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 Lexington, 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 Specialists 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.

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

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

Chapter 1 Organizer

Chapter 1 Review Problems

How Am I Doing? Chapter 1 Test

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2. Equations and Inequalities

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

2.5. Formulas

2.6 Solving Inequalities in One Variable

Chapter 2 Organizer

Chapter 2 Review Problems

How Am I Doing? Chapter 2 Test

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3. Solving Applied Problems

3.1 Translating English Phrases into Algebraic Expressions

3.2 Using Equations to Solve Word Problems

3.3 Solving Word Problems: Comparisons

3.4 Solving Word Problems: The Value of Money and Percents

3.5 Solving Word Problems Using Geometric Formulas

3.6 Using Inequalities to Solve Word Problems

Chapter 3 Organizer

Chapter 3 Review Problems

How Am I Doing? Chapter 3 Test

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4. Exponents and Polynomials

4.1 The Rules of Exponents

4.2 Negative Exponents and Scientific Notation

4.3 Fundamental Polynomial Operations

4.4 Multiplying Polynomials

4.5 Multiplication: Special Cases

4.6 Dividing Polynomials

Chapter 4 Organizer

Chapter 4 Review Problems

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5. Factoring

5.1 Removing a Common Factor

5.2 Factoring by Grouping

5.3 Factoring Trinomials of the Form x2 + bx + c

5.4 Factoring Trinomials of the Form ax2 + bx+ c

5.5 Special Cases of Factoring

5.6. A Brief Review of Factoring

5.7 Solving Quadratic Equations by Factoring

Chapter 5 Organizer

Chapter 5 Review Problems

How Am I Doing? Chapter 5 Test

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6. Rational Expressions and Equations

6.1 Simplifying Rational Expressions

6.2 Multiplying and Dividing Rational Expressions

6.3 Adding and Subtracting Rational Expressions

6.4 Simplifying Complex Rational Expressions

6.5 Solving Equations Involving Rational Expressions

6.6 Ratio, Proportion, and Other Applied Problems

Chapter 6 Organizer

Chapter 6 Review Problems

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7. Graphing and Functions

7.1 The Rectangular Coordinate System

7.2 Graphing Linear Equations

7.3 The Slope of a Line

7.4 Writing the Equation of a Line

7.5 Graphing Linear Inequalities

7.6 Functions

Chapter 7 Organizer

Chapter 7 Review Problems

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8. Systems of Equations

8.1 Solving a System of Equations in Two Variables by Graphing

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

8.3 Solving A System of Equations in Two Variables by the Addition Method

8.4 Review of Methods for Solving Systems of Equations

8.5 Solving Word Problems Using Systems of Equations

Chapter 8 Organizer

Chapter 8 Review Problems

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9. Radicals

9.1 Square Roots

9.2 Simplifying Radical Expressions

9.3 Adding and Subtracting Radical Expressions

9.4 Multiplying Radical Expressions

9.5 Dividing Radical Expressions

9.6 The Pythagorean Theorem and Radical Equations

9.7 Word Problems Involving Radicals: Direct and Inverse Variation

Chapter 9 Organizer

Chapter 9 Review Problems

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10. Quadratic Equations

10.1 Introduction to Quadratic Equations

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

10.3 Using the Quadratic Formula to Find Solutions

10.4 Graphing Quadratic Equations

10.5 Formulas and Applied Problems

Chapter 10 Organizer

Chapter 10 Review Problems

How Am I Doing? Chapter 10 Test

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