The determinant of an upper triangular matrix

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-simpler-4x4-determinant?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-after-row-operations?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Solid waste disposal| Aquatic and Terrestrial Pollution| AP Environmental science| Khan Academy

Sat, 12 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:aquatic-and-terrestrial-pollution/x0b0e430a38ebd23f:waste-disposal-reduction-and-treatment/e/waste-disposal-reduction-and-treatment

Uploaded 23-07-21

Solid waste is any discarded material that is not a liquid or gas. It is generated in domestic, industrial, business, and agricultural sectors. Solid waste is most often disposed of in landfills. Landfills can contaminate groundwater and release harmful gases. A sanitary municipal landfill consists of a bottom liner (plastic or clay), a storm water collection system, a leachate collection system, a cap, and a methane collection system. Factors in landfill decomposition include the composition of the trash and conditions needed for microbial decomposition of the waste. Solid waste can also be disposed of through incineration, where waste is burned at high temperatures. This method significantly reduces the volume of solid waste but releases air pollutants.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

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Simpler 4x4 determinant | Matrix transformations | Linear Algebra | Khan Academy

Sat, 12 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-simpler-4x4-determinant

Uploaded 03-11-09

Calculating a 4x4 determinant by putting in in upper triangular form first.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-and-area-of-a-parallelogram?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-upper-triangular-determinant?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Extinction | Common ancestry and phylogeny | High school biology | Khan Academy

Sat, 12 Sep 2026 16:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:common-ancestry-and-phylogeny/x230b3ff252126bb6:key-events-in-the-history-of-life/v/extinction

Uploaded 22-07-21

Species become extinct because they can no longer survive and reproduce in their altered environment. If members cannot adjust to change that is too fast or drastic, the opportunity for the species’ evolution is lost.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

Credits:
"Extinctions since 1500" from IPBES (2019): Global assessment report on biodiversity and ecosystem services of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services. E. S. Brondizio, J. Settele, S. Díaz, and H. T. Ngo (editors). IPBES secretariat, Bonn, Germany. 1148 pages., licensed under a Creative Commons Attribution License (Attribution 4.0 International):
https://doi.org/10.5281/zenodo.3831673
https://creativecommons.org/licenses/by/4.0/legalcode

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Determinant and area of a parallelogram | Matrix transformations | Linear Algebra | Khan Academy

Sat, 12 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-determinant-and-area-of-a-parallelogram

Uploaded 04-11-09

Realizing that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-as-scaling-factor?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Species and the environment | Mechanisms of evolution | High school biology | Khan Academy

Sat, 12 Sep 2026 12:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:mechanisms-of-evolution-hs/x230b3ff252126bb6:speciation-and-other-patterns-of-evolution/v/species-and-the-environment

Uploaded 21-07-21

Changes in the physical environment, whether naturally occurring or human induced, have contributed to the expansion of some species, the emergence of new distinct species as populations diverge under different conditions, and the decline—and sometimes the extinction—of some species.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Determinant as scaling factor | Matrix transformations | Linear Algebra | Khan Academy

Sat, 12 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-determinant-as-scaling-factor

Uploaded 04-11-09

Viewing the determinant of the transformation matrix as a scaling factor of regions

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-transpose-of-a-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-and-area-of-a-parallelogram?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Introduction to sustainability| Land and water use| AP Environmental science| Khan Academy

Sat, 12 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:land-and-water-use/x0b0e430a38ebd23f:intro-to-sustainable-practices/e/intro-to-sustainable-practices

Uploaded 21-07-21

Sustainability refers to humans living on Earth and their use of resources without depletion of the resources for future generations. Environmental indicators that can guide humans to sustainability include biological diversity, food production, average global surface temperatures and CO2 concentrations, human population, and resource depletion. Sustainable yield is the amount of a renewable resource that can be taken without reducing the available supply.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Transpose of a matrix | Matrix transformations | Linear Algebra | Khan Academy

Sat, 12 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/linear-algebra-transpose-of-a-matrix

Uploaded 04-11-09

Transpose of a matrix

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-determinant-of-transpose?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-as-scaling-factor?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Heat transfer | Thermodynamics | High school physics | Khan Academy

Sat, 12 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-physics/x215e29cb31244fa1:modeling-energy/x215e29cb31244fa1:thermodynamics/v/specific-heat-and-latent-leat-of-fusion-and-vaporization-2

Uploaded 19-07-21

Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down).

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Transpose of a matrix product | Matrix transformations | Linear Algebra | Khan Academy

Sat, 12 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/linear-algebra-transpose-of-a-matrix-product

Uploaded 04-11-09

Taking the transpose of the product of two matrices

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-transposes-of-sums-and-inverses?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-determinant-of-transpose?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Solar Energy| Energy Resources and Consumption| AP Environmental science| Khan Academy

Sat, 12 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:energy-resources-and-consumption/x0b0e430a38ebd23f:fuel-types-and-uses-ii/e/fuel-types-and-uses-ii

Uploaded 19-07-21

Passive solar energy systems absorb heat directly from the sun without the use of mechanical and electric equipment, and energy cannot be collected or stored. Active solar energy systems use solar energy to heat a liquid through mechanical and electric equipment to collect and store the energy captured from the sun. Photovoltaic solar cells capture light energy from the sun and transform it directly into electrical energy. Their use is limited by the availability of sunlight.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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"Greenroof" by pnwra [Public domain], via Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:Green_Roof_(460698511).jpg

"Santa Fe adobe" by Carol m [Public domain], via Wikimedia Commons:
https://en.wikipedia.org/wiki/Adobe#/media/File:Santa_Fe_adobe.jpg

"Home awnings" by Conarty [Public domain], via Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:Home_Awnings.jpg

"Thermal solar collector" by Norbert Nagel [Public domain], via Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:Solar_heating_system_-_Thermosolaranlage_-_M%C3%B6rfelden-Walldorf_-_Germany.jpg

"Ivanpah" by Craig Butz [Public domain], via Wikimedia Commons:
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"Heliostats" by Alexchris [Public domain], via Wikimedia Commons:
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"Mersin CSP field" by Kohsman [Public domain], via Wikimedia Commons:
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"Solar calculator" by Rfassbind [Public domain], via Wikimedia Commons:
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Determinant of transpose | Matrix transformations | Linear Algebra | Khan Academy

Fri, 11 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/linear-algebra-determinant-of-transpose

Uploaded 05-11-09

Proof by induction that transposing a matrix does not change its determinant

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-transpose-of-a-matrix-product?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-transpose-of-a-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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The Indefinite Article | Parts of Speech | Grammar | Khan Academy

Fri, 11 Sep 2026 20:06:00 -0000

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https://www.khanacademy.org/humanities/grammar/parts-of-speech-the-modifier/introduction-to-adjectives-and-articles/e/choosing-between-definite-and-indefinite-articles

Uploaded 19-07-21

Articles are special adjectives, like "A", "An", and "The". But when do you choose "A", and when do you choose "An"? Let's find out.

