# Intermediate Algebra

**by**Tobey, John Jr; Slater, Jeffrey; Blair, Jamie; Crawford, Jennifer

### 9780321769503

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## Summary

## Author Biography

**John Tobey** received his BA in mathematics from Wheaton College in Wheaton, Illinois in 1965, his MA in mathematics education from Harvard University in 1966, and his PhD in mathematics education from Boston University in 1980. He has taught in the mathematics department at the United States Military Academy at West Point and served as the Mathematics Department Chairman at North Shore Community College in Danvers, Massachusetts for five years. John has served as the president of the New England Mathematics Association of Two Year Colleges. He has received the NISOD award for outstanding teaching from the University of Texas at Austin. John is the author of seven mathematics books published by Pearson Education. John has spoken to many mathematics departments and at many professional meetings throughout the country on the topic of developmental mathematics education and distance learning in mathematics. He lives in Massachusetts.

**Jeffrey Slater** has been a professor at North Shore Community College for thirty-eight years and received the Teacher of the Year award in 2002. Jeff travels around the country speaking on student retention and is also a consultant to the Federal Government. He lives in Marblehead, Massachusetts with his wife Shelley and his yellow lab Gracie.

**Jamie Blair** has directed the Mathematics Learning Center at Orange Coast College for the past seventeen years. She designed, developed, and implemented the Center, and as a result of this effort has provided technical expertise related to the particulars of the Math Center to numerous other two-year colleges and at many conferences. In 2007 Jamie was appointed to the Team of Basic Skills Specialist by the California State Academic Senate. She is also currently participating on Title 3 committees on her campus. She specializes in teaching students who have never been successful in mathematics. She is an expert in the area of basic skills in relation to the learning needs of students. She lives in California.

**Jennifer Crawford **received her BS in mathematics from the University of Minnesota – Duluth in 1995 and her MS in mathematics from the University of Minnesota – Twin Cities in 1998. She taught a wide range of courses at North Shore Community College in Danvers, Massachusetts for five years. She currently teaches at Normandale Community College in Bloomington, Minnesota where her focus is working with developmental math students. She lives in Minneapolis, Minnesota with her husband, two young children, and black lab.

