Algebra (all content) khan academy -- Free

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Unit 1: Introduction to algebra
Overview and history of algebra: Introduction to algebra
Introduction to variables: Introduction to algebra
Substitution and evaluating expressions: Introduction to algebra
Evaluating expressions word problems: Introduction to algebra
Writing algebraic expressions introduction: Introduction to algebra
Introduction to equivalent algebraic expressions: Introduction to algebra
Dependent & independent variables: Introduction to algebra
Combining like terms: Introduction to algebra
Interpreting linear expressions: Introduction to algebra
Irrational numbers: Introduction to algebra
Sums and products of rational and irrational numbers: Introduction to algebra
Proofs concerning irrational numbers: Introduction to algebra
Division by zero: Introduction to algebra
Binary and hexadecimal number systems: Introduction to algebra

Unit 2: Solving basic equations & inequalities (one variable, linear)
Algebraic equations basics: Solving basic equations & inequalities (one variable, linear)
Why we do the same thing to both sides of an equation: Solving basic equations & inequalities (one variable, linear)
One-step addition & subtraction equations: Solving basic equations & inequalities (one variable, linear)
One-step multiplication & division equations: Solving basic equations & inequalities (one variable, linear)
Two-steps equations intro: Solving basic equations & inequalities (one variable, linear)
Two-step equation word problems: Solving basic equations & inequalities (one variable, linear)
Linear equations with variables on both sides: Solving basic equations & inequalities (one variable, linear)
Linear equations with parentheses: Solving basic equations & inequalities (one variable, linear)
Analyzing the number of solutions to linear equations: Solving basic equations & inequalities (one variable, linear)
Linear equations word problems: Solving basic equations & inequalities (one variable, linear)
Linear equations with unknown coefficients: Solving basic equations & inequalities (one variable, linear)
Old school equations with Sal: Solving basic equations & inequalities (one variable, linear)
Introduction to inequalities with variables: Solving basic equations & inequalities (one variable, linear)
One-step inequalities: Solving basic equations & inequalities (one variable, linear)
Two-step inequalities: Solving basic equations & inequalities (one variable, linear)
Multi-step inequalities: Solving basic equations & inequalities (one variable, linear)
Compound inequalities: Solving basic equations & inequalities (one variable, linear)

Unit 3: Linear equations, functions, & graphs
Two-variable linear equations intro: Linear equations, functions, & graphs
x-intercepts and y-intercepts: Linear equations, functions, & graphs
Slope: Linear equations, functions, & graphs
Horizontal & vertical lines: Linear equations, functions, & graphs
Intro to slope-intercept form: Linear equations, functions, & graphs
Graphing slope-intercept equations: Linear equations, functions, & graphs
Writing slope-intercept equations: Linear equations, functions, & graphs
Point-slope form: Linear equations, functions, & graphs
Standard form: Linear equations, functions, & graphs
Summary: Forms of two-variable linear equations: Linear equations, functions, & graphs
Interpreting linear functions and equations: Linear equations, functions, & graphs
Comparing linear functions: Linear equations, functions, & graphs
Constructing linear models for real-world relationships: Linear equations, functions, & graphs
Linear models word problems: Linear equations, functions, & graphs

Unit 4: Sequences
Introduction to arithmetic sequences: Sequences
Constructing arithmetic sequences: Sequences
Introduction to geometric sequences: Sequences
Constructing geometric sequences: Sequences
Modeling with sequences: Sequences
General sequences: Sequences

Unit 5: System of equations
Systems of equations overview: System of equations
Introduction to systems of equations: System of equations
Equivalent systems of equations and the elimination method: System of equations
Solving systems of equations with substitution: System of equations
Manipulating expressions with unknown variables: System of equations
Number of solutions to systems of equations: System of equations
Systems of equations word problems: System of equations
Solving equations by graphing (Algebra 2 level): System of equations
Systems with three variables: System of equations

Unit 6: Two-variable inequalities
Checking solutions of two-variable inequalities: Two-variable inequalities
Constraining solutions of two-variable inequalities: Two-variable inequalities
Graphing two-variable inequalities: Two-variable inequalities
Modeling with linear inequalities: Two-variable inequalities

