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Overview

This clear, accessible treatment of mathematics features a building-block approach toward problem solving, realistic and diverse applications, and chapter organizer to help users focus their study and become effective and confident problem solvers. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life. The Fourth Edition contains additional modeling and real-data coverage. A conceptual approach to functions is introduced early in the book and revisited in Ch. 5, 6, 7, 8, and 10—readers are exposed to a variety of realistic situations where functions are used to explain and record the changes we observe in the world. A discussion of solving linear equations in Chapter 2 now includes coverage of equations with no solution and equations with infinitely many solutions. The sections on determinants and Cramer's rule have been moved out of Chapter 4 into an appendix. This material can be covered with ease after Section 4.3.
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Editorial Reviews

Booknews
Progresses from linear equations and polynomials through to quadratic equations and exponential functions. Bright colors and countless graphics will keep even nodding-off students up to speed. The new edition focuses on real world math problems and includes practice problems with solutions, application problems, and chapter summaries presented in chart form. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780131865877
  • Publisher: Pearson
  • Publication date: 2/28/2005
  • Edition description: Older Edition
  • Edition number: 5
  • Product dimensions: 8.20 (w) x 10.80 (h) x 1.20 (d)

Read an Excerpt

To the Instructor

We share a partnership with you. For over thirty years we have taught mathematics courses at North Shore Community College. Each semester we join you in the daily task of sharing the knowledge of mathematics with students who often struggle with this subject. We enjoy teaching and helping students—and we are confident that you share these joys with us.

Mathematics instructors and students face many challenges today. Intermediate Algebra was written with these needs in mind. This textbook explains mathematics slowly, clearly, and in a way that is relevant to everyday life for the college student. As with previous editions, special attention has been given in the fourth edition to problem solving. This text is written to help students organize the information in any problemsolving situation, to reduce anxiety, and to provide a guide that enables students to become confident problem solvers.

One of the hallmark characteristics of Intermediate Algebra that makes the text easy to learn and teach from is the building block organization. Each section is written to stand on its own, and each homework set is completely selftesting. Exercises are paired and graded and are of varying levels and types to ensure that all skills and concepts are covered. As a result, the text offers students an effective and proven learning program suitable for a variety of course formats—including lecturebased classes; discussionoriented classes; distance learning centers; modular, selfpaced courses; mathematics laboratories; and computersupported centers.

Intermediate Algebra is part of a series that includes the following:

  • Tobey/Slater, Basic College Mathematics, Fourth Edition
  • Blair/Tobey/Slater, Prealgebra, Second Edition
  • Tobey/Slater, Beginning Algebra, Fifth Edition
  • Tobey/Slater, Beginning and Intermediate Algebra

We have visited and listened to teachers across the country and have incorporated a number of their suggestions into this edition to help you with the particular learning delivery system at your school. The following pages describe the key continuing features and the key changes in the fourth edition.

Key Features and Changes in the Fourth Edition

Developing ProblemSolving Abilities

We are committed as authors to producing a textbook that emphasizes mathematical reasoning and problemsolving techniques as recommended by AMATYC, NCTM, AMS, NADE, MAA, and other groups. To this end, the exercise sets are built on a wealth of reallife and realdata applications. Unique exercises that help train students in data interpretation, mental mathematics, estimation, geometry and graphing, number sense, critical thinking, and decision making have been developed and incorporated into the exercise sets.

More Applied Exercises

The exercises and applications have been extensively revised. Numerous realworld and realdata application exercises show students the relevance of the math they are learning. The applications relate to everyday life, global issues beyond the borders of the United States, and other academic disciplines. Many include source citations. Nearly 50 percent of the applications are revised or new. The number of realdata applications has significantly increased. Many applications were contributed by actual students based on scenarios they encountered in their home or work lives.

Math in the Media

New Math in the Media applications appear at the end of each chapter to offer students yet another opportunity to see why developing mastery of mathematical concepts enhances their understanding of the world around them. The applications are based on information from familiar media sources. Students may interpret or verify information, perform calculations, make decisions or predictions, or provide a rationale for their responses.

Putting Your Skills to Work Applications

This highly successful feature has been revised in the fourth edition. There are eleven new Putting Your Skills to Work applications in the new edition. These nonroutine application exercises challenge students to synthesize the knowledge they have gained and apply it to a totally new area. Each exercise is specifically arranged for independent and cooperative learning or group investigation. Students are given the opportunity to help one another discover mathematical solutions to extended exercises. The investigations feature openended questions and extrapolation of data to areas beyond what is normally covered.