Practice this yourself on Khan Academy right now: https://www.khanacademy.org/humanities/grammar/parts-of-speech-the-modifier/introduction-to-adjectives-and-articles/e/choosing-between-definite-and-indefinite-articles?utm_source=YT&utm_medium=Desc&utm_campaign=grammar

Watch the next lesson: https://www.khanacademy.org/humanities/grammar/parts-of-speech-the-modifier/introduction-to-adverbs/v/intro-to-adverbs?utm_source=YT&utm_medium=Desc&utm_campaign=grammar

Missed the previous lesson? https://www.khanacademy.org/humanities/grammar/parts-of-speech-the-modifier/introduction-to-adjectives-and-articles/v/intro-to-articles-v1?utm_source=YT&utm_medium=Desc&utm_campaign=grammar

Grammar on Khan Academy: Grammar is the collection of rules and conventions that make languages go. This section is about Standard American English, but there's something here for everyone.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Transposes of sums and inverses | Matrix transformations | Linear Algebra | Khan Academy

Fri, 11 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/linear-algebra-transposes-of-sums-and-inverses

Uploaded 05-11-09

Transposes of sums and inverses

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-transpose-of-a-vector?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-transpose-of-a-matrix-product?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Pollution and human health| Aquatic and Terrestrial Pollution| Khan Academy

Fri, 11 Sep 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:aquatic-and-terrestrial-pollution/x0b0e430a38ebd23f:pollution-and-health/e/pollution-and-health

Uploaded 16-07-21

It can be difficult to establish a cause and effect between pollutants and human health issues because humans experience exposure to a variety of chemicals and pollutants.
Mesothelioma is a type of cancer caused mainly by exposure to asbestos.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

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"Crossfit gym" by IKjub [Public domain], via Wikimedia Commons
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"Chicago" by Space-Age Meat [Public domain], via Wikimedia Commons
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"Health effects of pollution" by Mikael Häggström [Public domain], via Wikimedia Commons
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"Vehicle emissions" by State of Washington [Public domain], via https://ecology.wa.gov/
https://ecology.wa.gov/Air-Climate/Air-quality/Vehicle-emissions#gallery

"A woman having a dry cough" by unsplash [Public domain], via Wikimedia Commons
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"Lung x-ray" James Heilman, MD [Public domain], via Wikimedia Commons
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"Asbestos mineral" by Aram Dulyan [Public domain], via Wikimedia Commons
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"Chimney" [top right] by 攝影師 [Public domain], via Wikimedia Commons/
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"Roofing" [bottom right] by Андрей Перцев [Public domain], via Wikimedia Commons
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"Asbestos dump sign" by Hollingsworth John and Karen, [Public domain], via Wikimedia Commons
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Transpose of a vector | Matrix transformations | Linear Algebra | Khan Academy

Fri, 11 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/linear-algebra-transpose-of-a-vector

Uploaded 05-11-09

Transpose of a column vector. Matrix-matrix products using vectors

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-rowspace-and-left-nullspace?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-transposes-of-sums-and-inverses?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Mendelian inheritance and Punnett squares | High school biology | Khan Academy

Fri, 11 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-biology/x4c673362230887ef:inheritance-and-variation/x4c673362230887ef:genes-traits-and-the-environment/v/dihybrid-cross-and-the-law-of-independent-assortment

Uploaded 15-07-21

Gregor Mendel followed patterns of inheritance in pea plants, allowing him to elucidate the rules of inheritance, which we can now attribute to the behavior of chromosomes during meiosis. Punnett squares can be used to predict the outcome of a cross between two parents.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Credits:
"Gregor Mendel 2" by Unknown author [Public domain], via Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:Gregor_Mendel_2.jpg

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Introduction to ratios | Ratios, proportions, units, and rates | Pre-Algebra | Khan Academy

Fri, 11 Sep 2026 10:06:00 -0000

What a ratio is. Simple ratio problems.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/ratios_and_proportions/e/ratio_word_problems?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/ratios_and_proportions/v/ratios-as-fractions-in-simplest-form?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/number-sets-pre-alg/v/number-sets-3?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

Uploaded 05-11-09

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Sources of genetic variation | Inheritance and variation | High school biology | Khan Academy

Fri, 11 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-biology/x4c673362230887ef:inheritance-and-variation/x4c673362230887ef:sources-of-genetic-variation/e/understand-sources-of-genetic-variation

Uploaded 15-07-21

In sexual reproduction, chromosomes can sometimes swap sections during the process of meiosis (cell division), thereby creating new genetic combinations and thus more genetic variation. Although DNA replication is tightly regulated and remarkably accurate, errors do occur and result in mutations, which are also a source of genetic variation. Environmental factors can also cause mutations in genes, and viable mutations are inherited.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

Credits:
Meiosis diagram modified from "MajorEventsInMeiosis" by the National Institutes of Health [Public domain]:
https://commons.wikimedia.org/wiki/File:MajorEventsInMeiosis.jpg

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Ratio problem with basic algebra | Linear equations and inequalities | Algebra Basics | Khan Academy

Fri, 11 Sep 2026 06:06:00 -0000

A slightly more involved ratio problem with algebra. Created by Sal Khan.

