Beginning 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 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.

Preface

Diagnostic Pretest

 

0. Prealgebra Review

0.1 Simplifying Fractions

0.2 Adding and Subtracting Fractions

0.3 Multiplying and Dividing Fractions

0.4 Using Decimals

            How Am I Doing? Sections 0.1–0.4

0.5 Percents, Rounding, and Estimating

0.6 Using the Mathematics Blueprint for Problem Solving

            Use Math to Save Money

            Chapter 0 Organizer

            Chapter 0 Review Problems

            How Am I Doing? Chapter 0 Test

            Math Coach

 

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

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            Chapter 1 Organizer

            Chapter 1 Review Problems

            How Am I Doing? Chapter 1 Test

            Math Coach

 

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: The Value of Money and Percents

2.8 Solving Inequalities in One Variable

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            Chapter 2 Organizer

            Chapter 2 Review Problems

            How Am I Doing? Chapter 2 Test

            Math Coach

 

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

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            Chapter 3 Organizer

            Chapter 3 Review Problems

            How Am I Doing? Chapter 3 Test

            Math Coach

 

4. Systems of Equations

4.1 Solving a System of Equations in Two Variables by Graphing

4.2 Solving a System of Equations in Two Variables by the Substitution Method

4.3 Solving a System of Equations in Two Variables by the Addition Method

            How Am I Doing? Sections 4.1–4.3

4.4 Review of Methods for Solving Systems

4.5 Solving Word Problems Using Systems of Equations

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            Chapter 4 Organizer

            Chapter 4 Review Problems

            How Am I Doing? Chapter 4 Test

            Math Coach

 

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

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            Chapter 5 Organizer

            Chapter 5 Review Problems

            How Am I Doing? Chapter 5 Test

            Math Coach

 

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

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            Chapter 6 Organizer

            Chapter 6 Review Problems

            How Am I Doing? Chapter 6 Test

            Math Coach

            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

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            Chapter 7 Organizer

            Chapter 7 Review Problems

            How Am I Doing? Chapter 7 Test

            Math Coach

 

8. Radicals

8.1 Square Roots

8.2 Simplifying Radical Expressions

8.3 Adding and Subtracting Radical Expressions

8.4 Multiplying Radical Expressions

            How Am I Doing? Sections 8.1–8.4

8.5 Dividing Radical Expressions

8.6 The Pythagorean Theorem and Radical Equations

8.7 Word Problems Involving Radicals: Direct and Inverse Variation

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            Chapter 8 Organizer

            Chapter 8 Review Problems

            How Am I Doing? Chapter 8 Test

            Math Coach

 

9. Quadratic Equations

9.1 Introduction to Quadratic Equations

9.2 Using the Square Root Property and Completing the Square to Find Solutions

9.3 Using the Quadratic Formula to Find Solutions

            How Am I Doing? Sections 9.1–9.3

9.4 Graphing Quadratic Equations

9.5 Formulas and Applied Problems

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            Chapter 9 Organizer

            Chapter 9 Review Problems

            How Am I Doing? Chapter 9 Test

            Math Coach

           

Practice Final Examination

 

Appendix A: Table of Square Roots

Appendix B: Practice with Operations of Whole Numbers

Appendix C: The Point–Slope Form of a Line

 

Solutions to Practice Problems

Answers to Selected Exercises

Glossary

Subject Index

Photo Credits

Index of Applications (Available in MyMathLab)