Internet Connections

As an integral part of each Putting Your Skills to Work exercise, students are exposed to an interesting application of the Internet and encouraged to continue their investigations. This use of technology inspires students' confidence in their abilities to successfully use mathematics. In the fourth edition, the Internet Connections have been completely revised and updated.

The companion Web site now features annotated links to help students navigate the sites more efficiently and to provide a more userfriendly experience.

Increased Integration and Emphasis on Geometry

Due to the emphasis on geometry in many statewide exams, geometry exercises are integrated throughout the text. The new edition contains approximately 20 percent more geometry exercises. Additionally, examples and exercises that incorporate a principle of geometry are now marked with a triangle icon for easy identification.

Developing Your Study Skills

This highly successful feature has been retained in the new edition. The boxed notes are integrated throughout the text to provide students with techniques for improving their study skills and succeeding in math courses.

Graphs, Charts, and Tables

When students find mathematics in realworld publications, they often see data represented in a graph, chart, or table and are asked to make a reasonable conclusion based on the data presented. This emphasis on graphical interpretation is a continuing trend with the expanding technology of our day. Therefore, the number of mathematical exercises based on charts, graphs, and tables has been significantly increased in this edition.

New Design

The fourth edition has a new design and art program that enhances the accessible, studentfriendly writing style. See the walkthrough of features in the preface.

Mastering Mathematical Concepts

Text features that develop the mastery of concepts include the following:

Learning Objectives

Concise learning objectives listed at the beginning of each section allow students to preview the goals of that section.

Examples and Exercises

The examples and exercises in this text have been carefully chosen to guide students through Intermediate Algebra. We have incorporated several different types of exercises and examples to assist your students in retaining the content of this course.

Chapter Pretests

Each chapter opens with a concise pretest to familiarize students with the learning objectives for that particular chapter. The exercises are keyed to the appropriate sections of the chapter. All answers appear in the back of the book.

Practice Problems

Practice Problems are found throughout the chapter after the examples and are designed to provide students with immediate practice of the skills presented in the examples. The complete workedout solution to each Practice Problem appears in the back of the book.

To Think About

These critical thinking questions follow some of the examples in the text and also appear in the exercise sets. They extend the concept being taught, providing the opportunity for students to stretch their minds, to look for patterns, and to make conclusions based on previous experience. The new edition includes approximately 30 percent more of these exercises.

Exercise Sets

Exercise sets are paired and graded. This design helps ease the students into the exercises, and the answers provide students with immediate feedback.

Cumulative Review Problems

Each exercise set concludes with a section of Cumulative Review Problems. These exercises review topics previously covered and are designed to assist students in retaining the material. Many additional applied exercises have been added to these sections.

Graphing and Scientific Calculator Exercises

Calculator boxes are placed in the margins of the text to alert students to a scientific or graphing calculator application. In the exercise sections, icons indicate exercises that are designed for solving with a graphing or scientific calculator.

Reviewing Mathematical Concepts

At the end of each chapter, we have included exercises and tests that provide students with several different formats to help them review and reinforce the ideas that they have learned. This not only assists the students with the present chapter but also reviews previously covered topics.

Chapter Organizers

The concepts and mathematical procedures covered in each chapter are reviewed at the end of the chapter in a unique Chapter Organizer. This device has been extremely popular with faculty and students alike. It not only lists concepts and methods but also provides a completely workedout example for each type of exercise. Students often find that preparing a similar chapter organizer on their own in higherlevel math courses becomes an invaluable way to master the content of a chapter of material.

Verbal and Writing Skills

These exercises provide students with the opportunity to extend a mathematical concept by allowing them to use their own words, to clarify their thinking, and to become familiar with mathematical terms.

Chapter Review Problems

These exercises serve as a quick refresher at the end of each chapter. They can also be used by the student as a quiz of the chapter material.

Tests

Found at the end of each chapter, the Chapter Test is a representative review of the material from that particular chapter and simulates an actual testing format.

Cumulative Tests

At the end of each chapter is a Cumulative Test. Onehalf of the content of each Cumulative Test is based on the math skills learned in previous chapters. By completing these tests, students build confidence that they have mastered the concepts of the present chapter as well as concepts from previous chapters.