Uploaded 05-11-09

Practice this yourself on Khan Academy right now: https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/ratios-core-algebra/e/constructing-proportions-to-solve-application-problems?utm_source=YT&utm_medium=Desc&utm_campaign=algebrabasics

Watch the next lesson: https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebra-direct-inverse-variation/v/direct-and-inverse-variation?utm_source=YT&utm_medium=Desc&utm_campaign=algebrabasics

Missed the previous lesson? https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/ratios-core-algebra/v/constructing-proportions-to-solve-application-problems?utm_source=YT&utm_medium=Desc&utm_campaign=algebrabasics

Algebra basics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Feedback in living systems | Growth and feedback in organisms | High school biology | Khan Academy

Fri, 11 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-biology/x4c673362230887ef:growth-and-feedback-in-organisms/x4c673362230887ef:feedback-in-living-systems/e/understand-feedback-in-living-systems

Uploaded 14-07-21

Feedback mechanisms maintain a living system’s internal conditions within certain limits and mediate behaviors, allowing it to remain alive and functional even as external conditions change within some range. Feedback mechanisms can encourage (through positive feedback) or discourage (negative feedback) what is going on inside the living system.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

Credits:
"Hike 1" by Absjin [Public domain], via Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Hike_1.jpg

"Hike 2" by Absjin [Public domain], via Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:Hike_2.jpg

"Hike 3" by Absjin [Public domain], via Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:Hike_3.jpg

"Pink salmon FWS" by Timothy Knepp [Public domain], via Wikimedia Commons:
https://commons.wikimedia.org/wiki/File:Pink_salmon_FWS.jpg

"106 Pregnancy- Positive Feedback" by OpenStax, licensed under a Creative Commons Attribution License (CC BY 4.0):
https://commons.wikimedia.org/wiki/File:106_Pregnancy-Positive_Feedback.jpg
https://creativecommons.org/licenses/by/4.0/deed.en

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Inertial Mass vs. Gravitational Mass | Circular motion and gravitation | AP Physics 1 | Khan Academy

Fri, 11 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-college-physics-1/xf557a762645cccc5:circular-motion-and-gravitation/xf557a762645cccc5:centripetal-acceleration-and-centripetal-force/e/centripetal-acceleration-and-centripetal-force

Uploaded 14-07-21

The inertial and gravitational mass of an object might be the same number, but they tell you two different things about an object. Learn about the two concepts each type of mass describes and how to measure each independently of each other.

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Alternate Solution to Ratio Problem (HD Version)

Thu, 10 Sep 2026 22:06:00 -0000

An alternate solution to the advanced ratio problem in the last video.
More free lessons at: http://www.khanacademy.org/video?v=-xyTz0WZ1W4

Uploaded 05-11-09

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Work-energy theorem example | Physics | Khan Academy

Thu, 10 Sep 2026 20:06:00 -0000

Want to explore more? Check out the full energy and work playlist here: https://www.youtube.com/playlist?list=PLSQl0a2vh4HA528Zyvlu2giom7XkHj_OM

Uploaded 14-07-21

The work-energy theorem tells us the the net work done on an object will equal the change in kinetic energy of that object. Follow along in this worked example and understand about how to calculate the net work on an object and solve for the change in velocity.

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Rowspace and left nullspace | Matrix transformations | Linear Algebra | Khan Academy

Thu, 10 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/linear-algebra-rowspace-and-left-nullspace

Uploaded 05-11-09

Rowspace and Left Nullspace

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/lin-alg-visualizations-of-left-nullspace-and-rowspace?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-transpose-of-a-vector?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Torque | Physics | Khan Academy

Thu, 10 Sep 2026 16:06:00 -0000

A torque is the rotational equivalent of a force. When a torque is applied to an object it causes the object to rotate. Learn how forces create torques and how to calculate the net torque on a rotating object.

Uploaded 14-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

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Visualizations of left nullspace and rowspace | Linear Algebra | Khan Academy

Thu, 10 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/lin-alg-visualizations-of-left-nullspace-and-rowspace

Uploaded 06-11-09

Relationship between left nullspace, rowspace, column space and nullspace.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-rank-a-rank-transpose-of-a?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-rowspace-and-left-nullspace?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Period of a Pendulum | Simple harmonic motion and rotational motion | AP Physics 1 | Khan Academy

Thu, 10 Sep 2026 12:06:00 -0000

A pendulum behaves as a simple harmonic oscillator. Learn about the period of a pendulum, how it can be adjusted, and how it compares to a mass on a spring.

Uploaded 14-07-21

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Orthogonal complements | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

Thu, 10 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/linear-algebra-orthogonal-complements

Uploaded 06-11-09

Orthogonal Complements as subspaces.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/linear-algebra-dim-v-dim-orthogonal-complement-of-v-n?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/lin-alg-showing-that-a-transpose-x-a-is-invertible?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Dihybrid cross and the Law of Independent Assortment | High school biology | Khan Academy

Thu, 10 Sep 2026 08:06:00 -0000

The probabilities of different offspring genotypes and phenotypes can be determined using a Punnett square. A dihybrid cross results in a roughly 9:3:3:1 ratio of offspring phenotypes.

Uploaded 13-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

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rank(a) = rank(transpose of a) | Matrix transformations | Linear Algebra | Khan Academy

Thu, 10 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/linear-algebra-rank-a-rank-transpose-of-a

Uploaded 06-11-09

Rank(A) = Rank(transpose of A)

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/lin-alg-showing-that-a-transpose-x-a-is-invertible?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/lin-alg-visualizations-of-left-nullspace-and-rowspace?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Calculating gravitational potential energy | Modeling energy | High school physics | Khan Academy

Thu, 10 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-physics/x215e29cb31244fa1:modeling-energy/x215e29cb31244fa1:calculating-energy/a/spring-force-and-energy-ap1

Uploaded 12-07-21

Mathematical expressions, which quantify how the stored energy in a system depends on its configuration (e.g. relative positions of charged particles, compression of a spring) and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

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dim(v) + dim(orthogonal complement of v) = n | Linear Algebra | Khan Academy

Thu, 10 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/linear-algebra-dim-v-dim-orthogonal-complement-of-v-n

Uploaded 06-11-09

Showing that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/lin-alg-representing-vectors-in-rn-using-subspace-members?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/linear-algebra-orthogonal-complements?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Calculating kinetic energy | Modeling energy | High school physics | Khan Academy

Thu, 10 Sep 2026 00:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-physics/x215e29cb31244fa1:modeling-energy/x215e29cb31244fa1:calculating-energy/v/calculating-gravitational-potential-energy

Uploaded 12-07-21

Mathematical expressions, which quantify how the stored energy in a system depends on its configuration (e.g. relative positions of charged particles, compression of a spring) and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Area and Perimeter

Wed, 09 Sep 2026 22:06:00 -0000

Area of rectangles and triangles. Perimeter of rectangles.

