Developmental Mathematics Prealgebra, Elementary Algebra, and Intermediate Algebra

Developmental Mathematics, 2nd Edition by Sullivan, Struve, and Mazzella utilizes the authors’ hallmark engaging features to introduce students to the logic, precision and rigor of mathematics, while building a foundation for success in future math courses.  Known for their unique examples that give students extra step-by-step support, the authors have maintained their successful learning aids, and in this revision focused on translating it to the MyLab™ Math course–resulting in a truly dynamic print and digital learning and teaching experience.  

To this end, the authors have created pre-built assignments for the accompanying MyLab Math course, making it easy for instructors to assign homework that utilizes all of the author-created learning features and leads to the best possible student outcomes.  Developmental Mathematics offers market-leading content written by author-educators, tightly integrated with MyLab Math–the #1 choice in digital learning. Bringing the authors’ voice and approach into the MyLab course gives students the motivation, engagement, and skill sets they need to master algebra.

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With training in mathematics, statistics, and economics, Michael Sullivan, III has a varied teaching background that includes 27 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series, which he writes with his father, Michael Sullivan.

Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series. When not in the classroom or writing, Michael enjoys spending time with his three children, Michael, Kevin, and Marissa, and playing golf. Now that his two sons are getting older, he has the opportunity to do both at the same time!

Kathy Struve

Kathy Struve has been a classroom teacher for nearly 35 years, first at the high school level and, for the past 27 years, at Columbus State Community College. Kathy embraces classroom diversity: diversity of students’ age, learning styles, and previous learning success. She is aware of the challenges of teaching mathematics at a large, urban community college, where students have varied mathematics backgrounds and may enter college with a high level of mathematics anxiety.

Kathy served as Lead Instructor of the Developmental Algebra sequence at Columbus State, where she developed curriculum, conducted workshops, and provided leadership to adjunct faculty in the mathematics department. She embraces the use of technology in instruction, and has taught web and hybrid classes in addition to traditional face-to-face and emporium-style classes. She is always looking for ways to more fully involve students in the learning process. In her spare time Kathy enjoys spending time with her two adult daughters, her four granddaughters, and biking, hiking, and traveling with her husband.

Janet Mazzarella

Born and raised in San Diego county, Janet Mazzarella spent her career teaching in culturally and economically diverse high schools before taking a position at Southwestern College 25 years ago. Janet has taught a wide range of mathematics courses, from arithmetic through calculus for math/science/engineering majors and has training in mathematics, education, engineering, and accounting.

Janet has worked to incorporate technology into the curriculum by participating in the development of Interactive Math and Math Pro. At Southwestern College, she helped develop the self-paced developmental mathematics program. In addition, Janet was the Dean of the School of Mathematics, Science, and Engineering, the Chair of the Mathematics Department, the faculty union president, and the faculty coordinator for Intermediate Algebra. In the past, free time consisted of racing motorcycles off-road in the Baja 500 and rock climbing, but recently she has given up the adrenaline rush of these activities for the thrill of traveling in Europe.

Jessica Bernards, Contributor

Jessica Bernards has been teaching mathematics since 2005. She began her career at the high school level and then transitioned to teaching at Portland Community College in 2010. She has taught a wide range of mathematics courses from Developmental Math up to Calculus and has created curriculum for all of these levels. Additionally, Jessica is a member of AMATYC's Project ACCCESS Cohort 9 where she developed a Math Study Skills Program which is now used across the nation. In 2017, she was the honored recipient of the Leila and Simon Peskoff AMATYC Award for her work with Project ACCCESS.

When not working, Jessica loves spending time with her husband and two boys in the Pacific Northwest. She enjoys running races, cooking, and hiking and is also an active member of her community; coordinating a neighborhood group that brings local moms together.

Wendy Fresh, Contributor

Wendy Fresh has been full-time instructor at Portland Community College since 1997 and has taught a wide range of classes from Developmental Math through Calculus, both on campus and online. Before teaching at PCC, Wendy began her teaching career in 1992, teaching high school at both rural and urban schools. Her love of creating curriculum to make the classroom come alive, has led her to working with technologies that can be incorporated into her many courses.

She earned her Bachelor’s Degree in Mathematics Education from the University of Oregon and her Master’s Degree in the Teaching of Mathematics from Portland State University.  When not teaching, Wendy loves hanging out at home with her husband and two college age “kids”. In addition, she enjoys running, gardening, watching soccer and reading.