Unit 7: Functions
Evaluating functions: Functions
Inputs and outputs of a function: Functions
Functions and equations: Functions
Interpreting function notation: Functions
Introduction to the domain and range of a function: Functions
Determining the domain of a function: Functions
Recognizing functions: Functions
Piecewise functions: Functions
Maximum and minimum points: Functions
Intervals where a function is positive, negative, increasing, or decreasing: Functions
Interpreting features of graphs: Functions
Average rate of change: Functions
Average rate of change word problems: Functions
Combining functions: Functions
Composing functions (Algebra 2 level): Functions
Shifting functions: Functions
Stretching functions: Functions
Modeling situations by combining and composing functions (Algebra 2 level): Functions
Introduction to inverses of functions (Algebra 2 level): Functions
Finding inverse functions (Algebra 2 level): Functions
Verifying that functions are inverses (Algebra 2 level): Functions
Determining whether a function is invertible (Algebra 2 level): Functions
Determining the domain of advanced functions (Algebra 2 level): Functions
Determining the range of a function (Algebra 2 level): Functions
Graphing nonlinear piecewise functions (Algebra 2 level): Functions
Interpreting the symmetry of algebraic models (Algebra 2 level): Functions
Interpreting the end behavior of algebraic models (Algebra 2 level): Functions
Interpreting the periodicity of algebraic models (Algebra 2 level): Functions
Comparing features of functions (Algebra 2 level): Functions
Two-variable functions: Functions

Unit 8: Absolute value equations, functions, & inequalities
Graphs of absolute value functions: Absolute value equations, functions, & inequalities
Solving absolute value equations: Absolute value equations, functions, & inequalities
Solving absolute value inequalities: Absolute value equations, functions, & inequalities

Unit 9: Quadratic equations & functions
Parabolas intro: Quadratic equations & functions
Quadratic factored form: Quadratic equations & functions
Solving quadratics by taking square roots: Quadratic equations & functions
Quadratic vertex form: Quadratic equations & functions
Solving quadratics by factoring: Quadratic equations & functions
Completing the square: Quadratic equations & functions
The quadratic formula: Quadratic equations & functions
Quadratic standard form: Quadratic equations & functions
Features & forms of quadratic functions: Quadratic equations & functions
Transforming parabolas: Quadratic equations & functions
Systems of quadratic equations: Quadratic equations & functions
Quadratic inequalities: Quadratic equations & functions

Unit 10: Polynomial expressions, equations, & functions
Intro to polynomials: Polynomial expressions, equations, & functions
Adding & subtracting polynomials: Polynomial expressions, equations, & functions
Adding & subtracting polynomials: two variables: Polynomial expressions, equations, & functions
Multiplying monomials: Polynomial expressions, equations, & functions
Multiplying monomials by polynomials: Polynomial expressions, equations, & functions
Multiplying binomials: Polynomial expressions, equations, & functions
Special products of binomials: Polynomial expressions, equations, & functions
Multiplying binomials by polynomials: Polynomial expressions, equations, & functions
Polynomials word problems: Polynomial expressions, equations, & functions
Introduction to factorization: Polynomial expressions, equations, & functions
Factoring monomials: Polynomial expressions, equations, & functions
Factoring polynomials by taking common factors: Polynomial expressions, equations, & functions
Evaluating expressions with unknown variables: Polynomial expressions, equations, & functions
Factoring quadratics intro: Polynomial expressions, equations, & functions
Factoring quadratics by grouping: Polynomial expressions, equations, & functions
Factoring polynomials with quadratic forms: Polynomial expressions, equations, & functions
Factoring quadratics: Difference of squares: Polynomial expressions, equations, & functions
Factoring quadratics: Perfect squares: Polynomial expressions, equations, & functions
Strategy in factoring quadratics: Polynomial expressions, equations, & functions
Factoring polynomials with special product forms: Polynomial expressions, equations, & functions
Long division of polynomials: Polynomial expressions, equations, & functions
Synthetic division of polynomials: Polynomial expressions, equations, & functions
Practice dividing polynomials with remainders: Polynomial expressions, equations, & functions
Polynomial Remainder Theorem: Polynomial expressions, equations, & functions
Binomial theorem: Polynomial expressions, equations, & functions
Understanding the binomial theorem: Polynomial expressions, equations, & functions
Advanced polynomial factorization methods: Polynomial expressions, equations, & functions
Proving polynomial identities: Polynomial expressions, equations, & functions
Polynomial identities with complex numbers: Polynomial expressions, equations, & functions
Quadratic equations with complex numbers: Polynomial expressions, equations, & functions
Fundamental Theorem of Algebra: Polynomial expressions, equations, & functions
Finding zeros of polynomials: Polynomial expressions, equations, & functions
Zeros of polynomials and their graphs: Polynomial expressions, equations, & functions
End behavior of polynomial functions: Polynomial expressions, equations, & functions
Graphs of polynomials: Polynomial expressions, equations, & functions
Introduction to symmetry of functions: Polynomial expressions, equations, & functions
Symmetry of polynomial functions: Polynomial expressions, equations, & functions

