Beginning & Intermediate Algebra

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 has 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 in 2002. Jeff travels around the country speaking on student retention and is also a consultant to the Federal Government. He lives in Marblehead, Mass. 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.

How Am I Doing? Guide to Math Success (inside front cover)

To the Student

Preface

Acknowledgments

Diagnostic Pretest

 

0. Prealgebra Review

0.1 Simplifying Fractions

0.2 Adding and Subtracting Fractions

0.3 Multiplying and Dividing Fractions

            How Am I Doing? Sections 0.1—0.3

0.4 Using Decimals

0.5 Percents, Rounding, and Estimating

            Putting Your Skills to Work: Use Math to Save Money


            Chapter 0 Organizer

            Chapter 0 Review Problems

            How Am I Doing? Chapter 0 Test

 

1. Real Numbers and Variables

1.1 Adding Real Numbers

1.2 Subtracting Real Numbers

1.3 Multiplying and Dividing Real Numbers

1.4 Exponents

1.5 The Order of Operations

            How Am I Doing? Sections 1.1—1.5

1.6 Using the Distributive Property to Simplify Algebraic Expressions

1.7 Combining Like Terms

1.8 Using Substitution to Evaluate Algebraic Expressions and Formulas

1.9 Grouping Symbols

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 1 Organizer

            Chapter 1 Review Problems

            How Am I Doing? Chapter 1 Test

 

2. Equations, Inequalities, and Applications

2.1 The Addition Principle of Equality

2.2 The Multiplication Principle of Equality

2.3 Using the Addition and Multiplication Principles Together

2.4 Solving Equations with Fractions

            How Am I Doing? Sections 2.1—2.4

2.5 Translating English Phrases into Algebraic Expressions

2.6 Using Equations to Solve Word Problems

2.7 Solving Word Problems Using Geometric Formulas

2.8 Solving Inequalities in One Variable

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 2 Organizer

            Chapter 2 Review Problems

            How Am I Doing? Chapter 2 Test

            Cumulative Test for Chapters 0—2

 

3. Graphing and Functions

3.1 The Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 The Slope of a Line

            How Am I Doing? Sections 3.1—3.3

3.4 Writing the Equation of a Line

3.5 Graphing Linear Inequalities

3.6 Functions

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 3 Organizer

            Chapter 3 Review Problems

            How Am I Doing? Chapter 3 Test

            Cumulative Test for Chapters 0—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

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 4 Organizer

            Chapter 4 Review Problems

            How Am I Doing? Chapter 4 Test

            Cumulative Test for Chapters 0—4

 

5. Exponents and Polynomials

5.1 The Rules of Exponents

5.2 Negative Exponents and Scientific Notation

5.3 Fundamental Polynomial Operations

            How Am I Doing? Sections 5.1—5.3

5.4 Multiplying Polynomials

5.5 Multiplication: Special Cases

5.6 Dividing Polynomials

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 5 Organizer

            Chapter 5 Review Problems

            How Am I Doing? Chapter 5 Test

            Cumulative Test for Chapters 0—5

 

6. Factoring

6.1 Removing a Common Factor

6.2 Factoring by Grouping

6.3 Factoring Trinomials of the Form x2 + bx + c

6.4 Factoring Trinomials of the Form ax2 + bx + c

            How Am I Doing? Sections 6.1—6.4

6.5 Special Cases of Factoring

6.6 A Brief Review of Factoring

6.7 Solving Quadratic Equations by Factoring

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 6 Organizer

            Chapter 6 Review Problems

            How Am I Doing? Chapter 6 Test

            Cumulative Test for Chapters 0—6

 

 

7. Rational Expressions and Equations

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions

            How Am I Doing? Sections 7.1—7.3

7.4 Simplifying Complex Rational Expressions

7.5 Solving Equations Involving Rational Expressions

7.6 Ratio, Proportion, and Other Applied Problems

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 7 Organizer

            Chapter 7 Review Problems

            How Am I Doing? Chapter 7 Test

            Cumulative Test for Chapters 0—7

 

8. Rational Exponents and Radicals

8.1 Rational Exponents

8.2 Radical Expressions and Functions

8.3 Simplifying, Adding, and Subtracting Radicals

8.4 Multiplying and Dividing Radicals

            How Am I Doing? Sections 8.1—8.4

8.5 Radical Equations

8.6 Complex Numbers

8.7 Variation

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 8 Organizer

            Chapter 8 Review Problems

            How Am I Doing? Chapter 8 Test

            Cumulative Test for Chapters 0—8

 

9. Quadratic Equations and Inequalities

9.1 Quadratic Equations

9.2 The Quadratic Formula and Solutions to Quadratic Equations

9.3 Equations that can be Transformed into Quadratic Form

            How Am I Doing? Sections 9.1—9.3

9.4 Formulas and Applications

9.5 Quadratic Functions

9.6 Compound Inequalities and Quadratic Inequalities

9.7 Absolute Value Equations and Inequalities

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 9 Organizer

            Chapter 9 Review Problems

            How Am I Doing? Chapter 9 Test

            Cumulative Test for Chapters 0—9

 

10. The Conic Sections

10.1 The Distance Formula and the Circle

10.2 The Parabola

10.3 The Ellipse

            How Am I Doing? Sections 10.1—10.3

10.4 The Hyperbola

10.5 Nonlinear Systems of Equations

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 10 Organizer

            Chapter 10 Review Problems

            How Am I Doing? Chapter 10 Test

            Cumulative Test for Chapters 0—10

 

11. Additional Properties of Functions

11.1 Function Notation

11.2 General Graphing Procedures for Functions

            How Am I Doing? Sections 11.1—11.2

11.3 Algebraic Operations on Functions

11.4 Inverse of a Function

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 11 Organizer

            Chapter 11 Review Problems

            How Am I Doing? Chapter 11 Test

            Cumulative Test for Chapters 0—11

 

12. Logarithmic and Exponential Functions

12.1 The Exponential Function

12.2 The Logarithmic Function

12.3 Properties of Logarithms

            How Am I Doing? Sections 12.1—12.3

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


12.5 Exponential and Logarithmic Equations

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 12 Organizer

            Chapter 12 Review Problems

            How Am I Doing? Chapter 12 Test

 

Practice Final Examination

Glossary

Appendix A: Foundations for Intermediate Algebra

            A.1 Exponents and the Order of Operations

            A.2 Polynomial Operations

            A.3 Factoring

Appendix B: Mathematics Blueprint for Problem Solving

Appendix C: Practice with Operations of Whole Numbers

Appendix D: Tables

Appendix E: Determinants and Cramer's Rule

Appendix F: Solving Systems of Linear Equations Using Matrices

Appendix G: Sets

Solutions to Practice Problems

Answers to Selected Exercises

Applications Index

Index

Photo Credits