## Table of Contents

P. Prerequisites: Fundamental Concepts of Algebra

• P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
• P.2 Exponents and Scientific Notation
• P.3 Radicals and Rational Exponents
• P.4 Polynomials
• P.5 Factoring Polynomials
• P.6 Rational Expressions

1. Equations and Inequalities

• 1.1 Graphs and Graphing Utilities
• 1.2 Linear Equations and Rational Equations
• 1.3 Models and Applications
• 1.4 Complex Numbers
• 1.5 Quadratic Equations
• 1.6 Other Types of Equations
• 1.7 Linear Inequalities and Absolute Value Inequalities

2. Functions and Graphs

• 2.1 Basics of Functions and Their Graphs
• 2.2 More on Functions and Their Graphs
• 2.3 Linear Functions and Slope
• 2.4 More on Slope
• 2.5 Transformations of Functions
• 2.6 Combinations of Functions; Composite Functions
• 2.7 Inverse Functions
• 2.8 Distance and Midpoint Formulas; Circles

3. Polynomial and Rational Functions

• 3.1 Quadratic Functions
• 3.2 Polynomial Functions and Their Graphs
• 3.3 Dividing Polynomials; Remainder and Factor Theorems
• 3.4 Zeros of Polynomial Functions
• 3.5 Rational Functions and Their Graphs
• 3.6 Polynomial and Rational Inequalities
• 3.7 Modeling Using Variation

4. Exponential and Logarithmic Functions

• 4.1 Exponential Functions
• 4.2 Logarithmic Functions
• 4.3 Properties of Logarithms
• 4.4 Exponential and Logarithmic Equations
• 4.5 Exponential Growth and Decay; Modeling Data

5. Trigonometric Functions

• 5.1 Angles and Radian Measure
• 5.2 Right Triangle Trigonometry
• 5.3 Trigonometric Functions of Any Angle
• 5.4 Trigonometric Functions of Real Numbers; Periodic Functions
• 5.5 Graphs of Sine and Cosine Functions
• 5.6 Graphs of Other Trigonometric Functions
• 5.7 Inverse Trigonometric Functions
• 5.8 Applications of Trigonometric Functions

6. Analytic Trigonometry

• 6.1 Verifying Trigonometric Identities
• 6.2 Sum and Difference Formulas
• 6.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
• 6.4 Product-to-Sum and Sum-to-Product Formulas
• 6.5 Trigonometric Equations

7. Additional Topics in Trigonometry

• 7.1 The Law of Sines
• 7.2 The Law of Cosines
• 7.3 Polar Coordinates
• 7.4 Graphs of Polar Equations
• 7.5 Complex Numbers in Polar Form; DeMoivre's Theorem
• 7.6 Vectors
• 7.7 The Dot Product

8. Systems of Equations and Inequalities

• 8.1 Systems of Linear Equations in Two Variables
• 8.2 Systems of Linear Equations in Three Variables
• 8.3 Partial Fractions
• 8.4 Systems of Nonlinear Equations in Two Variables
• 8.5 Systems of Inequalities
• 8.6 Linear Programming

9. Matrices and Determinants

• 9.1 Matrix Solutions to Linear Systems
• 9.2 Inconsistent and Dependent Systems and Their Applications
• 9.3 Matrix Operations and Their Applications
• 9.4 Multiplicative Inverses of Matrices and Matrix Equations
• 9.5 Determinants and Cramer's Rule

10. Conic Sections and Analytic Geometry

• 10.1 The Ellipse
• 10.2 The Hyperbola
• 10.3 The Parabola
• 10.4 Rotation of Axes
• 10.5 Parametric Equations
• 10.6 Conic Sections in Polar Coordinates

11. Sequences, Induction, and Probability

• 11.1 Sequences and Summation Notation
• 11.2 Arithmetic Sequences
• 11.3 Geometric Sequences and Series
• 11.4 Mathematical Induction
• 11.5 The Binomial Theorem
• 11.6 Counting Principles, Permutations, and Combinations
• 11.7 Probability