Elementary Algebra

Mike Sullivan, III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.

1. Operations on Real Numbers and Algebraic Expressions

1.1 Success in Mathematics

1.2 Fractions, Decimals, and Percents

1.3 The Number Systems and the Real Number Line

1.4 Adding, Subtracting, Multiplying, and Dividing Integers

1.5 Adding, Subtracting, Multiplying, and Dividing Rational Numbers Expressed as Fractions and Decimals

            Putting the Concepts Together (Sections 1.2—1.5)

1.6 Properties of Real Numbers

1.7 Exponents and the Order of Operations

1.8 Simplifying Algebraic Expressions

            Chapter 1 Activity: The Math Game

            Chapter 1 Review

            Chapter 1 Test

 

2. Equations and Inequalities in One Variable

2.1 Linear Equations: The Addition and Multiplication Properties of Equality

2.2 Linear Equations: Using the Properties Together

2.3 Solving Linear Equations Involving Fractions and Decimals; Classifying Equations

2.4 Evaluating Formulas and Solving Formulas for a Variable

            Putting the Concepts Together (Sections 2.1—2.4)

2.5 Introduction to Problem Solving: Direct Translation Problems

2.6 Problem Solving: Direct Translation Problems Involving Percent

2.7 Problem Solving: Geometry and Uniform Motion

2.8 Solving Linear Inequalities in One Variable

            Chapter 2 Activity: Pass to the Right

            Chapter 2 Review

            Chapter 2 Test

 

3. Introduction to Graphing and Equations of Lines

3.1 The Rectangular Coordinate System and Equations in Two Variables

3.2 Graphing Equations in Two Variables

3.3 Slope

3.4 Slope-Intercept Form of a Line

3.5 Point-Slope Form of a Line

3.6 Parallel and Perpendicular Lines

            Putting the Concepts Together (Sections 3.1—3.6)

3.7 Linear Inequalities in Two Variables

            Chapter 3 Activity: Graphing Practice

            Chapter 3 Review

            Chapter 3 Test

            Cumulative Review Chapters 1—3

 

4. Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations Using Substitution

4.3 Solving Systems of Linear Equations Using Elimination

            Putting the Concepts Together (Sections 4.1—4.3)

4.4 Solving Direct Translation, Geometry, and Uniform Motion Problems Using Systems of Linear Equations

4.5 Solving Mixture Problems Using Systems of Linear Equations

4.6 Systems of Linear Inequalities

            Chapter 4 Activity: Find the Numbers

            Chapter 4 Review

            Chapter 4 Test

 

5. Exponents and Polynomials

5.1 Adding and Subtracting Polynomials

5.2 Multiplying Monomials: The Product and Power Rules

5.3 Multiplying Polynomials

5.4 Dividing Monomials: The Quotient Rule and Integer Exponents

            Putting the Concepts Together (Sections 5.1—5.4)

5.5 Dividing Polynomials

5.6 Applying the Exponent Rules: Scientific Notation

            Chapter 5 Activity: What Is the Question?

            Chapter 5 Review

            Chapter 5 Test

            Cumulative Review Chapters 1—5

 

6. Factoring Polynomials

6.1 Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the Form x2 + bx + c

6.3 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1

6.4 Factoring Special Products

6.5 Summary of Factoring Techniques

            Putting the Concepts Together (Sections 6.1—6.5)

6.6 Solving Polynomial Equations by Factoring

6.7 Modeling and Solving Problems with Quadratic Equations

            Chapter 6 Activity: Which One Does Not Belong?

            Chapter 6 Review

            Chapter 6 Test

 

7. Rational Expressions and Equations

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with a Common Denominator

7.4 Finding the Least Common Denominator and Forming Equivalent Rational Expressions

7.5 Adding and Subtracting Rational Expressions with Unlike Denominators

7.6 Complex Rational Expressions

            Putting the Concepts Together (Sections 7.1—7.6)

7.7 Rational Equations

7.8 Models Involving Rational Equations

7.9 Variation

            Chapter 7 Activity: Correct the Quiz

            Chapter 7 Review

            Chapter 7 Test

            Cumulative Review Chapters 1—7

 

8. Roots and Radicals

8.1 Introduction to Square Roots

8.2 Simplifying Square Roots

8.3 Adding and Subtracting Square Roots

8.4 Multiplying Expressions with Square Roots

8.5 Dividing Expressions with Square Roots

            Putting the Concepts Together (Sections 8.1—8.5)

8.6 Solving Equations Containing Square Roots

8.7 Higher Roots and Rational Exponents

            Chapter 8 Activity: Working Together with Radicals

            Chapter 8 Review

            Chapter 8 Test

 

9. Quadratic Equations

9.1 Solving Quadratic Equations Using the Square Root Property

9.2 Solving Quadratic Equations by Completing the Square

9.3 Solving Quadratic Equations Using the Quadratic Formula

            Putting the Concepts Together (Sections 9.1—9.3)

9.4 Problem Solving Using Quadratic Equations

9.5 The Complex Number System

            Chapter 9 Activity: The Math Game

            Chapter 9 Review

            Chapter 9 Test

            Cumulative Review Chapters 1—9

 

10. Graphs of Quadratic Equations in Two Variables and an Introduction to Functions

10.1 Quadratic Equations in Two Variables

10.2 Relations

            Putting the Concepts Together (Sections 10.1—10.2)

10.3 An Introduction to Functions

            Chapter 10 Activity: Discovering Shifting

            Chapter 10 Review

            Chapter 10 Test

 

Appendix A: Table of Square Roots

Appendix B: Geometry Review

Answers to Selected Exercises

Graphing Answers Section

Applications Index

Subject Index

Photo Credits