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John Tobey received his BA in mathematics from Wheaton College in Wheaton, Illinois in 1965, his MA in mathematics education from Harvard University in 1966, and his PhD in mathematics education from Boston University in 1980. He has taught in the mathematics department at the United States Military Academy at West Point and served as the Mathematics Department Chairman at North Shore Community College in Danvers, Massachusetts for five years. John has served as the president of the New England Mathematics Association of Two Year Colleges. He has received the NISOD award for outstanding teaching from the University of Texas at Austin. John is the author of seven mathematics books published by Pearson Education. John has spoken to many mathematics departments and at many professional meetings throughout the country on the topic of developmental mathematics education and distance learning in mathematics. He lives in Massachusetts.
Jeffrey Slater has been a professor at North Shore Community College for thirty-eight years and received the Teacher of the Year award in 2002. Jeff travels around the country speaking on student retention and is also a consultant to the Federal Government. He lives in Marblehead, Massachusetts with his wife Shelley and his yellow lab Gracie.
Jamie Blair has directed the Mathematics Learning Center at Orange Coast College for the past seventeen years. She designed, developed, and implemented the Center, and as a result of this effort has provided technical expertise related to the particulars of the Math Center to numerous other two-year colleges and at many conferences. In 2007 Jamie was appointed to the Team of Basic Skills Specialist by the California State Academic Senate. She is also currently participating on Title 3 committees on her campus. She specializes in teaching students who have never been successful in mathematics. She is an expert in the area of basic skills in relation to the learning needs of students. She lives in California.
Jennifer Crawford received her BS in mathematics from the University of Minnesota – Duluth in 1995 and her MS in mathematics from the University of Minnesota – Twin Cities in 1998. She taught a wide range of courses at North Shore Community College in Danvers, Massachusetts for five years. She currently teaches at Normandale Community College in Bloomington, Minnesota where her focus is working with developmental math students. She lives in Minneapolis, Minnesota with her husband, two young children, and black lab.
Preface
Diagnostic Pretest
1. Basic Concepts
1.1 The Real Number System
1.2 Operations with Real Numbers
1.3 Powers, Square Roots, and the Order of Operations
How Am I Doing? Sections 1.1–1.3
1.4 Integer Exponents and Scientific Notation
1.5 Operations with Variables and Grouping Symbols
1.6 Evaluating Variable Expressions and Formulas
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Chapter 1 Organizer
Chapter 1 Review Problems
How Am I Doing? Chapter 1 Test
Math Coach
2. Linear Equations and Inequalities
2.1 First-Degree Equations with One Unknown
2.2 Literal Equations and Formulas
2.3 Absolute Value Equations
2.4 Using Equations to Solve Word Problems
How Am I Doing? Sections 2.1–2.4
2.5 Solving More-Involved Word Problems
2.6 Linear Inequalities
2.7 Compound Inequalities
2.8 Absolute Value Inequalities
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Chapter 2 Organizer
Chapter 2 Review Problems
How Am I Doing? Chapter 2 Test
Math Coach
3. Equations and Inequalities in Two Variables and Functions
3.1 Graphing Linear Equations with Two Unknowns
3.2 Slope of a Line
3.3 Graphs and the Equations of a Line
How Am I Doing? Sections 3.1–3.3
3.4 Linear Inequalities in Two Variables
3.5 Concept of a Function
3.6 Graphing Functions from Equations and Tables of Data
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Chapter 3 Organizer
Chapter 3 Review Problems
How Am I Doing? Chapter 3 Test
Math Coach
Cumulative Test for Chapters 1–3
4. Systems of Linear Equations and Inequalities
4.1 Systems of Linear Equations in Two Variables
4.2 Systems of Linear Equations in Three Variables
How Am I Doing? Sections 4.1–4.2
4.3 Applications of Systems of Linear Equations
4.4 Systems of Linear Inequalities
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Chapter 4 Organizer
Chapter 4 Review Problems
How Am I Doing? Chapter 4 Test
Math Coach
5. Polynomials
5.1 Introduction to Polynomials and Polynomial Functions: Adding, Subtracting, and Multiplying
5.2 Dividing Polynomials
5.3 Synthetic Division
5.4 Removing Common Factors; Factoring by Grouping
5.5 Factoring Trinomials
How Am I Doing? Sections 5.1–5.5
5.6 Special Cases of Factoring
5.7 Factoring a Polynomial Completely
5.8 Solving Equations and Applications Using Polynomials
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Chapter 5 Organizer
Chapter 5 Review Problems
How Am I Doing? Chapter 5 Test
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6. Rational Expressions and Equations
6.1 Rational Expressions and Functions: Simplifying, Multiplying, and Dividing
6.2 Adding and Subtracting Rational Expressions
6.3 Complex Rational Expressions
How Am I Doing? Sections 6.1–6.3
6.4 Rational Equations
6.5 Applications: Formulas and Advanced Ratio Exercises
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Chapter 6 Organizer
Chapter 6 Review Problems
How Am I Doing? Chapter 6 Test
Math Coach
Cumulative Test for Chapters 1–6
7. Rational Exponents and Radicals
7.1 Rational Exponents
7.2 Radical Expressions and Functions
7.3 Simplifying, Adding, and Subtracting Radicals
7.4 Multiplying and Dividing Radicals
How Am I Doing? Sections 7.1–7.4
7.5 Radical Equations
7.6 Complex Numbers
7.7 Variation
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Chapter 7 Organizer
Chapter 7 Review Problems
How Am I Doing? Chapter 7 Test
Math Coach
8. Quadratic Equations and Inequalities
8.1 Quadratic Equations
8.2 The Quadratic Formula and Solutions to Quadratic Equations
8.3 Equations That Can Be Transformed into Quadratic Form
How Am I Doing? Sections 8.1–8.3
8.4 Formulas and Applications
8.5 Quadratic Functions
8.6 Quadratic Inequalities in One Variable
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Chapter 8 Organizer
Chapter 8 Review Problems
How Am I Doing? Chapter 8 Test
Math Coach
9. The Conic Sections
9.1 The Distance Formula and the Circle
9.2 The Parabola
9.3 The Ellipse
How Am I Doing? Sections 9.1–9.3
9.4 The Hyperbola
9.5 Nonlinear Systems of Equations
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Chapter 9 Organizer
Chapter 9 Review Problems
How Am I Doing? Chapter 9 Test
Math Coach
10. Additional Properties of Functions
10.1 Function Notation
10.2 General Graphing Procedures for Functions
How Am I Doing? Sections 10.1–10.2
10.3 Algebraic Operations on Functions
10.4 Inverse of a Function
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Chapter 10 Organizer
Chapter 10 Review Problems
How Am I Doing? Chapter 10 Test
Math Coach
11. Logarithmic and Exponential Functions
11.1 The Exponential Function
11.2 The Logarithmic Function
11.3 Properties of Logarithms
How Am I Doing? Sections 11.1–11.3
11.4 Common Logarithms, Natural Logarithms, and Change of Base of Logarithms
11.5 Exponential and Logarithmic Equations
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Chapter 11 Organizer
Chapter 11 Review Problems
How Am I Doing? Chapter 11 Test
Math Coach
Practice Final Examination
Appendix A: Tables
Table A-1: Table of Square Roots
Table A-2: Table of Exponential Values
Appendix B: Determinants and Cramer's Rule
Appendix C: Solving Systems of Linear Equations Using Matrices
Solutions to Practice Problems
Answers to Selected Exercises
Glossary
Applications Index (Available in MyMathLab)
Index
Photo Credits