About the Book
Table of Contents:
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 the Author :
Michael Sullivan, III
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.
