AP Precalculus

I. Polynomial and Rational Functions

Operations on Polynomials

Division of Polynomials

Identity and Remainder Theorem

Cubic and Quartic Equations

Rational Expressions

II. Exponential and Logarithmic Functions

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Exponential and Logarithmic Equations

III. Trigonometry

General Angles and Radian Measure

Sinusoidal Functions

Trigonometric Functions of Any Angle

Graphs of Trigonometric Functions

Transformations of Trigonometric Graphs

Inverse Trigonometric Functions

Transformations of Inverse Trigonometric Functions

Fundamental Trigonometric Identities

Sum and Difference Formulas for Trigonometric Functions

Multiple-Angle and Product-to-Sum Formulas

Exercises - Trigonometry

IV. Polar Functions

Polar Coordinates

Fill in the blanks: Polar Coordinates

Exercises - Polar Coordinates

V. Matrices

Definition Matrix

Matrix Addition, Subtraction, and Scalar Multiplication

Matrix Multiplication

Properties of Matrix Multiplication

Cayley-Hamilton Theorem

Transformation Matrix

Applications of Matrices in Coordinate Geometry and Transformations

Exercises - Matrices

VI. Sequences and Series

Sequences and Series

Mathematical Induction

VII. Probability

Matrices

Practice Test

Dimensions of Matrices
Elements of a Matrix
Determinant of a Square Matrix
Inverse of a Square Matrix
Addition, Subtraction, and Scalar Multiplication of Matrices
Cayley-Hamilton Theorem
Transformation Matrices
Area of a Triangle and a Parallelogram