## Table of Contents

**P. Basic Concepts of Algebra**

P.1 The Real Numbers and Their Properties

P.2 Integer Exponents and Scientific Notation

P.3 Polynomials

P.4 Factoring Polynomials

P.5 Rational Expressions

P.6 Rational Exponents and Radicals

Chapter P Summary

Chapter P Review Exercises

Chapter P Practice Test A

Chapter P Practice Test B

**1. Equations and Inequalities**

1.1 Linear Equations in One Variable

1.2 Quadratic Equations

1.3 Complex Numbers: Quadratic Equations with Complex Solutions

1.4 Solving Other Types of Equations

1.5 Inequalities

1.6 Equations and Inequalities Involving Absolute Value

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Practice Test A

Chapter 1 Practice Test B

**2. Graphs and Functions**

2.1 The Coordinate Plane

2.2 Graphs of Equations

2.3 Lines

2.4 Functions

2.5 Properties of Functions

2.6 A Library of Functions

2.7 Transformations of Functions

2.8 Combining Functions; Composite Functions

2.9 Inverse Functions

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Practice Test A

Chapter 2 Practice Test B

Cumulative Review Exercises- Chapters P-2

**3. Polynomial and Rational Functions**

3.1 Quadratic Functions

3.2 Polynomial Functions

3.3 Dividing Polynomials

3.4 The Real Zeros of a Polynomial Function

3.5 The Complex Zeros of a Polynomial Function

3.6 Rational Functions

3.7 Variation

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Practice Test A

Chapter 3 Practice Test B

Cumulative Review Exercises- Chapters P-3

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Rules of Logarithms

4.4 Exponential and Logarithmic Equations and Inequalities

4.5 Logarithmic Scales

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Practice Test A

Chapter 4 Practice Test B

Cumulative Review Exercises- Chapters P-4

**5. Trigonometric Functions**

5.1 Angles and Their Measure

5.2 Right-Triangle Trigonometry

5.3 Trigonometric Functions of Any Angle; The Unit Circle

5.4 Graphs of the Sine and Cosine Functions

5.5 Graphs of the Other Trigonometric Functions

5.6 Inverse Trigonometric Functions

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Practice Test A

Chapter 5 Practice Test B

Cumulative Review Exercises- Chapters P-5

**6. Trigonometric Identities and Equations**

6.1 Verifying Identities

6.2 Sum and Difference Formulas

6.3 Double-Angle and Half-Angle Formulas

6.4 Product-to-Sum and Sum-to-Product Formulas

6.5 Trigonometric Equations I

6.6 Trigonometric Equations II

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Practice Test A

Chapter 6 Practice Test B

Cumulative Review Exercises- Chapters P-6

**7. Applications of Trigonometric Functions**

7.1 The Law of Sines

7.2 The Law of Cosines

7.3 Areas of Polygons Using Trigonometry

7.4 Vectors

7.5 The Dot Product

7.6 Polar Coordinates

7.7 Polar Form of Complex Numbers; DeMoivre’s Theorem

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Practice Test A

Chapter 7 Practice Test B

Cumulative Review Exercises- Chapters P-7

**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-Fraction Decomposition

8.4 Systems of Nonlinear Equations

8.5 Systems of Inequalities

8.6 Linear Programming

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Practice Test A

Chapter 8 Practice Test B

Cumulative Review Exercises- Chapters P-8

**9. Matrices and Determinants**

9.1 Matrices and Systems of Equations

9.2 Matrix Algebra

9.3 The Matrix Inverse

9.4 Determinants and Cramer’s Rule

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Practice Test A

Chapter 9 Practice Test B

Cumulative Review Exercises- Chapters P-9

**10. Conic Sections**

10.1 Conic Sections: Overview

10.2 The Parabola

10.3 The Ellipse

10.4 The Hyperbola

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Practice Test A

Chapter 10 Practice Test B

Cumulative Review Exercises- Chapters P-10

**11. Further Topics in Algebra**

11.1 Sequences and Series

11.2 Arithmetic Sequences; Partial Sums

11.3 Geometric Sequences and Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

11.6 Counting Principles

11.7 Probability

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Practice Test A

Chapter 11 Practice Test B

Cumulative Review Exercises- Chapters P-11