Developmental Mathematics: Prealgebra, Elementary Algebra, and Intermediate Algebra, 2nd edition

Published by Pearson (January 9, 2018) © 2019

  • Michael Sullivan Joliet Junior College
  • Katherine R. Struve
  • Janet Mazzarella

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For courses in Prealgebra and Beginning Algebra (combined courses).

Helps students innovatively "do the math"

Developmental Mathematics, 2nd Edition by Sullivan, Struve and Mazzella utilizes the authors' hallmark engaging features to introduce 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 text learning aids while offering a full suite of resources that support a variety of learning environments; instructors can choose the ideal combination for their students.

Hallmark features of this title

  • Examples and Showcase Examples offer guidance and instruction when students are away from the instructor and class.
    • Left-to-Right Examples provide annotations to the left of the algebra in 2-column format, mirroring the way we read and explaining what the authors are about to do in each step.
    • Showcase Examples provide instruction in a clear 3-column format. The left column describes a step, the middle provides a brief annotation and the right presents the algebra.
    • Quick Check exercises follow most examples so students can apply what they have just learned, and are assignable as homework.
  • Exercise sets give ample practice for procedures and concepts. They are paired and offer problems of every possible derivative, with gradual increase in difficulty. 

New and updated features of this title

  • REVISED - Systems of linear equations with dependent systems no longer have a solution of simply “infinitely many solutions.” Rather, the authors express the solution of the dependent system using set builder notation. 
  • NEW - Discovery activities using applets:
    • These explorations are carefully crafted to allow students to develop understanding of mathematical concepts through experiential learning.
    • The applets may also be accessed using the QR code at the beginning of the section.
  • NEW - Quick Response (QR) codes now appear at each section opener, at section-level exercises and as part of the Chapter Tests.
    • Students can simply use their smartphones for easy access to the popular Author in Action lecture videos, select end-of-section exercise videos, the discovery applets, and the Chapter Test Prep videos.

Features of MyLab Math for the 2nd Edition

  • A new pre-made author-created MyLab Math course utilizes the latest MyLab Math features. Each section has two MyLab Math assignments:
    • 1: Amultimedia assignment that incorporates the Author in Action lecture videos, the new discovery applet exercises, the new How To guided exercises and the Quick Check exercises from the text. The Quick Check exercises follow many of the examples in the text. The Textbook learning aid for each Quick Check exercise links to the corresponding text example.
    • 2: An assignment based on the Skill Building and Mixed Practice exercises from the text. Skill building exercises are tied to objectives within the text; the Textbook learning aid links directly to the objective.
  • Guided Exercises are now available in MyLab Math, based on the popular Showcase Examples. Showcase Examples from the text are easy to recognize with the words “How To” in the example title and provide step-by-step solutions to examples. 
    • This example structure was written into 55 new MyLab Math exercises that require students to respond to questions as the steps to solving problems are developed, similar to the “Help Me Solve This” feature of MyLab Math. 
    • These exercises are easy to identify in the Assignment Builder as they are designated “How-To-#.# Ex #-. For example, “How-To-2.2 Ex 6-Solve a Linear Equation.”
  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
      • Putting the Concepts Together (Sections 1.1—1.4)
    • 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
      • Putting the Concepts Together (Sections 2.1—2.4)
    • 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
      • Putting the Concepts Together (Sections 3.1—3.3)
    • 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
      • Putting the Concepts Together (Sections 4.1—4.4)
    • 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
      • Putting the Concepts Together (Sections 5.1—5.3)
    • 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
      • Putting the Concepts Together (Sections 6.1—6.2)
    • 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
      • Putting the Concepts Together (Sections 7.1 and 7.2)
    • 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
      • Putting the Concepts Together (Sections 9.1—9.6)
    • 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
      • Putting the Concepts Together (Sections 10.1—10.3)
    • 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
      • Putting the Concepts Together (Sections 11.1—11.4)
    • 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
      • Putting the Concepts Together (Sections 12.1—12.5)
    • 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
      • Putting the Concepts Together (Sections 13.1—13.6)
    • 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
      • Putting the Concepts Together (Sections 14.1—14.4)
    • 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
      • Putting the Concepts Together (Sections 15.1—15.6)
    • 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
      • Putting the Concepts Together (Sections 16.1—16.3)
    • 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
      • Putting the Sections Together (17.1—17.3)
    • 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
      • Putting the Concepts Together (Sections 18.1—18.5)
    • 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
      • Putting the Concepts Together (Sections 19.1—19.3)
    • 19.4 The Binomial Theorem
    • Chapter 19 Activity: Discover the Relation
    • Chapter 19 Review
    • Chapter 19 Test
    • Cumulative Review Chapters 1—19

APPENDICES

  • Appendix A. Synthetic Division
    • A.1.1 Divide Polynomials Using Synthetic Division
    • A.1.2 Use the Remainder and Factor Theorems
  • Appendix B. More on Systems of Linear Equations
    • 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

About our authors 

Michael Sullivan, III has training in mathematics, statistics and economics, with 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 3 children, Michael, Kevin and Marissa, and playing golf. Now that his 2 sons are getting older, he has the opportunity to do both at the same time!

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: of students' ages, 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 online and hybrid classes as well as traditional face-to-face and emporium-style classes. She is always looking for ways to fully involve students in the learning process. In her spare time Kathy enjoys spending time with her 2 adult daughters and her 4 granddaughters, biking, hiking and traveling with her husband.

Janet Mazzarella was born and raised in San Diego County, and 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) 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 2 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) has been a 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 2 college age “kids”. In addition, she enjoys running, gardening, watching soccer and reading.

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