Derivative applications (Khan Academy)

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The reason we study calculus, and the reason it was invented, is for its many uses in real-world problems. In particular, derivatives let us optimize functions and study their rates of change. Here we cover optimization, rates of change, L’Hopital’s rule, the mean value theorem, and more! (1) Equations of normal and tangent lines Equation […]

Trigonometric equations and identities (Khan Academy)

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Learn how to solve trigonometric equations and how to use trigonometric identities to solve various problems. (1) Trig identity reference Trig identity reference (2) The inverse trigonometric functions Intro to arcsine Intro to arctangent Intro to arccosine Evaluate inverse trig functions Restricting domains of functions to make them invertible Domain & range of inverse tangent […]

Seeing structure in expressions (Khan Academy)

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Learn how to use algebra in order to solve problems that involve variables whose values are unknown. (1) Evaluating expressions with unknown variables Evaluating expressions using structure Evaluate expressions using structure Evaluating expressions using structure (advanced) Evaluate expressions using structure (advanced) (2) Manipulating expressions with unknown variables Manipulating expressions using structure Manipulating expressions using structure […]

Rational and irrational numbers (Khan Academy)

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Learn about irrational numbers and how to identify them. (1) Irrational numbers Intro to rational & irrational numbers Classifying numbers: rational & irrational Classify numbers: rational & irrational Classifying numbers Classify numbers (2) Proofs concerning irrational numbers Proof: √2 is irrational Proof: square roots of prime numbers are irrational Proof: there’s an irrational number between […]

Introduction to polynomials (Khan Academy)

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Learn how to add, subtract, and multiply polynomial expressions. For example, write (2x+3)(x-1) as 2x²+x-3. (1) Intro to polynomials The parts of polynomial expressions Evaluating polynomials Simplifying polynomials (2) Adding & subtracting polynomials Adding polynomials Add polynomials Subtracting polynomials Subtract polynomials Polynomial subtraction & set closure Adding & subtracting multiple polynomials Add & subtract polynomials […]

Expressions with rational exponents and radicals (Khan Academy)

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Learn about expressions with rational exponents like x^(2/3), about radical expressions like √(2t^5), and about the relationship between these two forms of representation. Learn how to evaluate and simplify such expression. (1) Introduction to rational exponents and radicals Intro to rational exponents Radicals and exponents Rational exponents: unit fractions Rewriting roots as rational exponents Evaluating […]

Functions (Khan Academy)

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Functions are mathematical entities that assign unique outputs to given inputs. Sounds simple? Think again! In this topic you will evaluate, graph, analyze, and create various types of functions. (1) Introduction to functions What is a function? (2) Evaluating functions Evaluating a function: formula Evaluate functions Evaluate a function: graph Evaluate functions from their graph […]

One-variable linear equations (Khan Academy)

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Learn how to solve linear equations that contain a single variable. For example, solve 2(x+3)=(4x-1)/2+7. (1) Algebraic equations basics Variables, expressions, & equations Testing solutions to equations Intro to equations Testing solutions to equations (2) Why we do the same thing to both sides of an equation Same thing to both sides of equations Representing […]

Introduction to algebra (Khan Academy)

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This topic is an overview of the fundamental ideas and tools of algebra. (1) Overview and history of algebra Origins of algebra Abstract-ness The beauty of algebra Intro to the coordinate plane Why all the letters in algebra? (2) Introduction to variables What is a variable? Why aren’t we using the multiplication sign? Evaluating an […]

Fractions (Khan Academy)

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Understanding fractions conceptually, using operations with fractions, and converting fractions. (1) Understanding fractions Introduction to fractions Identifying fraction parts Recognizing fractions exercise Recognize fractions 1 Identifying numerators and denominators Identify numerators and denominators Plotting basic fractions on the number line Fractions on the number line Fraction word problem: pizza Add and subtract fractions: word problems […]

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