Additional Content Changes in the Fourth Edition

In addition to the improvements listed previously, the new edition contains the following changes.

  • Throughout the text, explanations, definitions, and procedures have been carefully revised for greater clarity and precision.
  • The discussion in Chapter 2 of solving linear equations now includes coverage of equations with no solution and equations with infinitely many solutions.
  • To help prepare students better for college algebra, the concept of a function (first discussed in Chapter 3) is now integrated into Chapters 5, 6, and 7, where we discuss polynomial, rational, and radical functions. As in the previous edition, functions are also discussed in Chapters 8 and 10.
  • The sections on determinants and Cramer's rule have been moved from Chapter 4 to Appendix B. This material can be covered with ease after Section 4.3.

Expanded and Enhanced Supplements Resource Package

The fourth edition is supported by a wealth of new supplements designed for added effectiveness and efficiency. New items include: MathPro 4.0 Explorer tutorial software; MathPro 5—the new online version of the popular tutorial program—providing online access anytime and anywhere with assessment and enhanced course management; TestGenEQ with QuizmasterEQ; allnew lecture videos; lecture videos digitized on CDROM; Prentice Hall Tutor Center; and options for online and distance learning courses. Please see the list of supplements for their descriptions.

Options for Online and Distance Learning

For maximum convenience, Prentice Hall offers online interactivity and delivery options for a variety of distance learning needs.

Companion Web Site

The companion Web site includes basic distance learning access to links to the text's Internet Connections activities. For the fourth edition, the Internet Connections activities have been completely revised and updated. The Web site now features annotated links to facilitate student navigation of the sites associated with the exercises.

This textspecific site offers students online selfquizzes. Questions are graded, and students can email their results to the instructor. Syllabus Manager gives professors the option of creating their own online custom syllabus. Visit the Web site to learn more.

WebCT

WebCT includes distance learning access to content found in the Tobey/Slater companion Web site and more. WebCT provides tools to create, manage, and use online course materials. Contact your local Prentice Hall sales representative for details.

BlackBoard

BlackBoard includes distance learning access to content and features from the Tobey/Slater companion Web site and more. BlackBoard provides simple templates and tools to create, manage, and use online course materials. Instructors can take advantage of items such as online help, course management tools, communication tools, and access to instructor and student manuals. Contact your local Prentice Hall sales representative for details.

CourseCompass™ Powered by BlackBoard

This program includes distance learning access to content and features from the Tobey/Slater companion Web site and more. Prentice Hall content is preloaded in a customized version of BlackBoard 5. CourseCompass™ provides all BlackBoard 5's powerful course management tools to create, manage, and use online course materials. Contact your local Prentice Hall sales representative for details.

Supplements for the Instructor

Printed Resources

Annotated Instructor's Edition (<%ISBN%>0130328383)
• Complete student text
• Answers in place on the same text page as the exercises
• Teaching Tips at key points where students historically need extra help
• Answers to all exercises in pretests, review problems, tests, cumulative tests, diagnostic pretest, and practice final

Instructor's Solutions Manual (<%ISBN%>0130342041)
• Detailed stepbystep solutions to the evennumbered exercises
• Solutions to every exercise (odd and even) in the diagnostic pretest, pretests, review problems, tests, cumulative tests, and practice final
• Solution methods that reflect those emphasized in the text

Instructor's Resource Manual with Tests (<%ISBN%>0130342033)
• Nine test forms per chaptersix free response, three multiple choice. Two of the freeresponse tests are cumulative in nature.
• Two forms of pretests per chapter
• Eight forms of final examination
• Twenty additional exercises per section
• Answers to all tests and additional exercises

Media Resources

New TestGenEQ with QuizMasterEQ (Windows/Macintosh) (<%ISBN%>0130600237)
• Algorithmically driven, textspecific testing program
• Networkable for administering tests and capturing grades online
• The builtin Question Editor allows you to edit or add your own questions to create a nearly unlimited number of tests and worksheets.
• Use the Function Plotter to create graphs.
• Sidebyside "Testbank" window and "Test" window show your test as you build it and as it will be printed.
• Extensive symbol palettes and expression templates to assist in writing questions that include specialized tables and notation
• QuizMasterEQ tests can be used for practice and graded tests. Instructors can set preferences to determine test availability, time limits, and number of tries. It provides detailed exam reports for individual students, classes, or the course.