1. Whole Numbers 

1.1 Success in Mathematics

1.2 Fundamentals of Whole Numbers

1.3 Adding and Subtracting Whole Numbers

1.4 Multiplying Whole Numbers; Exponents

1.5 Dividing Whole Numbers

1.6 Prime Numbers

1.7 Order of Operations

Chapter 1 Review

Chapter 1 Test

Getting Ready for Chapter 2: A Review of Whole Numbers

2. Integers and an Introduction to Algebra

2.1 Fundamentals of Integers

2.2 Adding and Subtracting Integers

2.3 Multiplying and Dividing Integers

2.4 Exponents; Order of Operations

2.5 Simplifying Algebraic Expressions

2.6 Linear Equations: The Addition and Multiplication Properties

2.7 Linear Equations: Using the Properties Together

2.8 Introduction to Problem Solving: Direct Translation Problems

Chapter 2 Review

Chapter 2 Test

Getting Ready for Chapter 3: A Review of Chapters 1 and 2

3. Rational Numbers Expressed as Fractions

3.1 Fundamentals of Fractions

3.2 Multiplying and Dividing Fractions

3.3 Adding and Subtracting Like Fractions

3.4 Adding and Subtracting Unlike Fractions

3.5 Order of Operations and Complex Fractions

3.6 Operations with Mixed Numbers

3.7 Solving Equations That Contain Fractions

Chapter 3 Review

Chapter 3 Test

Getting Ready for Chapter 4: A Review of Chapters 1—3

4. Rational Numbers as Decimals

4.1 Fundamentals of Decimals

4.2 Adding and Subtracting Decimals

4.3 Multiplying Decimals

4.4 Dividing Decimals

4.5 Solving Equations That Contain Decimals

Chapter 4 Review

Chapter 4 Test

Getting Ready for Chapter 5: A Review of Chapters 1—4

Putting It Together: Real Numbers

5. Ratio, Proportion, and Percent

5.1 Ratios and Unit Rates

5.2 Proportions

5.3 Fundamentals of Percent Notation

5.4 Solving Percent Problems: Proportion Method

5.5 Solving Percent Problems: Equation Method

5.6 Applications Involving Percent

Chapter 5 Review

Chapter 5 Test

Getting Ready for Chapter 6: A Review of Chapters 1—5

6. Measurement and Geometry

6.1 The U.S. Standard (English) System of Measurement

6.2 The Metric System of Measurement

6.3 Fundamentals of Geometry

6.4 Introduction to Square Roots and the Pythagorean Theorem

6.5 Polygons

6.6 Perimeter and Area of Polygons and Circles

6.7 Volume and Surface Area

Chapter 6 Review

Chapter 6 Test

Getting Ready for Chapter 7: A Review of Chapters 1—6

7. Introduction to Statistics and the Rectangular Coordinate System

7.1 Tables and Graphs

7.2 Mean, Median, and Mode

7.3 The Rectangular Coordinate System and Equations in Two Variables

7.4 Graphing Equations in Two Variables

Chapter 7 Review

Chapter 7 Test

Getting Ready for Elementary Algebra: A Review of Chapters 1—7

8. Equations and Inequalities in One Variable

8.1 Linear Equations: The Addition and Multiplication Properties of Equality

8.2 Linear Equations: Using the Properties Together

8.3 Solving Linear Equations Involving Fractions and Decimals; Classifying Equations

8.4 Evaluating Formulas and Solving Formulas for a Variable

8.5 Problem Solving: Direct Translation

8.6 Problem Solving: Problems Involving Percent

8.7 Problem Solving: Geometry and Uniform Motion

8.8 Solving Linear Inequalities in One Variable

Chapter 8 Review

Chapter 8 Test

9. Introduction to Graphing and Equations of Lines

9.1 The Rectangular Coordinate System and Equations in Two Variables

9.2 Graphing Equations in Two Variables

9.3 Slope

9.4 Slope-Intercept Form of a Line

9.5 Point-Slope Form of a Line

9.6 Parallel and Perpendicular Lines

9.7 Linear Inequalities in Two Variables

Chapter 9 Activity: Graphing Practice

Chapter 9 Review

Chapter 9 Test

Cumulative Review Chapters 1—9

10. Systems of Linear Equations and Inequalities

10.1 Solving Systems of Linear Equations by Graphing

10.2 Solving Systems of Linear Equations Using Substitution

10.3 Solving Systems of Linear Equations Using Elimination

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

10.5 Solving Mixture Problems Using Systems of Linear Equations

10.6 Systems of Linear Inequalities

Chapter 10 Activity: Find the Numbers

Chapter 10 Review

Chapter 10 Test

11. Exponents and Polynomials

11.1 Adding and Subtracting Polynomials

11.2 Multiplying Monomials: The Product and Power Rules

11.3 Multiplying Polynomials

11.4 Dividing Monomials: The Quotient Rule and Integer Exponents

11.5 Dividing Polynomials

11.6 Applying Exponent Rules: Scientific Notation

Chapter 11 Activity: What Is the Question?

Chapter 11 Review

Chapter 11 Test

Cumulative Review Chapters 1—11

12. Factoring Polynomials

12.1 Greatest Common Factor and Factoring by Grouping

12.2 Factoring Trinomials of the Form x2 + bx + c

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

12.4 Factoring Special Products 837

12.5 Summary of Factoring Techniques

12.6 Solving Polynomial Equations by Factoring

12.7 Modeling and Solving Problems with Quadratic Equations

Chapter 12 Activity: Which One Does Not Belong?