## Table of Contents

Preface

Diagnostic Pretest

**1. Basic Concepts**

1.1 The Real Number System

1.2 Operations with Real Numbers

1.3 Powers, Square Roots, and the Order of Operations

How Am I Doing? Sections 1.1–1.3

1.4 Integer Exponents and Scientific Notation

1.5 Operations with Variables and Grouping Symbols

1.6 Evaluating Variable Expressions and Formulas

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Chapter 1 Organizer

Chapter 1 Review Problems

How Am I Doing? Chapter 1 Test

Math Coach

**2. Linear Equations and Inequalities**

2.1 First-Degree Equations with One Unknown

2.2 Literal Equations and Formulas

2.3 Absolute Value Equations

2.4 Using Equations to Solve Word Problems

How Am I Doing? Sections 2.1–2.4

2.5 Solving More-Involved Word Problems

2.6 Linear Inequalities

2.7 Compound Inequalities

2.8 Absolute Value Inequalities

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Chapter 2 Organizer

Chapter 2 Review Problems

How Am I Doing? Chapter 2 Test

Math Coach

**3. Equations and Inequalities in Two Variables and Functions**

3.1 Graphing Linear Equations with Two Unknowns

3.2 Slope of a Line

3.3 Graphs and the Equations of a Line

How Am I Doing? Sections 3.1–3.3

3.4 Linear Inequalities in Two Variables

3.5 Concept of a Function

3.6 Graphing Functions from Equations and Tables of Data

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Chapter 3 Organizer

Chapter 3 Review Problems

How Am I Doing? Chapter 3 Test

Math Coach

Cumulative Test for Chapters 1–3

**4. Systems of Linear Equations and Inequalities**

4.1 Systems of Linear Equations in Two Variables

4.2 Systems of Linear Equations in Three Variables

How Am I Doing? Sections 4.1–4.2

4.3 Applications of Systems of Linear Equations

4.4 Systems of Linear Inequalities

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Chapter 4 Organizer

Chapter 4 Review Problems

How Am I Doing? Chapter 4 Test

Math Coach

**5. Polynomials**

5.1 Introduction to Polynomials and Polynomial Functions: Adding, Subtracting, and Multiplying

5.2 Dividing Polynomials

5.3 Synthetic Division

5.4 Removing Common Factors; Factoring by Grouping

5.5 Factoring Trinomials

How Am I Doing? Sections 5.1–5.5

5.6 Special Cases of Factoring

5.7 Factoring a Polynomial Completely

5.8 Solving Equations and Applications Using Polynomials

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Chapter 5 Organizer

Chapter 5 Review Problems

How Am I Doing? Chapter 5 Test

Math Coach

**6. Rational Expressions and Equations**

6.1 Rational Expressions and Functions: Simplifying, Multiplying, and Dividing

6.2 Adding and Subtracting Rational Expressions

6.3 Complex Rational Expressions

How Am I Doing? Sections 6.1–6.3

6.4 Rational Equations

6.5 Applications: Formulas and Advanced Ratio Exercises

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Chapter 6 Organizer

Chapter 6 Review Problems

How Am I Doing? Chapter 6 Test

Math Coach

Cumulative Test for Chapters 1–6

**7. Rational Exponents and Radicals**

7.1 Rational Exponents

7.2 Radical Expressions and Functions

7.3 Simplifying, Adding, and Subtracting Radicals

7.4 Multiplying and Dividing Radicals

How Am I Doing? Sections 7.1–7.4

7.5 Radical Equations

7.6 Complex Numbers

7.7 Variation

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Chapter 7 Organizer

Chapter 7 Review Problems

How Am I Doing? Chapter 7 Test

Math Coach

**8. Quadratic Equations and Inequalities**

8.1 Quadratic Equations

8.2 The Quadratic Formula and Solutions to Quadratic Equations

8.3 Equations That Can Be Transformed into Quadratic Form

How Am I Doing? Sections 8.1–8.3

8.4 Formulas and Applications

8.5 Quadratic Functions

8.6 Quadratic Inequalities in One Variable

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Chapter 8 Organizer

Chapter 8 Review Problems

How Am I Doing? Chapter 8 Test

Math Coach

**9. The Conic Sections**

9.1 The Distance Formula and the Circle

9.2 The Parabola

9.3 The Ellipse

How Am I Doing? Sections 9.1–9.3

9.4 The Hyperbola

9.5 Nonlinear Systems of Equations

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Chapter 9 Organizer

Chapter 9 Review Problems

How Am I Doing? Chapter 9 Test

Math Coach

**10. Additional Properties of Functions**

10.1 Function Notation

10.2 General Graphing Procedures for Functions

How Am I Doing? Sections 10.1–10.2

10.3 Algebraic Operations on Functions

10.4 Inverse of a Function

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Chapter 10 Organizer

Chapter 10 Review Problems

How Am I Doing? Chapter 10 Test

Math Coach

**11. Logarithmic and Exponential Functions**

11.1 The Exponential Function

11.2 The Logarithmic Function

11.3 Properties of Logarithms

How Am I Doing? Sections 11.1–11.3

11.4 Common Logarithms, Natural Logarithms, and Change of Base of Logarithms

11.5 Exponential and Logarithmic Equations

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Chapter 11 Organizer

Chapter 11 Review Problems

How Am I Doing? Chapter 11 Test

Math Coach

Practice Final Examination

**Appendix A: Tables**

Table A-1: Table of Square Roots

Table A-2: Table of Exponential Values

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

**Appendix C: Solving Systems of Linear Equations Using Matrices**

Solutions to Practice Problems

Answers to Selected Exercises

Glossary

Applications Index (Available in MyMathLab)

Index

Photo Credits