Beginning & Intermediate Algebra

About our authors 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 5 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 7 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 38 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 Lexington, 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 17 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 2-year colleges and at many conferences. In 2007, Jamie was appointed to the Team of Basic Skills Specialists 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 5 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, 2 young children, and black lab. 

Preface Diagnostic Pretest 0. Prealgebra Review

Career Opportunities
0.1 Simplifying Fractions
0.2 Adding and Subtracting Fractions
0.3 Multiplying and Dividing Fractions
0.4 Using Decimals Use Math to Save Money
0.5 Percents, Rounding, and Estimating
0.6 Using the Mathematics Blueprint for Problem Solving Career Exploration Problems
Chapter 0 Organizer
Chapter 0 Review Problems
How Am I Doing? Chapter 0 Test
Math Coach

1. Real Numbers and Variables

Career Opportunities
1.1 Adding Real Numbers
1.2 Subtracting Real Numbers
1.3 Multiplying and Dividing Real Numbers
1.4 Exponents
1.5 The Order of Operations Use Math to Save Money
1.6 Using the Distributive Property to Simplify Algebraic Expressions
1.7 Combining Like Terms
1.8 Using Substitution to Evaluate Algebraic Expressions and Formulas
1.9 Grouping Symbols Career Exploration Problems
Chapter 1 Organizer
Chapter 1 Review Problems
How Am I Doing? Chapter 1 Test
Math Coach

2. Equations, Inequalities, and Applications

Career Opportunities
2.1 The Addition Principle of Equality
2.2 The Multiplication Principle of Equality
2.3 Using the Addition and Multiplication Principles Together
2.4 Solving Equations with Fractions Use Math to Save Money
2.5 Translating English Phrases into Algebraic Expressions
2.6 Using Equations to Solve Word Problems
2.7 Solving Word Problems: The Value of Money and Percents
2.8 Solving Inequalities in One Variable Career Exploration Problems
Chapter 2 Organizer
Chapter 2 Review Problems
How Am I Doing? Chapter 2 Test
Math Coach

3. Graphing and Functions

Career Opportunities
3.1 The Rectangular Coordinate System
3.2 Graphing Linear Equations
3.3 The Slope of a Line Use Math to Save Money
3.4 Writing the Equation of a Line
3.5 Graphing Linear Inequalities
3.6 Functions Career Exploration Problems
Chapter 3 Organizer
Chapter 3 Review Problems
How Am I Doing? Chapter 3 Test
Math Coach
Cumulative Test for Chapters 0-3

4. Systems of Linear Equations and Inequalities

Career Opportunities
4.1 Systems of Linear Equations in Two Variables
4.2 Systems of Linear Equations in Three Variables Use Math to Save Money
4.3 Applications of Systems of Linear Equations
4.4 Systems of Linear Inequalities Career Exploration Problems
Chapter 4 Organizer
Chapter 4 Review Problems
How Am I Doing? Chapter 4 Test
Math Coach

5. Exponents and Polynomials

Career Opportunities
5.1 The Rules of Exponents
5.2 Negative Exponents and Scientific Notation
5.3 Fundamental Polynomial Operations Use Math to Save Money
5.4 Multiplying Polynomials
5.5 Multiplication: Special Cases
5.6 Dividing Polynomials Career Exploration Problems
Chapter 5 Organizer
Chapter 5 Review Problems
How Am I Doing? Chapter 5 Test
Math Coach

6. Factoring

Career Opportunities
6.1 Removing a Common Factor
6.2 Factoring by Grouping
6.3 Factoring Trinomials of the Form x2 + bx + c
6.4 Factoring Trinomials of the Form ax2 + bx + c Use Math to Save Money
6.5 Special Cases of Factoring
6.6 A Brief Review of Factoring
6.7 Solving Quadratic Equations by Factoring Career Exploration Problems
Chapter 6 Organizer
Chapter 6 Review Problems
How Am I Doing? Chapter 6 Test
Math Coach
Cumulative Test for Chapters 0-6

7. Rational Expressions and Equations

Career Opportunities
7.1 Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions Use Math to Save Money
7.4 Simplifying Complex Rational Expressions
7.5 Solving Equations Involving Rational Expressions
7.6 Ratio, Proportion, and Other Applied Problems Career Exploration Problems
Chapter 7 Organizer
Chapter 7 Review Problems
How Am I Doing? Chapter 7 Test
Math Coach

T. A Transition from Beginning to Intermediate Algebra

T.1 Integer Exponents, Square Roots, Order of Operations, and Scientific Notation
T.2 Polynomial Operations
T.3 Factoring Polynomials
T.4 Special Cases of Factoring
T.5 The Point-Slope Form of a Line

8. Rational Exponents and Radicals

Career Opportunities
8.1 Rational Exponents
8.2 Radical Expressions and Functions
8.3 Simplifying, Adding, and Subtracting Radicals
8.4 Multiplying and Dividing Radicals Use Math to Save Money
8.5 Radical Equations
8.6 Complex Numbers
8.7 Variation Career Exploration Problems
Chapter 8 Organizer
Chapter 8 Review Problems
How Am I Doing? Chapter 8 Test
Math Coach

9. Quadratic Equations and Inequalities

Career Opportunities
9.1 Quadratic Equations
9.2 The Quadratic Formula and Solutions to Quadratic Equations
9.3 Equations That Can Be Transformed into Quadratic Form Use Math to Save Money
9.4 Formulas and Applications
9.5 Quadratic Functions
9.6 Compound and Quadratic Inequalities
9.7 Absolute Value Equations and Inequalities Career Exploration Problems
Chapter 9 Organizer
Chapter 9 Review Problems
How Am I Doing? Chapter 9 Test
Math Coach
Cumulative Test for Chapters 0-9

10. The Conic Sections

Career Opportunities
10.1 The Distance Formula and the Circle
10.2 The Parabola
10.3 The Ellipse Use Math to Save Money
10.4 The Hyperbola
10.5 Nonlinear Systems of Equations Career Exploration Problems
Chapter 10 Organizer
Chapter 10 Review Problems
How Am I Doing? Chapter 10 Test
Math Coach

11. Additional Properties of Functions

Career Opportunities
11.1 Function Notation
11.2 General Graphing Procedures for Functions Use Math to Save Money
11.3 Algebraic Operations on Functions
11.4 Inverse of a Function Career Exploration Problems
Chapter 11 Organizer
Chapter 11 Review Problems
How Am I Doing? Chapter 11 Test
Math Coach

12. Logarithmic and Exponential Functions

Career Opportunities
12.1 The Exponential Function
12.2 The Logarithmic Function
12.3 Properties of Logarithms Use Math to Save Money
12.4 Common Logarithms, Natural Logarithms, and Change of Base of Logarithms
12.5 Exponential and Logarithmic Equations Career Exploration Problems
Chapter 12 Organizer
Chapter 12 Review Problems
How Am I Doing? Chapter 12 Test
Math Coach
Practice Final Examination

Appendices

A: Practice with Operations of Whole Numbers
B: Determinants and Cramer's Rule
C: Solving Systems of Linear Equations Using Matrices
D: Sets

Solutions to Student Practice Problems Answers to Selected Exercises Beginning and Intermediate Algebra Glossary Photo Credits Subject Index Index of Applications