New MathPro Explorer 4.0 Network Version for Windows/Macintosh (<%ISBN%>0130600105)
• Enables instructors to create either customized or algorithmically generated practice tests from any section of a chapter or a test of random items
• Includes an email function for network users, enabling instructors to send a message to a specific student or an entire group
• Provides networkbased reports and summaries for a class or student and for cumulative or selected scores

New MathPro 5 Anytime. Anywhere. With Assessment.
• The popular MathPro tutorial program available over the Internet
• Online tutorial accessanytime and anywhere
• Enhanced course management tools

Companion Web Site

Internet Connections activities have been completely revised and updated. Annotated finks facilitate student navigation.
• Site provides online selfquizzes. Questions are graded, and students can email their results to the instructor.
• Syllabus Manager gives professors the option of creating their own online custom syllabus. Visit the Web site to learn more.

Supplements for Students

Printed Resources

Student Solutions Manual (<%ISBN%>0130342017)
• Solutions to all oddnumbered exercises
• Solutions to every (odd and even) exercise found in pretests, chapter tests, reviews, and cumulative reviews
• Solution methods that reflect those emphasized in the textbook
• Ask your bookstore about ordering.

Media Resources

New MathPro Explorer 4.0 CDROM (Student version: 0130600229)
• Keyed to each section of the text for textspecific tutorial exercises and instruction
• Warmup exercises and graded Practice Problems
• Video clips solve in detail an exercise similar to one being attempted.
• Algorithmically generated exercises; includes bookmark, online help, glossary, and summary of scores for the exercises tried
• Explorations enable students to explore concepts in more detail.

New MathPro 5 Anytime. Anywhere. With Assessment.
• The popular MathPro, tutorial program available over the Internet
• Online tutorial accessanytime and anywhere

New Lecture Videos (<%ISBN%>0130600180)
• All new videotapes accompany the fourth edition.
• Videos are keyed to each section of the text.
• Key concepts are explained stepbystep.

New Digitized Lecture Videos on CDROM (<%ISBN%>0130600199)
• The entire set of Intermediate Algebra, Fourth Edition lecture videotapes in digital form
• Convenient access to video tutorial support from home or campus computer
• Available shrinkwrapped with the text or standalone

New Prentice Hall Tutor Center
• Staffed by qualified math instructors and open 5 days a week, 7 hours a day
• Text specific tutoring provided via tollfree telephone, fax, or email.
• The Prentice Hall Tutor Center is accessed through a registration number that may be bundled with a new textbook or purchased separately.

Companion Web Site
Internet Connections activities have been completely revised and updated.
• Site provides an online study guide via selfquizzes. Questions are graded, and students can email their results to the instructor.

Additional Printed Material

Have your instructor contact the local Prentice Hall sales representative about the following resources.
• How to Study Mathematics
• Math on the Internet: A Student's Guide
• Prentice Hall/New York Times, Theme of the Times Newspaper Supplement

To the Student

This book was written with your needs and interests in mind. The original manuscript and the first three editions of this book have been classtested with students all across the country. Based on the suggestions of many students, the book has been refined and improved to maximize your learning while using this text.

We realize that some students who enter college have never enjoyed math or done well in a math course. You may find that you are anxious about taking this course. We want you to know that this book has been written to help you overcome those difficulties. Literally thousands of students across the country have found an amazing ability to learn math in using previous editions of this book. We have incorporated several learning tools and various types of exercises and examples to assist you in learning this material.

It helps to know that learning mathematics is going to help you in life. Perhaps you have entered this course feeling that little or no mathematics will be necessary in your future job. However, elementary school teachers, bus drivers, laboratory technicians, nurses, telephone operators, cable TV repair personnel, photographers, pharmacists, salespeople, doctors, architects, inspectors, counselors, and custodians who once believed that they needed little if any mathematics are finding that the mathematical skills presented in this course can help them. Mathematics, you will find, can help you too. In this book, a great number of examples and exercises come from everyday life. You will be amazed at the number of ways mathematics is used in the world each day.

Our greatest wish is that you will find success and personal satisfaction in your mathematics course. We have written this book to help you accomplish that very goal.

