## Table of Contents

Preface

Study Skills: Using Your Math Textbook

**R. Review of the Real Number System**

R.1 Basic Concepts

R.2 Operations on Real Numbers

R.3 Exponents, Roots, and Order of Operations

R.4 Properties of Real Numbers

Chapter R Summary

Chapter R Test

Study Skills: Reading Your Math Textbook

**1. Linear Equations, Inequalities, and Applications**

1.1 Linear Equations in One Variable

Study Skills: Completing Your Homework

1.2 Formulas and Percent

Study Skills: Taking Lecture Notes

1.3 Applications of Linear Equations

1.4 Further Applications of Linear Equations

Summary Exercises: Applying Problem-Solving Techniques

1.5 Linear Inequalities in One Variable

Study Skills: Using Study Cards

1.6 Set Operations and Compound Inequalities

Study Skills: Using Study Cards Revisited

1.7 Absolute Value Equations and Inequalities

Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities

Study Skills: Reviewing a Chapter

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Mixed Review Exercises

Chapter 1 Test

**2. Linear Equations, Graphs, and Functions**

2.1 Linear Equations in Two Variables

Study Skills: Managing Your Time

2.2 The Slope of a Line

2.3 Writing Equations of Lines

Study Skills: Taking Math Tests

Summary Exercises: Finding Slopes and Equations of Lines

2.4 Linear Inequalities in Two Variables

2.5 Introduction to Relations and Functions

Study Skills: Analyzing Your Test Results

2.6 Function Notation and Linear Functions

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Mixed Review Exercises

Chapter 2 Test

Chapters R---2 Cumulative Review Exercises

**3. Systems of Linear Equations**

3.1 Systems of Linear Equations in Two Variables

Study Skills: Preparing for Your Math Final Exam

3.2 Systems of Linear Equations in Three Variables

3.3 Applications of Systems of Linear Equations

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Mixed Review Exercises

Chapter 3 Test

Chapters R–3 Cumulative Review Exercises

**4. Exponents, Polynomials, and Polynomial Functions**

4.1 Integer Exponents and Scientific Notation

4.2 Adding and Subtracting Polynomials

4.3 Polynomial Functions, Graphs, and Composition

4.4 Multiplying Polynomials

4.5 Dividing Polynomials

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Mixed Review Exercises

Chapter 4 Test

Chapters R–4 Cumulative Review Exercises

**5. Factoring**

5.1 Greatest Common Factors and Factoring by Grouping

5.2 Factoring Trinomials

5.3 Special Factoring

5.4 A General Approach to Factoring

5.5 Solving Equations by the Zero-Factor Property

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Mixed Review Exercises

Chapter 5 Test

Chapters R–5 Cumulative Review Exercises

**6. Rational Expressions and Functions**

6.1 Rational Expressions and Functions; Multiplying and Dividing

6.2 Adding and Subtracting Rational Expressions

6.3 Complex Fractions

6.4 Equations with Rational Expressions and Graphs

Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations

6.5 Applications of Rational Expressions

6.6 Variation

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Mixed Review Exercises

Chapter 6 Test

Chapters R–6 Cumulative Review Exercises

**7. Roots, Radicals, and Root Functions**

7.1 Radical Expressions and Graphs

7.2 Rational Exponents

7.3 Simplifying Radicals, the Distance Formula, and Circles

7.4 Adding and Subtracting Radical Expressions

7.5 Multiplying and Dividing Radical Expressions

Summary Exercises: Performing Operations with Radicals and Rational Exponents

7.6 Solving Equations with Radicals

7.7 Complex Numbers

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Mixed Review Exercises

Chapter 7 Test

Chapters R–7 Cumulative Review Exercises

**8. Quadratic Equations and Inequalities**

8.1 The Square Root Property and Completing the Square

8.2 The Quadratic Formula

8.3 Equations Quadratic in Form

Summary Exercises: Applying Methods for Solving Quadratic Equations

8.4 Formulas and Further Applications

8.5 Polynomial and Rational Inequalities

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Mixed Review Exercises

Chapter 8 Test

Chapters R–8 Cumulative Review Exercises

**9. Additional Graphs of Functions and Relations**

9.1 Review of Operations and Composition

9.2 Graphs of Quadratic Functions

9.3 More About Parabolas and Their Applications

9.4 Symmetry; Increasing and Decreasing Functions

9.5 Piecewise Linear Functions

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Mixed Review Exercises

Chapter 9 Test

Chapters R–9 Cumulative Review Exercises

**10. Inverse, Exponential, and Logarithmic Functions**

10.1 Inverse Functions

10.2 Exponential Functions

10.3 Logarithmic Functions

10.4 Properties of Logarithms

10.5 Common and Natural Logarithms

10.6 Exponential and Logarithmic Equations; Further Applications

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Mixed Review Exercises

Chapter 10 Test

Chapters R–10 Cumulative Review Exercises

**11. Polynomial and Rational Functions**

11.1 Zeros of Polynomial Functions (I)

11.2 Zeros of Polynomial Functions (II)

11.3 Graphs and Applications of Polynomial Functions

Summary Exercises: Examining Polynomial Functions and Graphs

11.4 Graphs and Applications of Rational Functions

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Mixed Review Exercises

Chapter 11 Test

Chapters R–11 Cumulative Review Exercises

**12. Conic Sections and Nonlinear Systems**

12.1 Circles Revisited and Ellipses

12.2 Hyperbolas and Functions Defined by Radicals

12.3 Nonlinear Systems of Equations

12.4 Second-Degree Inequalities, Systems of Inequalities, and Linear Programming

Chapter 12 Summary

Chapter 12 Review Exercises

Chapter 12 Mixed Review Exercises

Chapter 12 Test

Chapters R–12 Cumulative Review Exercises

**13. Further Topics in Algebra**

13.1 Sequences and Series

13.2 Arithmetic Sequences

13.3 Geometric Sequences

13.4 The Binomial Theorem

13.5 Mathematical Induction

13.6 Counting Theory

13.7 Basics of Probability

Chapter 13 Summary

Chapter 13 Review Exercises

Chapter 13 Mixed Review Exercises

Chapter 13 Test

Chapters R–13 Cumulative Review Exercises

**Appendix A: Solving Systems of Linear Equations by Matrix Methods**

**Appendix B: Determinants and Cramer’s Rule**

**Appendix C: Properties of Matrices**

**Appendix D: Matrix Inverses**

Photo Credits

Answers to Selected Exercises

Index