Chapter P. Prerequisites: Fundamental Concepts of Algebra
Algebraic Expressions, Mathematical Models, and Real Numbers
Exponents and Scientific Notation
Radicals and Rational Exponents
Polynomials
Factoring Polynomials
Rational Expressions
Equations
Modeling with Equations
Linear Inequalities and Absolute Value Inequalities

Chapter 1. Functions and Graphs
Graphs and Graphing Utilities
Basics of Functions and Their Graphs
More on Functions and Their Graphs
Linear Functions and Slope
More on Slope
Transformations of Functions
Combinations of Functions; Composite Functions
Inverse Functions
Distance and Midpoint Formulas; Circles
Modeling with Functions

Chapter 2. Polynomial and Rational Functions
Complex Numbers
Quadratic Functions
Polynomial Functions and Their Graphs
Dividing Polynomials; Remainder and Factor Theorems
Zeros of Polynomial Functions
Rational Functions and Their Graphs
Polynomial and Rational Inequalities
Modeling Using Variation

Chapter 3. Exponential and Logarithmic Functions
Exponential Functions
Logarithmic Functions
Properties of Logarithms
Exponential and Logarithmic Equations
Exponential Growth and Decay; Modeling Data

Chapter 4. Trigonometric Functions
Angles and Radian Measure
Trigonometric Functions: The Unit Circle
Right Triangle Trigonometry
Trigonometric Functions of Any Angle
Graphs of Sine and Cosine Functions
Graphs of Other Trigonometric Functions
Inverse Trigonometric Functions
Applications of Trigonometric Functions

Chapter 5. Analytic Trigonometry
Verifying Trigonometric Identities
Sum and Difference Formulas
Double-Angle, Power-Reducing, and Half-Angle Formulas
Product-to-Sum and Sum-to-Product Formulas
Trigonometric Equations

Chapter 6. Additional Topics in Trigonometry
The Law of Sines
The Law of Cosines
Polar Coordinates
Graphs of Polar Equations
Complex Numbers in Polar Form; DeMoivre’s Theorem
Vectors
The Dot Product

Chapter 7. Systems of Equations and Inequalities
Systems of Linear Equations in Two Variables
Systems of Linear Equations in Three Variables
Partial Fractions
Systems of Nonlinear Equations in Two Variables
Systems of Inequalities
Linear Programming

Chapter 8. Matrices and Determinants
Matrix Solutions to Linear Systems
Inconsistent and Dependent Systems and Their Applications
Matrix Operations and Their Applications
Multiplicative Inverses of Matrices and Matrix Equations
Determinants and Cramer’s Rule

Chapter 9. Conic Sections and Analytic Geometry
The Ellipse
The Hyperbola
The Parabola
Rotation of Axes
Parametric Equations
Conic Sections in Polar Coordinates

Chapter 10. Sequences, Induction, and Probability
Sequences and Summation Notation
Arithmetic Sequences
Geometric Sequences and Series
Mathematical Induction
The Binomial Theorem
Counting Principles, Permutations, and Combinations
Probability

Chapter 11. Introduction to Calculus
Finding Limits Using Tables and Graphs
Finding Limits Using Properties of Limits
Limits and Continuity
Introduction to Derivatives