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# Algebra (all content)

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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

## Review articles

## Get StartedOverview and history of algebra

Did you realize that the word "algebra" comes from Arabic (just like "algorithm" and "al jazeera" and "Aladdin")? And what is so great about algebra anyway?

This tutorial doesn't explore algebra so much as it introduces the history and ideas that underpin it.

Start learningThis tutorial doesn't explore algebra so much as it introduces the history and ideas that underpin it.