Beginning & Intermediate Algebra (4e)

The Tobey/Slater/Blair/Crawford series builds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical “building block” organization makes it easy for students to understand each topic and gain confidence as they move through each section. Students will find many opportunities to check and reinforce their understanding of concepts throughout the text and its MyMathLab course. With this revision, the author team has added a new Math Coach feature that provides students with an office hour experience by helping them to avoid commonly made mistakes. With Tobey/Slater/Blair/Crawford, students have a tutor, a study companion, and now a coach, with them every step of the way.

Preface

Diagnostic Pretest

0. Prealgebra Review

0.1 Simplifying Fractions

0.2 Adding and Subtracting Fractions

0.3 Multiplying and Dividing Fractions

0.4 Using Decimals

            How Am I Doing? Sections 0.1–0.4

0.5 Percents, Rounding, and Estimating

0.6 Using the Mathematics Blueprint for Problem Solving

            Use Math to Save Money

            Chapter 0 Organizer

            Chapter 0 Review Problems

            How Am I Doing? Chapter 0 Test

            Math Coach

1. Real Numbers and Variables

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

            How Am I Doing? Sections 1.1–1.5

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

            Use Math to Save Money

            Chapter 1 Organizer

            Chapter 1 Review Problems

            How Am I Doing? Chapter 1 Test

            Math Coach

2. Equations, Inequalities, and Applications

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

            How Am I Doing? Sections 2.1–2.4

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

            Use Math to Save Money

            Chapter 2 Organizer

            Chapter 2 Review Problems

            How Am I Doing? Chapter 2 Test

            Math Coach

3. Graphing and Functions

3.1 The Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 The Slope of a Line

            How Am I Doing? Sections 3.1–3.3

3.4 Writing the Equation of a Line

3.5 Graphing Linear Inequalities

3.6 Functions

            Use Math to Save Money

            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

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

            Use Math to Save Money

            Chapter 4 Organizer

            Chapter 4 Review Problems

            How Am I Doing? Chapter 4 Test

            Math Coach

5. Exponents and Polynomials

5.1 The Rules of Exponents

5.2 Negative Exponents and Scientific Notation

5.3 Fundamental Polynomial Operations

            How Am I Doing? Sections 5.1–5.3

5.4 Multiplying Polynomials

5.5 Multiplication: Special Cases

5.6 Dividing Polynomials

            Use Math to Save Money

            Chapter 5 Organizer

            Chapter 5 Review Problems

            How Am I Doing? Chapter 5 Test

            Math Coach

6. Factoring

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

            How Am I Doing? Sections 6.1–6.4

6.5 Special Cases of Factoring

6.6 A Brief Review of Factoring

6.7 Solving Quadratic Equations by Factoring

            Use Math to Save Money

            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

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions

            How Am I Doing? Sections 7.1–7.3

7.4 Simplifying Complex Rational Expressions

7.5 Solving Equations Involving Rational Expressions

7.6 Ratio, Proportion, and Other Applied Problems

            Use Math to Save Money

            Chapter 7 Organizer

            Chapter 7 Review Problems

            How Am I Doing? Chapter 7 Test

            Math Coach

8. Rational Exponents and Radicals

8.1 Rational Exponents

8.2 Radical Expressions and Functions

8.3 Simplifying, Adding, and Subtracting Radicals

8.4 Multiplying and Dividing Radicals

            How Am I Doing? Sections 8.1—8.4

8.5 Radical Equations

8.6 Complex Numbers

8.7 Variation

            Use Math to Save Money

            Chapter 8 Organizer

            Chapter 8 Review Problems

            How Am I Doing? Chapter 8 Test

            Math Coach

9. Quadratic Equations and Inequalities

9.1 Quadratic Equations

9.2 The Quadratic Formula and Solutions to Quadratic Equations

9.3 Equations That Can Be Transformed into Quadratic Form

            How Am I Doing? Sections 9.1—9.3

9.4 Formulas and Applications

9.5 Quadratic Functions

9.6 Compound and Quadratic Inequalities in One Variable

9.7 Absolute Value Equations and Inequalities

            Use Math to Save Money

