Basic algebraic operations

Algebra and real numbers

Polynomials : basic operations

Polynomials : factoring

Rational expressions : basic operations

Integer exponents

Rational exponents

Radicals

Rational number representations

Equations and inequalities

Linear equations and applications

Systems of linear equations and applications

Linear inequalities

Absolute value in equations and inequalities

Complex numbers

Quadratic equations and applications

Equations reducible to quadratic form

Polynomial and rational inequalities

Rates of change

Cumulative review exercise

Graphs and functions

Basic tools : circles

Straight lines

Functions

Graphing functions

Combining functions

Inverse functions

Mathematical modeling in business

Polynomial and rational functions

Polynomial functions and graphs

Finding rational zeros of polynomials

Approximating real zeros of polynomials

Rational functions

Partial fractions

Interpolating polynomials

Exponential and logarithmic functions

Exponential functions

The exponential function with base e

Logarithmic functions

Common and natural logarithms

Exponential and logarithmic equations

Growth of increasing functions

Trigonometric functions

Angles and their measure

Acute angle domains

General angle and real number domains

Exact values for special angles and real numbers

Circular functions

Graphing basic trigonometric functions

Graphing y = k + A sin (Bx + C) and y = k + A cos (Bx + C)

Graphing more general tangent, cotangent, secant, and cosecant functions

Inverse trigonometric functions

A predator-prey analysis involving mountain lions and deer

Trigonometric identities and conditional equations

Basic identities and their use

Sum, difference, and cofunction identities

Double-angle and half-angle identities

Product-sum and sum-product identities

Trigonometric equations

From M sin Bt + N cos Bt to A sin (Bt + C)---a harmonic analysis tool

Additional topics in trigonometry

Law of sines

Law of cosines

Geometric vectors

Algebraic vectors

Polar coordinates and graphs

Complex numbers in rectangular and polar forms

De Moivre's theorem

Conic sections and planetary orbits

Systems of equations and inequalities

Systems of linear equations and augmented matrices

Gauss-Jordan elimination

Systems involving second-degree equations

Systems of linear inequalities in two variables

Linear programming

Modeling with systems of linear equations

Matrices and determinants

Matrices : basic operations

Inverse of a square matrix

Matrix equations and systems of linear equations

Determinants

Properties of determinants

Cramer's rule

Using matrices to find cost, revenue and profit

Sequences and series

Sequences and series

Mathematical induction

Arithmetic and geometric sequences

Binomial formula

Multiplication principle, permutations, and combinations

Sequences specified by recursion formulas

Additional topics in analytic geometry

Conic sections : parabola

Ellipse

Hyperbola

Translation of axes

Parametric equations