Chapter 12 Review

Chapter 12 Test

Getting Ready for Intermediate Algebra: A Review of Chapters 1—12

13. Rational Expressions and Equations

13.1 Simplifying Rational Expressions

13.2 Multiplying and Dividing Rational Expressions

13.3 Adding and Subtracting Rational Expressions with a Common Denominator

13.4 Finding the Least Common Denominator and Forming Equivalent Rational Expressions

13.5 Adding and Subtracting Rational Expressions with Unlike Denominators

13.6 Complex Rational Expressions

13.7 Rational Equations

13.8 Models Involving Rational Equations

Chapter 13 Activity: Correct the Quiz

Chapter 13 Review

Chapter 13 Test

Cumulative Review Chapters 1—13

Getting Ready for Intermediate Algebra: A Review of Chapters 1—13

Getting Ready for Chapter 14: Interval Notation

14. Graphs, Relations, and Functions

14.1 Graphs of Equations

14.2 Relations

14.3 An Introduction to Functions

14.4 Functions and Their Graphs

14.5 Linear Functions and Models

14.6 Compound Inequalities

14.7 Absolute Value Equations and Inequalities

14.8 Variation

Chapter 14 Activity: Shifting Discovery

Chapter 14 Review

Chapter 14 Test

15. Radicals and Rational Exponents

15.1 Square Roots

15.2 nth Roots and Rational Exponents

15.3 Simplifying Expressions Using the Laws of Exponents

15.4 Simplifying Radical Expressions Using Properties of Radicals

15.5 Adding, Subtracting, and Multiplying Radical Expressions

15.6 Rationalizing Radical Expressions

15.7 Functions Involving Radicals

15.7.4 Graph Functions Involving Cube Roots

15.8 Radical Equations and Their Applications

15.9 The Complex Number System

Chapter 15 Activity: Correct the Quiz

Chapter 15 Review

Chapter 15 Test

Cumulative Review Chapters 1—15

16. Quadratic Equations and Functions

16.1 Solving Quadratic Equations by Completing the Square

16.2 Solving Quadratic Equations by the Quadratic Formula

16.3 Solving Equations Quadratic in Form

16.4 Graphing Quadratic Functions Using Transformations

16.5 Graphing Quadratic Functions Using Properties

16.6 Polynomial Inequalities

16.7 Rational Inequalities

Chapter 16 Activity: Presidential Decision Making

Chapter 16 Review

Chapter 16 Test

17. Exponential and Logarithmic Functions

17.1 Composite Functions and Inverse Functions

17.2 Exponential Functions

17.3 Logarithmic Functions

17.4 Properties of Logarithms

17.5 Exponential and Logarithmic Equations

Chapter 17 Activity: Correct the Quiz

Chapter 17 Review

Chapter 17 Test

Cumulative Review Chapters 1—15

18. Conics

18.1 Distance and Midpoint Formulas

18.2 Circles

18.3 Parabolas

18.4 Ellipses

18.5 Hyperbolas

18.6 Systems of Nonlinear Equations

18.6.1 Solve a System of Nonlinear Equations Using Substitution

18.6.2 Solve a System of Nonlinear Equations Using Elimination

Chapter 18 Activity: How Do You Know That …?

Chapter 18 Review

Chapter 18 Test

19. Sequences, Series, and the Binomial Theorem

19.1 Sequences

19.2 Arithmetic Sequences

19.3 Geometric Sequences and Series

19.4 The Binomial Theorem

Chapter 19 Activity: Discover the Relation

Chapter 19 Review

Chapter 19 Test

Cumulative Review Chapters 1—19

APPENDICES

A.1.1  Divide Polynomials Using Synthetic Division

A.1.2  Use the Remainder and Factor Theorems

B.1  A Review of Systems of Linear Equations in Two Variables

B.1.1  Determine Whether an Ordered Pair Is a Solution of a System of Linear Equations

B.1.2  Solve a System of Two Linear Equations by Graphing

B.1.3  Solve a System of Two Linear Equations by Substitution

B.1.4  Solve a System of Two Linear Equations by Elimination

B.1.5  Identify Inconsistent Systems

B.1.6  Write the Solution of a System with Dependent Equations

B.2  Systems of Linear Equations in Three Variables

B.2.1  Solve Systems of Three Linear Equations

B.2.2  Identify Inconsistent Systems

B.2.3  Write the Solution of a System with Dependent Equations

B.2.4  Model and Solve Problems Involving Three Linear Equations

B.3  A Using Matrices to Solve Systems

B.3.1  Write the Augmented Matrix of a System

B.3.2  Write the System from the Augmented Matrix

B.3.3  Perform Row Operations on a Matrix

B.3.4  Solve Systems Using Matrices

B.3.5  Solve Consistent Systems with Dependent Equations and Solve Inconsistent Systems

B.4  Determinants and Cramer’s Rule

B.4.1  Evaluate the Determinant of a 2 x 2 Matrix

B.4.2  Use Cramer’s Rule to Solve a System of Two Equations

B.4.3  Evaluate the Determinant of a 3 x 3 Matrix

B.4.4  Use Cramer’s Rule to Solve a System of Three Equations

Appendix C.  Table of Square Roots

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