Uploaded 08-11-09

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pH and solubility | Equilibrium | AP Chemistry | Khan Academy

Wed, 09 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:solubility-equilibria/e/solubility-equilibria

Uploaded 08-07-21

For ionic compounds containing basic anions, solubility increases as the pH of the solution is decreased. For ionic compounds containing anions of negligible basicity (such as the conjugate bases of strong acids), solubility is unaffected by changes in pH. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:solubility-equilibria/v/solubility-and-the-ph-of-the-solution

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Circles: radius, diameter, circumference and Pi | Geometry | Khan Academy

Wed, 09 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-area-circumference/v/circles-radius-diameter-and-circumference

Uploaded 08-11-09

A circle is at the foundation of geometry and how its parts relate to each other is both completely logical and a wonder.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/basic-geometry/circum_area_circles/e/radius_diameter_and_circumference?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/basic-geometry/circum_area_circles/v/parts-of-a-circle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

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https://www.khanacademy.org/math/geometry/basic-geometry/heron_formula_tutorial/v/part-2-of-the-proof-of-heron-s-formula?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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The common-ion effect | Equilibrium | AP Chemistry | Khan Academy

Wed, 09 Sep 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:solubility-equilibria/v/solubility-and-the-ph-of-the-solution

Uploaded 08-07-21

The solubility of an ionic compound is decreased by the presence of a common ion (an ion that is also present in the compound); this is known as the common-ion effect. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:solubility-equilibria/v/solubility-and-the-common-ion-effect

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Area of a circle

Wed, 09 Sep 2026 14:06:00 -0000

Area of a circle and how it relates to radius and diameter

Uploaded 08-11-09

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Worked example: Predicting whether a precipitate forms by comparing Q and Kₛₚ | Khan Academy

Wed, 09 Sep 2026 12:06:00 -0000

We can use the reaction quotient to predict whether a precipitate will form when two solutions containing dissolved ionic compounds are mixed. If Q is less than Kₛₚ, the newly mixed solution is undersaturated and no precipitate will form. If Q is greater than Kₛₚ, the solution is oversaturated and a precipitate will form until Q = Kₛₚ. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:solubility-equilibria/v/worked-example-predicting-whether-a-precipitate-forms-by-comparing-q-and-k

Uploaded 08-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Basic Graphing and Coordinates

Wed, 09 Sep 2026 10:06:00 -0000

Learning to graph points in two dimensions using Cartesian coordinates.

Uploaded 08-11-09

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Worked example: Calculating solubility from Kₛₚ | Equilibrium | AP Chemistry | Khan Academy

Wed, 09 Sep 2026 08:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:solubility-equilibria/v/solubility-from-the-solubility-product-constant

Uploaded 08-07-21

A compound's molar solubility in water can be calculated from its Kₛₚ value at 25°C. To do so, first prepare an ICE (Initial, Change, and Equilibrium) table showing the equilibrium concentrations of the ions in terms of x, the molar solubility of the compound. Then, plug these expressions into the solubility-product expression for the compound and solve for the value of x.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Slope and Y-intercept Intuition

Wed, 09 Sep 2026 06:06:00 -0000

Using the "Graph of a line" module to understand how a line's graph changes when its slope or y-intercept is changed.
More free lessons at: http://www.khanacademy.org/video?v=8sz1IPjBRS8

Uploaded 08-11-09

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Introduction to solubility equilibria | Equilibrium | AP Chemistry | Khan Academy

Wed, 09 Sep 2026 04:06:00 -0000

The solubility product constant, Kₛₚ, is an equilibrium constant that reflects the extent to which an ionic compound dissolves in water. For compounds that dissolve to produce the same number of ions, we can directly compare their Kₛₚ values to determine their relative solubilities. If we know the solubility of a salt, we can use this information to calculate the Kₛₚ value for the compound. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:solubility-equilibria/v/solubility-product-constant-from-the-solubility

Uploaded 08-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Representing vectors in rn using subspace members | Linear Algebra | Khan Academy

Wed, 09 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/lin-alg-representing-vectors-in-rn-using-subspace-members

Uploaded 08-11-09

Showing that any member of Rn can be represented as a unique sum of a vector in subspace V and a vector in the orthogonal complement of V.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/lin-alg-orthogonal-complement-of-the-orthogonal-complement?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/linear-algebra-dim-v-dim-orthogonal-complement-of-v-n?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Worked example: Using Le Chȃtelier’s principle to predict shifts in equilibrium | Khan Academy

Wed, 09 Sep 2026 00:06:00 -0000

In this video, we'll use Le Chȃtelier’s principle to predict how an equilibrium system will shift in response to various stresses, including changes in concentration, volume, and temperature. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:le-chatelier-s-principle/v/worked-example-using-le-chateliers-principle-to-predict-shifts-in-equilibrium

Uploaded 08-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Orthogonal complement of the nullspace | Linear Algebra | Khan Academy

Tue, 08 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/lin-alg-orthogonal-complement-of-the-nullspace

Uploaded 09-11-09

The orthogonal complement of the nullspace and left nullspace.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/lin-alg-unique-rowspace-solution-to-ax-b?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/lin-alg-orthogonal-complement-of-the-orthogonal-complement?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Worked example: Calculating the equilibrium total pressure after a change in volume | Khan Academy

Tue, 08 Sep 2026 20:06:00 -0000

How does the total pressure change when the volume of a gaseous equilibrium system is reduced? In this video, we'll explore the answer to this question using both qualitative and quantitative approaches. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:le-chatelier-s-principle/v/worked-example-calculating-the-equilibrium-total-pressure-after-a-change-in-volume

Uploaded 08-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Orthogonal complement of the orthogonal complement | Linear Algebra | Khan Academy

Tue, 08 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/lin-alg-orthogonal-complement-of-the-orthogonal-complement

Uploaded 09-11-09

Finding that the orthogonal complement of the orthogonal complement of V is V

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/lin-alg-orthogonal-complement-of-the-nullspace?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/lin-alg-representing-vectors-in-rn-using-subspace-members?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Le Chȃtelier’s principle: Changing temperature | Equilibrium | AP Chemistry | Khan Academy

Tue, 08 Sep 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:le-chatelier-s-principle/v/worked-example-calculating-the-equilibrium-total-pressure-after-a-change-in-volume