Unit 11: Exponential & logarithmic functions
Exponent properties review: Exponential & logarithmic functions
Radicals: Exponential & logarithmic functions
Rational exponents intro: Exponential & logarithmic functions
Properties of exponents (rational exponents): Exponential & logarithmic functions
Advanced exponent & radical evaluation: Exponential & logarithmic functions
Simplifying square roots: Exponential & logarithmic functions
Simplifying radicals (higher-index roots): Exponential & logarithmic functions
Radicals (miscellaneous videos): Exponential & logarithmic functions
Exponential vs. linear growth: Exponential & logarithmic functions
Exponential expressions: Exponential & logarithmic functions
Graphs of exponential growth: Exponential & logarithmic functions
Exponential vs. linear growth over time: Exponential & logarithmic functions
Exponential decay: Exponential & logarithmic functions
Exponential functions from tables & graphs: Exponential & logarithmic functions
Equivalent forms of exponential expressions: Exponential & logarithmic functions
Solving exponential equations using properties of exponents: Exponential & logarithmic functions
Introduction to rate of exponential growth and decay: Exponential & logarithmic functions
Interpreting the rate of change of exponential models (Algebra 2 level): Exponential & logarithmic functions
Constructing exponential models according to rate of change (Algebra 2 level): Exponential & logarithmic functions
Advanced interpretation of exponential models (Algebra 2 level): Exponential & logarithmic functions
Distinguishing between linear and exponential growth (Algebra 2 level): Exponential & logarithmic functions
Introduction to logarithms (Algebra 2 level): Exponential & logarithmic functions
The constant e and the natural logarithm (Algebra 2 level): Exponential & logarithmic functions
Properties of logarithms (Algebra 2 level): Exponential & logarithmic functions
The change of base formula for logarithms (Algebra 2 level): Exponential & logarithmic functions
Logarithmic equations (Algebra 2 level): Exponential & logarithmic functions
Solving exponential equations with logarithms (Algebra 2 level): Exponential & logarithmic functions
Solving exponential models (Algebra 2 level): Exponential & logarithmic functions
Graphs of exponential functions (Algebra 2 level): Exponential & logarithmic functions
Graphs of logarithmic functions (Algebra 2 level): Exponential & logarithmic functions
Logarithmic scale (Algebra 2 level): Exponential & logarithmic functions

Unit 12: Radical equations & functions
Solving square-root equations: Radical equations & functions
Extraneous solutions of radical equations: Radical equations & functions
Solving cube-root equations: Radical equations & functions
Domain of radical functions: Radical equations & functions
Graphs of radical functions: Radical equations & functions

Unit 13: Rational expressions, equations, & functions
Intro to rational expressions: Rational expressions, equations, & functions
Simplifying rational expressions: Rational expressions, equations, & functions
Multiplying & dividing rational expressions: Rational expressions, equations, & functions
Adding & subtracting rational expressions: Rational expressions, equations, & functions
Nested fractions: Rational expressions, equations, & functions
Solving rational equations: Rational expressions, equations, & functions
Direct and inverse variation: Rational expressions, equations, & functions
End behavior of rational functions: Rational expressions, equations, & functions
Discontinuities of rational functions: Rational expressions, equations, & functions
Graphs of rational functions: Rational expressions, equations, & functions
Modeling with rational functions: Rational expressions, equations, & functions
Rational inequalities: Rational expressions, equations, & functions
Partial fraction expansion: Rational expressions, equations, & functions

