Precalculus

Preliminaries

Polynomials

Exponents

Rational and radical expressions

Linear and nonlinear equations

Linear and nonlinear inequalities

Absolute value in equations and inequalities

Analytic geometry

Functions

Linear functions

Transformations and graphs

Quadratic functions

Algebra of functions; inverse functions

Polynomial functions

Rational functions

Algebraic functions; variation

Exponential functions

Logarithmic functions

Exponential and logarithmic functions

Graphs of trigonometric functions

Angles

Trigonometric identities and equations

Sum, difference, multiple, and half-angle formulas

Inverse trigonometric functions

Trianges

Vectors

Polar coordinates; parametric equations

Trigonometric form of complex numbers

Systems of linear equations

Gaussian and Gauss-Jordan elimination

Partial fraction decomposition

Nonlinear systems of equations

Introduction to matrix algebra

Matrix multiplication and inverses

Determinants and Cramer's rule

Loci; parabolas

Ellipses and hyperboles

Rotation of axes

Conic sections

Sequences and series

The principle of mathematical induction

Special sequences and series

Binomial theorem

Limits, continuity, derivatives.