            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

10.1 The Distance Formula and the Circle

10.2 The Parabola

10.3 The Ellipse

            How Am I Doing? Sections 10.1—10.3

10.4 The Hyperbola

10.5 Nonlinear Systems of Equations

            Use Math to Save Money

            Chapter 10 Organizer

            Chapter 10 Review Problems

            How Am I Doing? Chapter 10 Test

            Math Coach

11. Additional Properties of Functions

11.1 Function Notation

11.2 General Graphing Procedures for Functions

            How Am I Doing? Sections 11.1—11.2

11.3 Algebraic Operations on Functions

11.4 Inverse of a Function

            Use Math to Save Money

            Chapter 11 Organizer

            Chapter 11 Review Problems

            How Am I Doing? Chapter 11 Test

            Math Coach

12. Logarithmic and Exponential Functions

12.1 The Exponential Function

12.2 The Logarithmic Function

12.3 Properties of Logarithms

            How Am I Doing? Sections 12.1—12.3

12.4 Common Logarithms, Natural Logarithms, and Change of Base of Logarithms

12.5 Exponential and Logarithmic Equations

            Use Math to Save Money

            Chapter 12 Organizer

            Chapter 12 Review Problems

            How Am I Doing? Chapter 12 Test

            Math Coach

Practice Final Examination

Appendix A: Foundations for Intermediate Algebra: A Transition from Beginning to Intermediate

Appendix B: Practice with Operations of Whole Numbers

Appendix C: Tables

Appendix D: Determinants and Cramer’s Rule

Appendix E: Solving Systems of Linear Equations Using Matrices

Appendix F: Sets

Solutions to Practice Problems

Answers to Selected Exercises

Glossary

Applications Index (Available in MyMathLab)

Index

New and Updated Features

• The end-of-chapter material has been further enhanced to provide more opportunities for review and reinforcement of key concepts:
• Updated! Chapter Organizers summarize the chapter topics, procedures, and corresponding examples all in one place to simplify chapter review. A “You Try It” column has been added to Chapter Organizers to provide another opportunity for practice!
• NEW! Assessment Check boxes on the “How Am I Doing?” Chapter Test encourage students to check their work. If students need extra help on any test problems, they can also watch the Chapter Test Prep Videos, where all test solutions are worked out on video.
• NEW! The Math Coach follows every chapter test and provides helpful hints and coaching on the most difficult concepts and exercise types in that particular chapter. Examples similar to the Math Coach problems have been noted throughout the chapter with side-by-side examples and practice problems that encourage students to try the practice problem on the spot. Students can have an office hour with the authors when they watch the authors solve these key problem types on the New Math Coach Videos.
• Use Math to Save Money features practical, realistic examples in every chapter of how students can use math to cut costs and spend less. The topics discussed in Use Math to Save Money have been updated based on a student survey of more than 1,000 developmental math college students.
• Steps to Success (formerly called “Develop Your Study Skills”) has been updated and expanded to provide students with more guided techniques for improving their study skills and succeeding in math.

New Instructor and Student Resources

• Worksheets with the Math Coach tie the complete learning package together, providing extra vocabulary and practice exercises for every section of the text. Every chapter also includes the Math Coach Problems from the book and videos so students can follow along, and have plenty of space to show their work.
• The Lectures Series on DVD featuring Math Coach and Chapter Test Prep Videos has been completely revised to provide students with extra help for each section of the textbook. The videos include:
• A new interface allows easy navigation to objectives and key examples and exercises.
• The new Math Coach Videos give students an office hour with the authors! In these videos, the authors expand upon the end-of-chapter Math Coach materials that are in the text and coach students on how to avoid commonly made mistakes.
• Chapter Test Prep Videos provide step-by-step video solutions to every problem in each “How Am I Doing?” Chapter Test in the textbook.
• Chapter Test Prep Videos and Math Coach Videos are available in MyMathLab and on YouTube^™.

New to MyMathLab

Two MyMathLab course options are now available: a standard course and a Ready to Go course.

