Elementary & Intermediate 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)

1.7 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

 

Getting Ready for Intermediate Algebra: A Review of Chapters 1 - 6

 

7. Rational Expresssions 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

            Chapter 7 Activity: Correct the Quiz

            Chapter 7 Review

            Chapter 7 Test

            Cumulative Review Chapters 1 - 7

 

Getting Ready for Intermediate Algebra: A Review of Chapters 1 - 7

 

8. Graphs, Relations, and Functions

8.1 Graphs of Equations

8.2 Relations

8.3 An Introduction to Functions

8.4 Functions and Their Graphs

            Putting the Concepts Together (Sections 8.1 - 8.4)

8.5 Linear Functions and Models

8.6 Compound Inequalities

8.7 Absolute Value Equations and Inequalities

8.8 Variation

            Chapter 8 Activity: Shifting Discovery

            Chapter 8 Review

            Chapter 8 Test

 

9. Radicals and Rational Exponents

9.1 Square Roots

9.2 nth Roots and Rational Exponents

9.3 Simplify Expressions Using the Laws of Exponents

9.4 Simplifying Radical Expressions Using Properties of Radicals

9.5 Adding, Subtracting, and Multiplying Radical Expressions

9.6 Rationalizing Radical Expressions

            Putting the Concepts Together (Sections 9.1 - 9.6)

9.7 Functions Involving Radicals

9.8 Radical Equations and Their Applications

9.9 The Complex Number System

            Chapter 9 Activity: Which One Does Not Belong?

            Chapter 9 Review

            Chapter 9 Test

            Cumulative Review Chapters 1 - 9

 

10. Quadratic Equations and Functions

10.1 Solving Quadratic Equations by Completing the Square

10.2 Solving Quadratic Equations by the Quadratic Formula

10.3 Solving Equations Quadratic in Form

            Putting the Concepts Together (Sections 10.1 - 10.3)

10.4 Graphing Quadratic Functions Using Transformations

10.5 Graphing Quadratic Functions Using Properties

10.6 Quadratic Inequalities

10.7 Rational Inequalities

            Chapter 10 Activity: Presidential Decision Making

            Chapter 10 Review

            Chapter 10 Test

 

11. Exponential and Logarithmic Functions

11.1 Composite Functions and Inverse Functions

11.2 Exponential Functions

11.3 Logarithmic Functions

            Putting the Concepts Together (Sections 11. 1 - 11.3)

11.4 Properties of Logarithms

11.5 Exponential and Logarithmic Equations

            Chapter 11 Activity: Correct the Quiz

            Chapter 11 Review

            Chapter 11 Test

            Cumulative Review Chapters 1 - 11

 

12. Conics

12.1 Distance and Midpoint Formulas

12.2 Circles

12.3 Parabolas

12.4 Ellipses

12.5 Hyperbolas

            Putting the Concepts Together (Sections 12.1 - 12.5)

12.6 Systems of Nonlinear Equations

            Chapter 12 Activity: How Do You Know That&?

            Chapter 12 Review

            Chapter 12 Test

 

13. Sequences, Series, and the Binomial Theorem

13.1 Sequences

13.2 Arithmetic Sequences

13.3 Geometric Sequences and Series

13.4 The Binomial Theorem

            Chapter 13 Activity: Pass to the Right

            Chapter 13 Review

            Chapter 13 Test

            Cumulative Review Chapters 1 - 13

 

Appendix A: Synthetic Division

Appendix B: Geometry Review

Appendix C: More on Systems of Linear Equations

Appendix D: Table of Square Roots

 

Answers to Selected Exercises