Uploaded 08-07-21

Le Chȃtelier’s principle can be used to predict the effect that a stress like changing temperature has on a system at equilibrium. If the temperature of the system is increased (at constant V), the system will shift in the direction that consumes the excess heat. If the temperature of the system is decreased, the reverse effect will be observed. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:le-chatelier-s-principle/v/le-chateliers-principle-changing-temperature

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Unique rowspace solution to Ax = b | Linear Algebra | Khan Academy

Tue, 08 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/lin-alg-unique-rowspace-solution-to-ax-b

Uploaded 09-11-09

Showing that, for any b that is in the column space of A, there is a unique member of the row space that is the "smallest" solution to Ax=b

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/linear-alg-rowspace-solution-to-ax-b-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/lin-alg-orthogonal-complement-of-the-nullspace?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Le Chȃtelier’s principle: Changing volume | Equilibrium | AP Chemistry | Khan Academy

Tue, 08 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:le-chatelier-s-principle/v/le-chateliers-principle-changing-temperature

Uploaded 08-07-21

Le Chȃtelier’s principle can be used to predict the effect that a stress like changing volume has on a system at equilibrium. If the volume of the container is increased (at constant T), the system will shift in the direction that increases the number of moles of gas in the container. If the volume is decreased, the reverse effect will occur. If the system has the same number of moles of gas on both sides of the chemical equation, a change in volume will have no impact on the equilibrium position. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:le-chatelier-s-principle/v/le-chateliers-principle-changing-volume

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Rowspace solution to Ax = b example | Linear Algebra | Khan Academy

Tue, 08 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/linear-alg-rowspace-solution-to-ax-b-example

Uploaded 09-11-09

Visualizing the rowspace solution to Ax=b

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-algebra-projections-onto-subspaces?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/lin-alg-unique-rowspace-solution-to-ax-b?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Le Chȃtelier’s principle: Changing concentration | Equilibrium | AP Chemistry | Khan Academy

Tue, 08 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:le-chatelier-s-principle/v/le-chateliers-principle-changing-volume

Uploaded 08-07-21

Le Chȃtelier’s principle can be used to predict the effect that a stress like changing concentration has on a reaction system at equilibrium. If the concentration of a reaction species is increased (at constant T and V), the equilibrium system will shift in the direction that reduces the concentration of that species. If the concentration of a reaction species is decreased, the reverse effect will be observed. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:le-chatelier-s-principle/v/le-chateliers-principle-changing-concentration

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Showing that A-transpose x A is invertible | Matrix transformations | Linear Algebra | Khan Academy

Tue, 08 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/lin-alg-showing-that-a-transpose-x-a-is-invertible

Uploaded 09-11-09

Showing that (transpose of A)(A) is invertible if A has linearly independent columns

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/linear-algebra-orthogonal-complements?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-rank-a-rank-transpose-of-a?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Worked example: Using the reaction quotient to find equilibrium partial pressures | Khan Academy

Tue, 08 Sep 2026 04:06:00 -0000

In some equilibrium problems, we first need to use the reaction quotient to predict the direction a reaction will proceed to reach equilibrium. Once we know this, we can build an ICE table, which we can then use to calculate the concentrations or partial pressures of the reaction species at equilibrium. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:using-the-reaction-quotient/v/worked-example-using-the-reaction-quotient-to-find-equilibrium-partial-pressures

Uploaded 08-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Projections onto subspaces | Linear Algebra | Khan Academy

Tue, 08 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/linear-algebra-projections-onto-subspaces

Uploaded 10-11-09

Projections onto subspaces

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-alg-visualizing-a-projection-onto-a-plane?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/linear-alg-rowspace-solution-to-ax-b-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Using the reaction quotient | Equilibrium | AP Chemistry | Khan Academy

Tue, 08 Sep 2026 00:06:00 -0000

By comparing the reaction quotient to the equilibrium constant, we can predict the direction a reaction will proceed to reach equilibrium. If Q is less than K, the reaction will proceed towards the products. If Q is greater than K, the reaction will proceed towards the reactants. If Q is equal to K, the reaction is already at equilibrium and will not change. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:using-the-reaction-quotient/v/using-the-reaction-quotient-ap

Uploaded 08-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Visualizing a projection onto a plane | Linear Algebra | Khan Academy

Mon, 07 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/linear-alg-visualizing-a-projection-onto-a-plane

Uploaded 10-11-09

Visualizing a projection onto a plane. Showing that the old and new definitions of projections aren't that different.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/lin-alg-a-projection-onto-a-subspace-is-a-linear-transforma?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-algebra-projections-onto-subspaces?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Worked example: Calculating equilibrium concentrations from initial concentrations | Khan Academy

Mon, 07 Sep 2026 20:06:00 -0000

In this video, we'll learn how to use initial concentrations along with the equilibrium constant to calculate the concentrations of reaction species at equilibrium. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:calculating-equilibrium-concentrations/v/worked-example-calculating-equilibrium-concentrations-from-initial-concentrations-and-the-equilibrium-constant

Uploaded 08-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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A projection onto a subspace is a linear transformation | Linear Algebra | Khan Academy

Mon, 07 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/lin-alg-a-projection-onto-a-subspace-is-a-linear-transforma

Uploaded 10-11-09

Showing that a projection onto a subspace is a linear transformation

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-algebra-subspace-projection-matrix-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-alg-visualizing-a-projection-onto-a-plane?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Worked example: Calculating an equilibrium constant from initial and equilibrium pressures

Mon, 07 Sep 2026 16:06:00 -0000

Given an initial partial pressure and the total pressure at equilibrium, we can use Dalton's law to determine the equilibrium partial pressures of the gases in a reaction mixture. Once we know the equilibrium partial pressures, we can calculate the equilibrium constant for the reaction. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:calculating-equilibrium-concentrations/v/worked-example-calculating-an-equilibrium-constant-from-initial-and-equilibrium-pressures

Uploaded 08-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Subspace projection matrix example | Linear Algebra | Khan Academy

Mon, 07 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/linear-algebra-subspace-projection-matrix-example

Uploaded 10-11-09

Example of a transformation matrix for a projection onto a subspace

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/lin-alg-another-example-of-a-projection-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/lin-alg-a-projection-onto-a-subspace-is-a-linear-transforma?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Properties of the equilibrium constant | Equilibrium | AP Chemistry | Khan Academy

Mon, 07 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:magnitude-and-properties-of-the-equilibrium-constant/e/magnitude-and-properties-of-the-equilibrium-constant