• Standard MyMathLab courses allow instructors to build their course their way, offering maximum flexibility and complete control over all aspects of assignment creation. 
• The new Ready to Go courses provide students with all the same great MyMathLab features, but make it easier for instructors to get started. Each course includes pre-assigned homework and quizzes to make creating a course even easier.

Both course options feature the following items:

• Pre-made (and pre-assigned in the Ready to Go course) section-level homework assignments.
• Pre-made (and pre-assigned in the Ready to Go course) “How Am I Doing?” mid-chapter review homework that lets students pause at critical junctures to make sure they are “getting it.”
• Pre-made chapter review quizzes that are pre-assigned in the Ready to Go course and generate personalized homework assignments based on students’ quiz results.
• A Pre-made (and pre-assigned in the Ready to Go Course) pre- and post- test for every chapter.
• A new Stepped-Out Concept Check Questions exercise style that guides students through solutions, helping them understand not only the steps involved, but the reasoning behind them.
• Pre-made (and pre-assigned in the Ready to Go course) Math Coach Homework for every chapter that uses the stepped-out concept check approach to coach students before the test to the areas where mistakes are most commonly made and show them how to avoid these pitfalls.
• Use Math to Save Money Animations are assignable and offer an interactive way for students to use the math they are learning to cut costs and spend less.
• All videos from the Lecture Series on DVD with Math Coach and Chapter Test Prep Videos.

Content Updates

• Section 0.6: Using the Mathematics Blueprint for Problem Solving has been added to Chapter 0.
• The presentation of topics in Chapter 2 has been refined, including the addition of Section 2.7: Solving Word Problems: The Value of Money and Percents
• Updates to Chapter 3 include the introduction of a new Graphing Organizer. This organizer summarizes the graphing methods presented in the chapter and notes the advantages and disadvantages of each. The objective of finding the slopes of parallel and perpendicular lines has been relocated to Section 3.4.

Students will find many opportunities to check and reinforce their understanding of concepts throughout each chapter:

• Student Practice problems are paired with every example in the text.  The full solutions to each practice problem are located in the back of the text, allowing students to check their work as they go.
• The “How Am I Doing?” mid-chapter review exercises let students pause at a critical juncture to make sure they are "getting it."
• End-of-Section Exercises progress from basic to challenging, and each exercise set includes Verbal and Writing Skills, and Mixed Practice exercises.
• A Quick Quiz at the end of each exercise set contains three problems that cover the essential content of that section. This simple assessment tool measures whether students know when they are ready for new material, and when they need further review.
• A Concept Check question at the end of each Quick Quiz asks students to explain how and why a method works in their own words, forcing students to analyze problems and reflect on the mathematical concepts.
• Classroom Quizzes in the Annotated Instructor's Edition parallel every Quick Quiz, which allows instructors to quickly assess the understanding of the class at any point in the chapter.
• The End-of-Chapter Material provides several opportunities for review and reinforcement of key concepts:

• Updated! Chapter Organizers summarize the chapter topics, procedures, and corresponding examples all in one place to simplify chapter review. A ”You Try It” column has been added to Chapter Organizers to provide another opportunity for practice!
• NEW! Assessment Check boxes on the “How Am I Doing?” Chapter Test encourage students to check their work. If students need extra help on any test problems, they can watch the Chapter Test Prep Videos, where all test solutions are worked out on video.

• NEW! The Math Coach follows every chapter test and provides helpful hints and coaching on the most difficult concepts and exercise types in that particular chapter. Examples similar to the Math Coach problems have been noted throughout the chapter with side-by-side examples and practice problems that encourage students to try the practice problem on the spot. Students can have an office hour with the authors when they watch the authors solve these key problem types on the New Math Coach Videos.

• The Chapter Test Prep and Math Coach Videos are available in MyMathLab and on YouTube.

• Use Math to Save Money features practical, realistic examples in every chapter of how students can use math to cut costs and spend less. Topics have been updated based on a student survey of more than 1,000 developmental math colleges.

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.