If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Start from the basics

Learn the basics, starting with Overview and history of algebra

Overview and history of algebra: Introduction to algebraIntroduction to variables: Introduction to algebraSubstitution and evaluating expressions: Introduction to algebraEvaluating expressions word problems: Introduction to algebraWriting algebraic expressions introduction: Introduction to algebraIntroduction to equivalent algebraic expressions: Introduction to algebraDependent & independent variables: Introduction to algebra

Combining like terms: Introduction to algebraInterpreting linear expressions: Introduction to algebraIrrational numbers: Introduction to algebraSums and products of rational and irrational numbers: Introduction to algebraProofs concerning irrational numbers: Introduction to algebraDivision by zero: Introduction to algebraBinary and hexadecimal number systems: Introduction to algebra

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)

Two-variable linear equations intro: Linear equations, functions, & graphsx-intercepts and y-intercepts: Linear equations, functions, & graphsSlope: Linear equations, functions, & graphsHorizontal & vertical lines: Linear equations, functions, & graphsIntro to slope-intercept form: Linear equations, functions, & graphsGraphing slope-intercept equations: Linear equations, functions, & graphsWriting slope-intercept equations: Linear equations, functions, & graphs

Point-slope form: Linear equations, functions, & graphsStandard form: Linear equations, functions, & graphsSummary: Forms of two-variable linear equations: Linear equations, functions, & graphsInterpreting linear functions and equations: Linear equations, functions, & graphsComparing linear functions: Linear equations, functions, & graphsConstructing linear models for real-world relationships: Linear equations, functions, & graphsLinear models word problems: Linear equations, functions, & graphs

Systems of equations overview: System of equationsIntroduction to systems of equations: System of equationsEquivalent systems of equations and the elimination method: System of equationsSolving systems of equations with substitution: System of equations

Manipulating expressions with unknown variables: System of equationsNumber of solutions to systems of equations: System of equationsSystems of equations word problems: System of equationsSolving equations by graphing (Algebra 2 level): System of equationsSystems with three variables: System of equations

Evaluating functions: FunctionsInputs and outputs of a function: FunctionsFunctions and equations: FunctionsInterpreting function notation: FunctionsIntroduction to the domain and range of a function: FunctionsDetermining the domain of a function: FunctionsRecognizing functions: FunctionsPiecewise functions: FunctionsMaximum and minimum points: FunctionsIntervals where a function is positive, negative, increasing, or decreasing: FunctionsInterpreting features of graphs: FunctionsAverage rate of change: FunctionsAverage rate of change word problems: FunctionsCombining functions: FunctionsComposing functions (Algebra 2 level): Functions

Shifting functions: FunctionsStretching functions: FunctionsModeling situations by combining and composing functions (Algebra 2 level): FunctionsIntroduction to inverses of functions (Algebra 2 level): FunctionsFinding inverse functions (Algebra 2 level): FunctionsVerifying that functions are inverses (Algebra 2 level): FunctionsDetermining whether a function is invertible (Algebra 2 level): FunctionsDetermining the domain of advanced functions (Algebra 2 level): FunctionsDetermining the range of a function (Algebra 2 level): FunctionsGraphing nonlinear piecewise functions (Algebra 2 level): FunctionsInterpreting the symmetry of algebraic models (Algebra 2 level): FunctionsInterpreting the end behavior of algebraic models (Algebra 2 level): FunctionsInterpreting the periodicity of algebraic models (Algebra 2 level): FunctionsComparing features of functions (Algebra 2 level): FunctionsTwo-variable functions: Functions

Parabolas intro: Quadratic equations & functionsQuadratic factored form: Quadratic equations & functionsSolving quadratics by taking square roots: Quadratic equations & functionsQuadratic vertex form: Quadratic equations & functionsSolving quadratics by factoring: Quadratic equations & functionsCompleting the square: Quadratic equations & functions

The quadratic formula: Quadratic equations & functionsQuadratic standard form: Quadratic equations & functionsFeatures & forms of quadratic functions: Quadratic equations & functionsTransforming parabolas: Quadratic equations & functionsSystems of quadratic equations: Quadratic equations & functionsQuadratic inequalities: Quadratic equations & functions