Uploaded 08-07-21

The equilibrium constant for a reaction depends on how the balanced equation is written. If the equation is reversed, K is inverted. If the equation is multiplied by a factor n, K is raised to the nth power. If multiple equations are added together, K for the overall equation is the product of the K values for the equations that were summed. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:magnitude-and-properties-of-the-equilibrium-constant/v/properties-of-the-equilibrium-constant

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc

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Another example of a projection matrix | Linear Algebra | Khan Academy

Mon, 07 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/lin-alg-another-example-of-a-projection-matrix

Uploaded 10-11-09

Figuring out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-alg-projection-is-closest-vector-in-subspace?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-algebra-subspace-projection-matrix-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Magnitude of the equilibrium constant | Equilibrium | AP Chemistry | Khan Academy

Mon, 07 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:magnitude-and-properties-of-the-equilibrium-constant/v/properties-of-the-equilibrium-constant

Uploaded 08-07-21

The magnitude of the equilibrium constant provides information about the relative amounts of reactants and products at equilibrium. A large K value (greater than 1) indicates that there are more products than reactants at equilibrium, while a small K value (less than 1) indicates that there are more reactants than products at equilibrium. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:magnitude-and-properties-of-the-equilibrium-constant/v/magnitude-of-the-equilibrium-constant

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Projection is closest vector in subspace | Linear Algebra | Khan Academy

Mon, 07 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/linear-alg-projection-is-closest-vector-in-subspace

Uploaded 10-11-09

Showing that the projection of x onto a subspace is the closest vector in the subspace to x

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-algebra-least-squares-approximation?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Worked examples: Calculating equilibrium constants | Equilibrium | AP Chemistry | Khan Academy

Mon, 07 Sep 2026 04:06:00 -0000

In this video, we'll calculate equilibrium constants using measurements of concentration and partial pressures at equilibrium. First, we'll find Kc for an equilibrium system using equilibrium concentrations. Then, we'll find Kp for a different system using equilibrium partial pressures. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:calculating-the-equilibrium-constant/v/worked-examples-calculating-equilibrium-constants-from-equilibrium-concentrations-or-partial-pressures

Uploaded 08-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Least squares approximation | Linear Algebra | Khan Academy

Mon, 07 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/linear-algebra-least-squares-approximation

Uploaded 10-11-09

The least squares approximation for otherwise unsolvable equations

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-algebra-least-squares-examples?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Writing equilibrium constant and reaction quotient expressions | AP Chemistry | Khan Academy

Mon, 07 Sep 2026 00:06:00 -0000

The equilibrium constant, K, describes the relative amounts of reaction species at equilibrium. The expression for K is equal to the concentrations (or partial pressures) of the products raised to their stoichiometric coefficients divided by the concentrations (or partial pressures) of the reactants raised to their stoichiometric coefficients. The reaction quotient, Q, has the same form as K but describes the relative amounts of reaction species at any point in time. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:reaction-quotient-and-equilibrium-constant/v/writing-equilibrium-constant-and-reaction-quotient-expressions

Uploaded 08-07-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Another least squares example | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

Sun, 06 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/linear-algebra-another-least-squares-example

Uploaded 10-11-09

Using least squares approximation to fit a line to points

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/linear-algebra-coordinates-with-respect-to-a-basis?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Direction of reversible reactions | Equilibrium | AP Chemistry | Khan Academy

Sun, 06 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:reaction-quotient-and-equilibrium-constant/v/writing-equilibrium-constant-and-reaction-quotient-expressions

Uploaded 08-07-21

For a reversible reaction, if the rate of the forward reaction is greater than the rate of the reverse reaction, there is a net conversion of reactants to products. If the rate of the forward reaction is less than the rate of the reverse reaction, there is a net conversion of products to reactants. If the two rates are equal, the reaction is at equilibrium. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:introduction-to-equilibrium/v/direction-of-reversible-reactions

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Least squares examples | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

Sun, 06 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/linear-algebra-least-squares-examples

Uploaded 10-11-09

An example using the least squares solution to an unsolvable system

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-algebra-another-least-squares-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Dynamic equilibrium | Equilibrium | AP Chemistry | Khan Academy

Sun, 06 Sep 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:introduction-to-equilibrium/v/direction-of-reversible-reactions

Uploaded 08-07-21

Many physical and chemical processes are reversible. A reversible process is said to be in dynamic equilibrium when the forward and reverse processes occur at the same rate, resulting in no observable change in the system. Once dynamic equilibrium is established, the concentrations or partial pressures of all species involved in the process remain constant. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:introduction-to-equilibrium/v/dynamic-equilibrium

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Coordinates with respect to a basis | Linear Algebra | Khan Academy

Sun, 06 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/change-of-basis/v/linear-algebra-coordinates-with-respect-to-a-basis

Uploaded 11-11-09

Understanding alternate coordinate systems

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/linear-algebra-change-of-basis-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Biodiversity | Biodiversity and human impacts | High school biology | Khan Academy

Sun, 06 Sep 2026 12:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:biodiversity-and-human-impacts/x230b3ff252126bb6:biodiversity/v/biodiversity

Uploaded 07-07-21

Biodiversity encompasses genetic, species, and ecosystem diversity. Biodiversity is dynamic and changes over time, influenced by speciation and extinction events. However, human actions—such as climate change and overexploitation—are increasing extinction rates. As extinction rates increase, ecosystems experience a loss in biodiversity.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Change of basis matrix | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

Sun, 06 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/change-of-basis/v/linear-algebra-change-of-basis-matrix

Uploaded 11-11-09

Using a change of basis matrix to get us from one coordinate system to another.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-invertible-change-of-basis-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Formation of biomolecules | High school biology | Khan Academy

Sun, 06 Sep 2026 08:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:energy-and-matter-in-biological-systems/x230b3ff252126bb6:biomolecules-and-reactions/v/introduction-to-proteins-and-amino-acids

Uploaded 06-07-21

Sugar molecules contain carbon, hydrogen, and oxygen: their hydrocarbon backbones are used to make amino acids and other carbon-based molecules that can be assembled into larger molecules (such as proteins or DNA), used for example to form new cells. As matter and energy flow through different organizational levels of living systems, chemical elements are recombined in different ways to form different products.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Invertible change of basis matrix | Linear Algebra | Khan Academy

Sun, 06 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/change-of-basis/v/lin-alg-invertible-change-of-basis-matrix

