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Algebra (all content)

Learn algebra—variables, equations, functions, graphs, and more.

20 units929 videos88 hours

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Unit 1: Introduction to algebra

Overview and history of algebra

Introduction to variables

Substitution and evaluating expressions

Evaluating expressions word problems

Writing algebraic expressions introduction

Introduction to equivalent algebraic expressions

Dependent & independent variables

Combining like terms

Interpreting linear expressions

Irrational numbers

Sums and products of rational and irrational numbers

Proofs concerning irrational numbers

Division by zero

Binary and hexadecimal number systems

Unit 2: Solving basic equations & inequalities (one variable, linear)

Algebraic equations basics

Why we do the same thing to both sides of an equation

One-step addition & subtraction equations

One-step multiplication & division equations

Two-steps equations intro

Two-step equation word problems

Linear equations with variables on both sides

Linear equations with parentheses

Analyzing the number of solutions to linear equations

Linear equations word problems

Linear equations with unknown coefficients

Old school equations with Sal

Introduction to inequalities with variables

One-step inequalities

Two-step inequalities

Multi-step inequalities

Compound inequalities

Unit 3: Linear equations, functions, & graphs

Two-variable linear equations intro

x-intercepts and y-intercepts

Slope

Horizontal & vertical lines

Intro to slope-intercept form

Graphing slope-intercept equations

Writing slope-intercept equations

Point-slope form

Standard form

Summary: Forms of two-variable linear equations

Interpreting linear functions and equations

Comparing linear functions

Constructing linear models for real-world relationships

Linear models word problems

Unit 4: Sequences

Introduction to arithmetic sequences

Constructing arithmetic sequences

Introduction to geometric sequences

Constructing geometric sequences

Modeling with sequences

General sequences

Unit 5: System of equations

Systems of equations overview

Introduction to systems of equations

Equivalent systems of equations and the elimination method

Solving systems of equations with substitution

Manipulating expressions with unknown variables

Number of solutions to systems of equations

Systems of equations word problems

Solving equations by graphing (Algebra 2 level)

Systems with three variables

Unit 6: Two-variable inequalities

Checking solutions of two-variable inequalities

Constraining solutions of two-variable inequalities

Graphing two-variable inequalities

Modeling with linear inequalities

Unit 7: Functions

Evaluating functions

Inputs and outputs of a function

Functions and equations

Interpreting function notation

Introduction to the domain and range of a function

Determining the domain of a function

Recognizing functions

Piecewise functions

Maximum and minimum points

Intervals where a function is positive, negative, increasing, or decreasing

Interpreting features of graphs

Average rate of change

Average rate of change word problems

Combining functions

Composing functions (Algebra 2 level)

Shifting functions

Stretching functions

Modeling situations by combining and composing functions (Algebra 2 level)

Introduction to inverses of functions (Algebra 2 level)

Finding inverse functions (Algebra 2 level)

Verifying that functions are inverses (Algebra 2 level)

Determining whether a function is invertible (Algebra 2 level)

Determining the domain of advanced functions (Algebra 2 level)

Determining the range of a function (Algebra 2 level)

Graphing nonlinear piecewise functions (Algebra 2 level)

Interpreting the symmetry of algebraic models (Algebra 2 level)

Interpreting the end behavior of algebraic models (Algebra 2 level)

Interpreting the periodicity of algebraic models (Algebra 2 level)

Comparing features of functions (Algebra 2 level)

Two-variable functions

Unit 8: Absolute value equations, functions, & inequalities

Graphs of absolute value functions

Solving absolute value equations

Solving absolute value inequalities

Unit 9: Quadratic equations & functions

Parabolas intro

Quadratic factored form

Solving quadratics by taking square roots

Quadratic vertex form

Solving quadratics by factoring

Completing the square

The quadratic formula

Quadratic standard form

Features & forms of quadratic functions

Transforming parabolas

Systems of quadratic equations

Quadratic inequalities

Unit 10: Polynomial expressions, equations, & functions

Intro to polynomials

Adding & subtracting polynomials

Adding & subtracting polynomials: two variables

Multiplying monomials

Multiplying monomials by polynomials

Multiplying binomials

Special products of binomials

Multiplying binomials by polynomials

Polynomials word problems

Introduction to factorization

Factoring monomials

Factoring polynomials by taking common factors

Evaluating expressions with unknown variables

Factoring quadratics intro

Factoring quadratics by grouping

Factoring polynomials with quadratic forms

Factoring quadratics: Difference of squares

Factoring quadratics: Perfect squares

Strategy in factoring quadratics

Factoring polynomials with special product forms

Long division of polynomials

Synthetic division of polynomials

Practice dividing polynomials with remainders

Polynomial Remainder Theorem

Binomial theorem

Understanding the binomial theorem

Advanced polynomial factorization methods

Proving polynomial identities

Polynomial identities with complex numbers

Quadratic equations with complex numbers

Fundamental Theorem of Algebra

Finding zeros of polynomials

Zeros of polynomials and their graphs

End behavior of polynomial functions

Introduction to symmetry of functions

Symmetry of polynomial functions

Unit 11: Exponential & logarithmic functions

Exponent properties review

Radicals

Rational exponents intro

Properties of exponents (rational exponents)