Intro to polynomials: Polynomial expressions, equations, & functionsAdding & subtracting polynomials: Polynomial expressions, equations, & functionsAdding & subtracting polynomials: two variables: Polynomial expressions, equations, & functionsMultiplying monomials: Polynomial expressions, equations, & functionsMultiplying monomials by polynomials: Polynomial expressions, equations, & functionsMultiplying binomials: Polynomial expressions, equations, & functionsSpecial products of binomials: Polynomial expressions, equations, & functionsMultiplying binomials by polynomials: Polynomial expressions, equations, & functionsPolynomials word problems: Polynomial expressions, equations, & functionsIntroduction to factorization: Polynomial expressions, equations, & functionsFactoring monomials: Polynomial expressions, equations, & functionsFactoring polynomials by taking common factors: Polynomial expressions, equations, & functionsEvaluating expressions with unknown variables: Polynomial expressions, equations, & functionsFactoring quadratics intro: Polynomial expressions, equations, & functionsFactoring quadratics by grouping: Polynomial expressions, equations, & functionsFactoring polynomials with quadratic forms: Polynomial expressions, equations, & functionsFactoring quadratics: Difference of squares: Polynomial expressions, equations, & functionsFactoring quadratics: Perfect squares: Polynomial expressions, equations, & functions

Strategy in factoring quadratics: Polynomial expressions, equations, & functionsFactoring polynomials with special product forms: Polynomial expressions, equations, & functionsLong division of polynomials: Polynomial expressions, equations, & functionsSynthetic division of polynomials: Polynomial expressions, equations, & functionsPractice dividing polynomials with remainders: Polynomial expressions, equations, & functionsPolynomial Remainder Theorem: Polynomial expressions, equations, & functionsBinomial theorem: Polynomial expressions, equations, & functionsUnderstanding the binomial theorem: Polynomial expressions, equations, & functionsAdvanced polynomial factorization methods: Polynomial expressions, equations, & functionsProving polynomial identities: Polynomial expressions, equations, & functionsPolynomial identities with complex numbers: Polynomial expressions, equations, & functionsQuadratic equations with complex numbers: Polynomial expressions, equations, & functionsFundamental Theorem of Algebra: Polynomial expressions, equations, & functionsFinding zeros of polynomials: Polynomial expressions, equations, & functionsZeros of polynomials and their graphs: Polynomial expressions, equations, & functionsEnd behavior of polynomial functions: Polynomial expressions, equations, & functionsGraphs of polynomials: Polynomial expressions, equations, & functionsIntroduction to symmetry of functions: Polynomial expressions, equations, & functionsSymmetry of polynomial functions: Polynomial expressions, equations, & functions

Exponent properties review: Exponential & logarithmic functionsRadicals: Exponential & logarithmic functionsRational exponents intro: Exponential & logarithmic functionsProperties of exponents (rational exponents): Exponential & logarithmic functionsAdvanced exponent & radical evaluation: Exponential & logarithmic functionsSimplifying square roots: Exponential & logarithmic functionsSimplifying radicals (higher-index roots): Exponential & logarithmic functionsRadicals (miscellaneous videos): Exponential & logarithmic functionsExponential vs. linear growth: Exponential & logarithmic functionsExponential expressions: Exponential & logarithmic functionsGraphs of exponential growth: Exponential & logarithmic functionsExponential vs. linear growth over time: Exponential & logarithmic functionsExponential decay: Exponential & logarithmic functionsExponential functions from tables & graphs: Exponential & logarithmic functionsEquivalent forms of exponential expressions: Exponential & logarithmic functions

Solving exponential equations using properties of exponents: Exponential & logarithmic functionsIntroduction to rate of exponential growth and decay: Exponential & logarithmic functionsInterpreting the rate of change of exponential models (Algebra 2 level): Exponential & logarithmic functionsConstructing exponential models according to rate of change (Algebra 2 level): Exponential & logarithmic functionsAdvanced interpretation of exponential models (Algebra 2 level): Exponential & logarithmic functionsDistinguishing between linear and exponential growth (Algebra 2 level): Exponential & logarithmic functionsIntroduction to logarithms (Algebra 2 level): Exponential & logarithmic functionsThe constant e and the natural logarithm (Algebra 2 level): Exponential & logarithmic functionsProperties of logarithms (Algebra 2 level): Exponential & logarithmic functionsThe change of base formula for logarithms (Algebra 2 level): Exponential & logarithmic functionsLogarithmic equations (Algebra 2 level): Exponential & logarithmic functionsSolving exponential equations with logarithms (Algebra 2 level): Exponential & logarithmic functionsSolving exponential models (Algebra 2 level): Exponential & logarithmic functionsGraphs of exponential functions (Algebra 2 level): Exponential & logarithmic functionsGraphs of logarithmic functions (Algebra 2 level): Exponential & logarithmic functionsLogarithmic scale (Algebra 2 level): Exponential & logarithmic functions

