Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:https://www.khanacademy.org/ma....th/precalculus/x9e81

Calculating the foci (or focuses) of an Ellipse.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/conics_precalc/ellipses-precalc/e/ellipse_intuition?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

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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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Another separable differential equation example.

Watch the next lesson: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/modeling-with-differential-equations/v/particular-solution-given-initial-conditions-for-population?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations

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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions 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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Determining the projection of a vector on s line

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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

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channe....l/UCGYSKl6e3HM0PP7QR
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/algebra/x2f8bb115

Sal evaluates -2*f(-6)+g(1) given the graphs of f and g.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/functions-and-function-notation/e/functions_2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Watch the next lesson: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/functions-and-function-notation/v/difference-between-equations-and-functions?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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It's nice to practice conversion problems, but how about applying our new knowledge of percentages to a real life problem like recycling? Hint: don't forget your long division!

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/percent-intro-pre-alg/e/finding_percents?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

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Introduction to molecular and empirical formulas. Calculating molecular mass.
More free lessons at: http://www.khanacademy.org/video?v=gfBcM3uvWfs

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/sc....ience/ap-biology/gen

Watch the next lesson: https://www.khanacademy.org/science/biology/macromolecules/nucleic-acids/v/molecular-structure-of-dna?utm_source=YT&utm_medium=Desc&utm_campaign=biology

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Biology on Khan Academy: Life is beautiful! From atoms to cells, from genes to proteins, from populations to ecosystems, biology is the study of the fascinating and intricate systems that make life possible. Dive in to learn more about the many branches of biology and why they are exciting and important. Covers topics seen in a high school or first-year college biology 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 Biology channel: https://www.youtube.com/channe....l/UC82qE46vcTn7lP4tK
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/linear-algebra/al

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

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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

Subscribe to KhanAcademy’s Linear Algebra channel: https://www.youtube.com/channe....l/UCGYSKl6e3HM0PP7QR
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/cc-seventh-grade-

In this video, we think about what |a-b| really means, and we verify that |a-b| = |b-a| by looking at an example.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-absolute-value/e/absolute-value-to-find-distance?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Watch the next lesson: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-absolute-value/v/interpreting-absolute-value-as-distance?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

Subscribe to Khan Academy à ªs 7th grade channel:
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More detail on the light reactions and photophorylation
More free lessons at: http://www.khanacademy.org/video?v=yfR36PMWegg

Worked example that thinks about the relationship between an arc length and the angle that is subtended by the arc.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/e/cc-radians-and-arc-length?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Watch the next lesson: https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/we-converting-degrees-to-radians?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

Subscribe to Khan Academy’s Trigonometry channel:
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/algebra/x2f8bb115

Multiple arguments for what we could get when we divide zero by zero. We will later see that this can be considered indeterminate

Watch the next 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

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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

Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channe....l/UCsCA3_VozRtgUT7wW
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-statistics/sum

Thinking about how we can estimate the variance of a population by looking at the data in a sample.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/descriptive-statistics/variance_std_deviation/e/variance?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/descriptive-statistics/variance_std_deviation/v/review-and-intuition-why-we-divide-by-n-1-for-the-unbiased-sample-variance?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

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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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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/hu....manities/world-histo

Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/humanities/world-history/euro-hist/wo/v/beginning-of-world-war-ii?utm_source=YT&utm_medium=Desc&utm_campaign=worldhistory

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World history on Khan Academy: From the earliest civilizations to the modern world, geography, religion, trade, and politics have bound peoples and nations together — and torn them apart. Take a journey through time and space and discover the fascinating history behind the complex world we inhabit today.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions 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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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/sc....ience/ap-biology/her

Heredity and Classical Genetics. Dominant and recessive traits. Heterozygous and homozygous genotypes.
More free lessons at: http://www.khanacademy.org/video?v=eEUvRrhmcxM

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/e/central--inscribed--and-circumscribed-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/v/hypotenuse-of-right-triangle-inscribed-in-circle?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

Subscribe to Khan Academy’s Geometry channel:
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Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/differential-calculus/limits_topic/continuity-limits/e/continuity?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/limits_topic/continuity-limits/v/fancy-algebra-to-find-a-limit-and-make-a-function-continuous?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

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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:
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"Identifying the anode and cathode in a galvanic cell, and calculating the voltage using standard electrode potentials.

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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 offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. 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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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/geometry/hs-geo-c

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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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How can we tell if a sequence converges or diverges? See Sal in action, determining the convergence/divergence of several sequences. Created by Sal Khan.

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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.

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