Unit 14: Trigonometric functions
Introduction to radians: Trigonometric functions
The unit circle definition of sine, cosine, & tangent: Trigonometric functions
The graphs of sine, cosine, & tangent: Trigonometric functions
Basic trigonometric identities: Trigonometric functions
Trigonometric values of special angles: Trigonometric functions
Pythagorean identity: Trigonometric functions
Introduction to amplitude, midline, & extrema of sinusoidal functions: Trigonometric functions
Finding amplitude & midline of sinusoidal functions from their formulas: Trigonometric functions
Period of sinusoidal functions: Trigonometric functions
Graphing sinusoidal functions: Trigonometric functions
Constructing sinusoidal functions: Trigonometric functions
The inverse trigonometric functions: Trigonometric functions
Solving basic sinusoidal equations: Trigonometric functions
Solving advanced sinusoidal equations: Trigonometric functions
Solving sinusoidal models: Trigonometric functions
Introduction to the trigonometric angle addition identities: Trigonometric functions
Using trigonometric identities to solve problems: Trigonometric functions
Parametric equations: Trigonometric functions

Unit 15: Algebraic modeling
Rate conversion: Algebraic modeling
Appropriate units: Algebraic modeling
Word problems with multiple units: Algebraic modeling
Modeling with one-variable equations & inequalities: Algebraic modeling
Manipulating formulas: Algebraic modeling

Unit 16: Complex numbers
What are the imaginary numbers?: Complex numbers
What are the complex numbers?: Complex numbers
The complex plane: Complex numbers
Adding & subtracting complex numbers: Complex numbers
Multiplying complex numbers: Complex numbers
Complex conjugates & dividing complex numbers: Complex numbers
Absolute value & angle of complex numbers: Complex numbers
Distance & midpoint of complex numbers: Complex numbers
Polar form of complex numbers: Complex numbers
Multiplying & dividing complex numbers in polar form: Complex numbers
Challenging complex number problems: Complex numbers

Unit 17: Conic sections
Introduction to conic sections: Conic sections
The features of a circle: Conic sections
Standard equation of a circle: Conic sections
Expanded equation of a circle: Conic sections
Center and radii of an ellipse: Conic sections
Foci of an ellipse: Conic sections
Focus and directrix of a parabola: Conic sections
Introduction to hyperbolas: Conic sections
Foci of a hyperbola: Conic sections
Hyperbolas not centered at the origin: Conic sections
Identifying conic sections from their expanded equations: Conic sections
Challenging conic section problems (IIT JEE): Conic sections

Unit 18: Series & induction
Basic sigma notation: Series & induction
Arithmetic series: Series & induction
Geometric sequences: Series & induction
Finite geometric series: Series & induction
Finite geometric series applications: Series & induction
Advanced sigma notation: Series & induction
Infinite geometric series: Series & induction
Infinite geometric series applications: Series & induction
Deductive and inductive reasoning: Series & induction
Induction: Series & induction
Sum of n squares: Series & induction

Unit 19: Vectors
Vector basics: Vectors
Magnitude of vectors: Vectors
Scalar multiplication: Vectors
Vector addition & subtraction: Vectors
Combined vector operations: Vectors
Unit vectors: Vectors
Magnitude & direction form of vectors: Vectors
Component form of vectors: Vectors
Adding vectors in magnitude & direction form: Vectors
Applications of vectors: Vectors

Unit 20: Matrices
Introduction to matrices: Matrices
Representing linear systems of equations with augmented matrices: Matrices
Elementary matrix row operations: Matrices
Row-echelon form & Gaussian elimination: Matrices
Adding & subtracting matrices: Matrices
Multiplying matrices by scalars: Matrices
Properties of matrix addition & scalar multiplication: Matrices
Multiplying matrices by matrices: Matrices
Properties of matrix multiplication: Matrices
Matrices as transformations: Matrices
Determinant of a 2x2 matrix: Matrices
Introduction to matrix inverses: Matrices
Finding the inverse of a matrix using its determinant: Matrices
Practice finding the inverses of 2x2 matrices: Matrices
Determinants & inverses of large matrices: Matrices
Solving equations with inverse matrices: Matrices
Model real-world situations with matrices
 

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