Intro to rational expressions: Rational expressions, equations, & functionsSimplifying rational expressions: Rational expressions, equations, & functionsMultiplying & dividing rational expressions: Rational expressions, equations, & functionsAdding & subtracting rational expressions: Rational expressions, equations, & functionsNested fractions: Rational expressions, equations, & functionsSolving rational equations: Rational expressions, equations, & functions

Direct and inverse variation: Rational expressions, equations, & functionsEnd behavior of rational functions: Rational expressions, equations, & functionsDiscontinuities of rational functions: Rational expressions, equations, & functionsGraphs of rational functions: Rational expressions, equations, & functionsModeling with rational functions: Rational expressions, equations, & functionsRational inequalities: Rational expressions, equations, & functionsPartial fraction expansion: Rational expressions, equations, & functions

Introduction to radians: Trigonometric functionsThe unit circle definition of sine, cosine, & tangent: Trigonometric functionsThe graphs of sine, cosine, & tangent: Trigonometric functionsBasic trigonometric identities: Trigonometric functionsTrigonometric values of special angles: Trigonometric functionsPythagorean identity: Trigonometric functionsIntroduction to amplitude, midline, & extrema of sinusoidal functions: Trigonometric functionsFinding amplitude & midline of sinusoidal functions from their formulas: Trigonometric functionsPeriod of sinusoidal functions: Trigonometric functions

Graphing sinusoidal functions: Trigonometric functionsConstructing sinusoidal functions: Trigonometric functionsThe inverse trigonometric functions: Trigonometric functionsSolving basic sinusoidal equations: Trigonometric functionsSolving advanced sinusoidal equations: Trigonometric functionsSolving sinusoidal models: Trigonometric functionsIntroduction to the trigonometric angle addition identities: Trigonometric functionsUsing trigonometric identities to solve problems: Trigonometric functionsParametric equations: Trigonometric functions

What are the imaginary numbers?: Complex numbersWhat are the complex numbers?: Complex numbersThe complex plane: Complex numbersAdding & subtracting complex numbers: Complex numbersMultiplying complex numbers: Complex numbers

Complex conjugates & dividing complex numbers: Complex numbersAbsolute value & angle of complex numbers: Complex numbersDistance & midpoint of complex numbers: Complex numbersPolar form of complex numbers: Complex numbersMultiplying & dividing complex numbers in polar form: Complex numbersChallenging complex number problems: Complex numbers

Introduction to conic sections: Conic sectionsThe features of a circle: Conic sectionsStandard equation of a circle: Conic sectionsExpanded equation of a circle: Conic sectionsCenter and radii of an ellipse: Conic sectionsFoci of an ellipse: Conic sections

Focus and directrix of a parabola: Conic sectionsIntroduction to hyperbolas: Conic sectionsFoci of a hyperbola: Conic sectionsHyperbolas not centered at the origin: Conic sectionsIdentifying conic sections from their expanded equations: Conic sectionsChallenging conic section problems (IIT JEE): Conic sections

Introduction to matrices: MatricesRepresenting linear systems of equations with augmented matrices: MatricesElementary matrix row operations: MatricesRow-echelon form & Gaussian elimination: MatricesAdding & subtracting matrices: MatricesMultiplying matrices by scalars: MatricesProperties of matrix addition & scalar multiplication: MatricesMultiplying matrices by matrices: Matrices

Properties of matrix multiplication: MatricesMatrices as transformations: MatricesDeterminant of a 2x2 matrix: MatricesIntroduction to matrix inverses: MatricesFinding the inverse of a matrix using its determinant: MatricesPractice finding the inverses of 2x2 matrices: MatricesDeterminants & inverses of large matrices: MatricesSolving equations with inverse matrices: MatricesModel real-world situations with matrices: Matrices