Advanced exponent & radical evaluation

Simplifying square roots

Simplifying radicals (higher-index roots)

Radicals (miscellaneous videos)

Exponential vs. linear growth

Exponential expressions

Graphs of exponential growth

Exponential vs. linear growth over time

Exponential decay

Exponential functions from tables & graphs

Equivalent forms of exponential expressions

Solving exponential equations using properties of exponents

Introduction to rate of exponential growth and decay

Interpreting the rate of change of exponential models (Algebra 2 level)

Constructing exponential models according to rate of change (Algebra 2 level)

Advanced interpretation of exponential models (Algebra 2 level)

Distinguishing between linear and exponential growth (Algebra 2 level)

Introduction to logarithms (Algebra 2 level)

The constant e and the natural logarithm (Algebra 2 level)

Properties of logarithms (Algebra 2 level)

The change of base formula for logarithms (Algebra 2 level)

Logarithmic equations (Algebra 2 level)

Solving exponential equations with logarithms (Algebra 2 level)

Solving exponential models (Algebra 2 level)

Graphs of exponential functions (Algebra 2 level)

Graphs of logarithmic functions (Algebra 2 level)

Logarithmic scale (Algebra 2 level)

Unit 12: Radical equations & functions

Solving square-root equations

Extraneous solutions of radical equations

Solving cube-root equations

Domain of radical functions

Graphs of radical functions

Unit 13: Rational expressions, equations, & functions

Simplifying rational expressions

Multiplying & dividing rational expressions

Adding & subtracting rational expressions

Nested fractions

Solving rational equations

Direct and inverse variation

End behavior of rational functions

Discontinuities of rational functions

Graphs of rational functions

Modeling with rational functions

Rational inequalities

Partial fraction expansion

Unit 14: Trigonometric functions

Introduction to radians

The unit circle definition of sine, cosine, & tangent

The graphs of sine, cosine, & tangent

Basic trigonometric identities

Trigonometric values of special angles

Pythagorean identity

Introduction to amplitude, midline, & extrema of sinusoidal functions

Finding amplitude & midline of sinusoidal functions from their formulas

Period of sinusoidal functions

Graphing sinusoidal functions

Constructing sinusoidal functions

The inverse trigonometric functions

Solving basic sinusoidal equations

Solving sinusoidal models

Introduction to the trigonometric angle addition identities

Using trigonometric identities to solve problems

Parametric equations

Unit 15: Algebraic modeling

Rate conversion

Appropriate units

Word problems with multiple units

Modeling with one-variable equations & inequalities

Manipulating formulas

Unit 16: Complex numbers

What are the imaginary numbers?

What are the complex numbers?

The complex plane

Adding & subtracting complex numbers

Multiplying complex numbers

Complex conjugates & dividing complex numbers

Absolute value & angle of complex numbers

Distance & midpoint of complex numbers

Polar form of complex numbers

Multiplying & dividing complex numbers in polar form

Challenging complex number problems

Unit 17: Conic sections

Introduction to conic sections

The features of a circle

Standard equation of a circle

Expanded equation of a circle

Center and radii of an ellipse

Foci of an ellipse

Focus and directrix of a parabola

Introduction to hyperbolas

Foci of a hyperbola

Hyperbolas not centered at the origin

Identifying conic sections from their expanded equations

Challenging conic section problems (IIT JEE)

Unit 18: Series & induction

Basic sigma notation

Arithmetic series

Geometric sequences

Finite geometric series

Finite geometric series applications

Advanced sigma notation

Infinite geometric series

Infinite geometric series applications

Deductive and inductive reasoning

Induction

Sum of n squares

Unit 19: Vectors

Vector basics

Magnitude of vectors

Scalar multiplication

Vector addition & subtraction

Combined vector operations

Unit vectors

Magnitude & direction form of vectors

Component form of vectors

Adding vectors in magnitude & direction form

Applications of vectors

Unit 20: Matrices

Introduction to matrices

Row-echelon form & Gaussian elimination

Adding & subtracting matrices

Multiplying matrices by scalars

Multiplying matrices by matrices

Properties of matrix multiplication

Matrices as transformations

Determinant of a 2x2 matrix

Introduction to matrix inverses

Finding the inverse of a matrix using its determinant

Determinants & inverses of large matrices

Solving equations with inverse matrices

Model real-world situations with matrices

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