Uploaded 11-11-09

Using an invertible change of basis matrix to go between different coordinate systems

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-transformation-matrix-with-respect-to-a-basis?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Photosynthesis | Energy and matter in biological systems | High school biology | Khan Academy

Sun, 06 Sep 2026 04:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:energy-and-matter-in-biological-systems/x230b3ff252126bb6:photosynthesis/v/photosynthesis-hs

Uploaded 06-07-21

The process of photosynthesis converts light energy to stored chemical energy by converting carbon dioxide and water into sugars plus released oxygen. Photosynthesis occurs in two phases: the light-dependent reactions, and the light-independent reactions.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Transformation matrix with respect to a basis | Linear Algebra | Khan Academy

Sun, 06 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/change-of-basis/v/lin-alg-transformation-matrix-with-respect-to-a-basis

Uploaded 11-11-09

Finding the transformation matrix with respect to a non-standard basis

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-alternate-basis-tranformation-matrix-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-invertible-change-of-basis-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Organization of multicellular organisms | High school biology | Khan Academy

Sun, 06 Sep 2026 00:06:00 -0000

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https://www.khanacademy.org/science/hs-biology/x4c673362230887ef:genes-cells-and-organisms/x4c673362230887ef:organization-of-multicellular-organisms/e/understand-organization-of-multicellular-organisms

Uploaded 06-07-21

Multicellular organisms have a hierarchical structural organization: cells make up tissues, tissues make up organs, and organs make up organ systems. Organ systems work together to carry out the many functions of the organism.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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"The Galaxy Within" by Dchordpdx, licensed under a Creative Commons Attribution License (CC BY 4.0):
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Alternate basis transformation matrix example | Linear Algebra | Khan Academy

Sat, 05 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/change-of-basis/v/lin-alg-alternate-basis-tranformation-matrix-example

Uploaded 11-11-09

Example of finding the transformation matrix for an alternate basis

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-alternate-basis-tranformation-matrix-example-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-transformation-matrix-with-respect-to-a-basis?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Genes, proteins, and cells | Genes, cells, and organisms | High school biology | Khan Academy

Sat, 05 Sep 2026 20:06:00 -0000

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https://www.khanacademy.org/science/hs-biology/x4c673362230887ef:genes-cells-and-organisms/x4c673362230887ef:organization-of-multicellular-organisms/e/understand-organization-of-multicellular-organisms

Uploaded 06-07-21

All cells contain genetic information in the form of DNA molecules. Genes are regions in the DNA that contain the instructions that code for the formation of proteins, which carry out most of the work of cells.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Alternate basis transformation matrix example part 2 | Linear Algebra | Khan Academy

Sat, 05 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/change-of-basis/v/lin-alg-alternate-basis-tranformation-matrix-example-part-2

Uploaded 12-11-09

Showing that the transformation matrix with respect to basis B actually works. Brief point on why someone would want to operate in a different basis to begin with.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-changing-coordinate-systems-to-help-find-a-transformation-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

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https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-alternate-basis-tranformation-matrix-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Greenhouse effect and greenhouse gases | High school biology | Khan Academy

Sat, 05 Sep 2026 16:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/science/hs-bio/x230b3ff252126bb6:biodiversity-and-human-impacts/x230b3ff252126bb6:global-change-biology/v/greenhouse-effect-and-greenhouse-gases

Uploaded 06-07-21

The greenhouse effect, driven by gases like carbon dioxide, methane, and water vapor, is essential for maintaining Earth's habitable temperatures. However, excessive concentrations of these gases—particularly due to human activities—can lead to global warming and climate change.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Changing coordinate systems to help find a transformation matrix | Linear Algebra | Khan Academy

Sat, 05 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/change-of-basis/v/lin-alg-changing-coordinate-systems-to-help-find-a-transformation-matrix

Uploaded 12-11-09

Changing our coordinate system to find the transformation matrix with respect to standard coordinates

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-introduction-to-orthonormal-bases?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-alternate-basis-tranformation-matrix-example-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Cell specialization | Genes, cells, and organisms | High school biology | Khan Academy

Sat, 05 Sep 2026 12:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/hs-biology/x4c673362230887ef:genes-cells-and-organisms/x4c673362230887ef:cell-specialization/v/creativity-break-why-is-learning-biology-important

Uploaded 01-07-21

Systems of specialized cells within organisms help them perform the essential functions of life.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

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Introduction to orthonormal bases | Linear Algebra | Khan Academy

Sat, 05 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthonormal-basis/v/linear-algebra-introduction-to-orthonormal-bases

Uploaded 12-11-09

Looking at sets and bases that are orthonormal -- or where all the vectors have length 1 and are orthogonal to each other.

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-coordinates-with-respect-to-orthonormal-bases?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-changing-coordinate-systems-to-help-find-a-transformation-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Taking and visualizing powers of a complex number | Precalculus | Khan Academy

Sat, 05 Sep 2026 08:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul-div-polar/v/exponential-form-to-find-complex-roots

Uploaded 01-07-21

Given a complex number in rectangular form, Sal converts it to polar form to show how to visualize powers of the complex number by scaling and rotating it by its own modulus and argument.

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Coordinates with respect to orthonormal bases | Linear Algebra | Khan Academy

Sat, 05 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthonormal-basis/v/linear-algebra-coordinates-with-respect-to-orthonormal-bases

Uploaded 12-11-09

Seeing that orthonormal bases make for good coordinate systems

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/lin-alg-projections-onto-subspaces-with-orthonormal-bases?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-introduction-to-orthonormal-bases?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Indoor air pollutants| Atmospheric pollution| AP Environmental science| Khan Academy

Sat, 05 Sep 2026 04:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/science/ap-college-environmental-science/x0b0e430a38ebd23f:atmospheric-pollution/x0b0e430a38ebd23f:air-pollution/e/air-pollution

Uploaded 29-06-21

Indoor air pollutants can come from natural sources, human-made sources, and combustion. Common natural pollutants include radon, mold, and dust. Common human-made pollutants include Volatile Organic Compounds (VOCs) and formaldehyde. Common combustion pollutants include carbon monoxide, nitrogen oxides, sulfur dioxide, particulates, and tobacco smoke.

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

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Finding projection onto subspace with orthonormal basis example | Linear Algebra | Khan Academy

Sat, 05 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthonormal-basis/v/lin-alg-finding-projection-onto-subspace-with-orthonormal-basis-example

Uploaded 12-11-09

Example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/lin-alg-example-using-orthogonal-change-of-basis-matrix-to-find-transformation-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/lin-alg-projections-onto-subspaces-with-orthonormal-bases?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Human impact on aquatic environments| AP Environmental science| Khan Academy

Sat, 05 Sep 2026 00:06:00 -0000

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Projections onto subspaces with orthonormal bases | Linear Algebra | Khan Academy

Fri, 04 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthonormal-basis/v/lin-alg-projections-onto-subspaces-with-orthonormal-bases

Uploaded 12-11-09

Projections onto subspaces with orthonormal bases

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/lin-alg-finding-projection-onto-subspace-with-orthonormal-basis-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-coordinates-with-respect-to-orthonormal-bases?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Dividing complex numbers in polar form | Precalculus | Khan Academy

Fri, 04 Sep 2026 20:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul-div-polar/e/multiplying_and_dividing_complex_number_polar_forms

Uploaded 27-06-21

Sal shows how to divide two complex numbers in polar form by dividing their moduli and subtracting their arguments.

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Example using orthogonal change-of-basis matrix to find transformation matrix | Khan Academy

Fri, 04 Sep 2026 18:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthonormal-basis/v/lin-alg-example-using-orthogonal-change-of-basis-matrix-to-find-transformation-matrix

Uploaded 13-11-09

Example using orthogonal change-of-basis matrix to find transformation matrix

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/lin-alg-orthogonal-matrices-preserve-angles-and-lengths?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/lin-alg-finding-projection-onto-subspace-with-orthonormal-basis-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Multiplying complex numbers in polar form | Precalculus | Khan Academy

Fri, 04 Sep 2026 16:06:00 -0000

Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul-div-polar/v/divide-complex-polar

Uploaded 27-06-21

Sal shows how to multiply two complex numbers in polar form by multiplying their moduli, adding their arguments, and simplifying.

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Orthogonal matrices preserve angles and lengths | Linear Algebra | Khan Academy

Fri, 04 Sep 2026 14:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthonormal-basis/v/lin-alg-orthogonal-matrices-preserve-angles-and-lengths

Uploaded 13-11-09

Showing that orthogonal matrices preserve angles and lengths

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-the-gram-schmidt-process?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/lin-alg-example-using-orthogonal-change-of-basis-matrix-to-find-transformation-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Multiplying complex numbers graphically example: -1-i | Precalculus | Khan Academy

Fri, 04 Sep 2026 12:06:00 -0000

Sal shows how we can multiply complex numbers graphically on the complex plane. We rotate an amount equal to the argument and scale by the modulus of the complex number by which we're multiplying.

Uploaded 27-06-21

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The Gram-Schmidt process | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

Fri, 04 Sep 2026 10:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthonormal-basis/v/linear-algebra-the-gram-schmidt-process

Uploaded 13-11-09

Finding an orthonormal basis for a subspace using the Gram-Schmidt Process

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-gram-schmidt-process-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/lin-alg-orthogonal-matrices-preserve-angles-and-lengths?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Multiplying complex numbers graphically example: -3i | Precalculus | Khan Academy

Fri, 04 Sep 2026 08:06:00 -0000

Sal shows how we can multiply complex numbers graphically on the complex plane by rotating and scaling. Multiplying a complex number z by -3i rotates and scales z.

Uploaded 27-06-21

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Gram-Schmidt process example | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

Fri, 04 Sep 2026 06:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthonormal-basis/v/linear-algebra-gram-schmidt-process-example

Uploaded 13-11-09

Using Gram-Schmidt to find an orthonormal basis for a plane in R3

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-gram-schmidt-example-with-3-basis-vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-the-gram-schmidt-process?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Converting a complex number from polar to rectangular form | Precalculus | Khan Academy

Fri, 04 Sep 2026 04:06:00 -0000

Given a complex number in polar form, Sal shows how to convert that number to rectangular form and plot it on the complex plane.

Uploaded 27-06-21

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Gram-Schmidt example with 3 basis vectors | Linear Algebra | Khan Academy

Fri, 04 Sep 2026 02:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthonormal-basis/v/linear-algebra-gram-schmidt-example-with-3-basis-vectors

Uploaded 13-11-09

Gram-Schmidt example with 3 basis vectors

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/eigen_everything/v/linear-algebra-introduction-to-eigenvalues-and-eigenvectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-gram-schmidt-process-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Energy Conservation| Energy Resources and Consumption| AP Environmental Science| Khan Academy

Fri, 04 Sep 2026 00:06:00 -0000

Some of the methods for conserving energy around the home include adjusting the thermostat to reduce the use of heat and air conditioning, conserving water, use of energy efficient appliances, and conservation landscaping. Methods for conserving energy on a large scale include improving fuel economy for vehicles, using BEV's and hybrid vehicles, using public transportation, and implementing green building design features.

Uploaded 22-06-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

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Introduction to eigenvalues and eigenvectors | Linear Algebra | Khan Academy

Thu, 03 Sep 2026 22:06:00 -0000

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/eigen-everything/v/linear-algebra-introduction-to-eigenvalues-and-eigenvectors

Uploaded 13-11-09

What eigenvectors and eigenvalues are and why they are interesting

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/eigen_everything/v/linear-algebra-proof-of-formula-for-determining-eigenvalues?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthonormal_basis/v/linear-algebra-gram-schmidt-example-with-3-basis-vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
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Reduction of Air Pollutants| Atmospheric Pollution| AP Environmental Science| Khan Academy

Thu, 03 Sep 2026 20:06:00 -0000

Methods to reduce air pollutants include regulatory practices, conservation practices, and alternative fuels.

Uploaded 22-06-21

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate

Volunteer here: https://www.khanacademy.org/contribute

Credits:

"Types of vehicles" by Skoda [Published consent], via skoda-storyboard.com
https://cdn.skoda-storyboard.com/2019/02/infographics-electrovehicles-english.jpg

"Clean Air Act overview" by USEPA [Public domain] via https://www.epa.gov
https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.epa.gov%2Fclean-air-act-overview&psig=AOvVaw1X-7RfpZsm6CMOolBtafmo&ust=1627420269937000&source=images&cd=vfe&ved=2ahUKEwiJxf6J04HyAhVFE80KHbJkBZgQjRx6BAgAEA8

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