Suggestions for Students

  1. Be sure to take the time to read the boxes marked Developing Your Study Skills. These ideas come from faculty and students throughout the United States, who have found ways to succeed in mathematics, and they want to share those ideas with you.
  2. Read through each section of the book that is assigned by your instructor. You will be amazed at how much information you will learn as you read. It will "fill in the pieces" of mathematical knowledge. Reading a math book is a key part of learning math.
  3. Study carefully each example. Then work out the related practice problem. Direct involvement in doing exercises and not just thinking about them is one of the greatest guarantees of success in this course.
  4. Work out all assigned homework exercises. Verify your answers in the back of the book. Ask questions when you don't understand or when you are not sure of an answer.
  5. Be sure to take advantage of endofchapter helps. Study the Chapter Organizers. Do the chapter review exercises and the practice test exercises.
  6. If you need help, remember that teachers and tutors can assist you. The Student Solutions Manual for this textbook is most valuable. This manual shows workedout solutions for all the oddnumbered exercises as well as diagnostic pretest, chapter review, chapter test, and cumulative test exercises in this book. (If your college bookstore does not carry the Student Solutions Manual, ask them to order a copy for you. <%ISBN%>0130342017)
  7. Watch the videotapes or digitized videos on CDROM, where every section of this text is explained in detail. The work is solved using the same methods explained in the text.
  8. Use MathPro. MathPro Explorer 4.0 is a tutorial software package that allows you to be tutored in any section of the book. It also allows you to test yourself on your mastery of any section of the text. Practice problem solving using the resources available to you. MathPro 5 is the online version of this comprehensive tutorial program.
  9. Remember that learning mathematics takes time. However, the time spent is well worth the effort. Take the time to study, do homework, review, ask questions, and just reflect over what you have learned. The time you invest in learning mathematics will reap dividends in your future courses and in your future life.

We encourage you to look over your textbook carefully. Many important features have been designed to make learning mathematics a more enjoyable activity. Some special features, unique to this textbook, are those that students throughout the country have told us that they found especially helpful.

Four Key Textbook features to Help You

  1. Practice problems with workedout solutions. Immediately following every example is a similar exercise called the Practice Problem. If you can work it out correctly by following the example as a general point of reference, you will likely be able to do the homework exercises. If you encounter some difficulty, you will find helpful the completely workedout solutions to the Practice Problems that appear at the end of the text.
  2. Studentfriendly application exercises. In every chapter of this book you will find application exercises that are realistic and interesting. Many of the exercises were actually written or suggested by students. As you develop your problemsolving and reasoning skills in this course, you will encounter a number of realworld situations that show you how very helpful mathematical skills are in today's complex world.
  3. Putting Your Skills to Work exercises. In each chapter unique exercise sets ask you to analyze in depth some mathematical aspect of daily life. You will be asked to extend your knowledge, to do some creative thinking, and to work in small groups in a cooperative learning situation. You will even have a chance to explore some Web sites and see how the Internet can assist you in learning. These sections will awaken some new interests and help you develop the critical thinking skills so necessary both in college and after you graduate.
  4. The Chapter Organizer. Everything you need to learn in any one chapter of this book is readily available at your fingertips in the Chapter Organizer. This very popular chart summarizes all methods covered in the chapter, gives page references, and shows an example completely worked out for every major topic covered. Students have found this tool very helpful in mastering the content of any chapter of the book.
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Table of Contents

Preface to the Student
Acknowledgments
Diagnostic Pretest
Ch. 1 Basic Concepts 1
Ch. 2 Linear Equations and Inequalities 57
Ch. 3 Equations, Inequalities, and Functions 129
Ch. 4 Systems of Linear Equations and Inequalities 197
Ch. 5 Polynomials 269
Ch. 6 Rational Algebraic Expressions and Equations 333
Ch. 7 Rational Exponents and Radicals 383
Ch. 8 Quadratic Equations and Inequalities 443
Ch. 9 The Conic Sections 503
Ch. 10 Functions 557
Ch. 11 Logarithmic and Exponential Functions 609
Practice Final Examination 667
Glossary G-1
App. A Table of Square Roots A-1
App. A Table of Exponential Values A-2
App. B Solving Systems of Linear Equations Using Matrices A-3
Solutions to Practice Problems SP-1
Selected Answers SA-1
Applications Index I-1
Index I-5
Photo Credits P-1
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Preface

To the Instructor

We share a partnership with you. For over thirty years we have taught mathematics courses at North Shore Community College. Each semester we join you in the daily task of sharing the knowledge of mathematics with students who often struggle with this subject. We enjoy teaching and helping students—and we are confident that you share these joys with us.

Mathematics instructors and students face many challenges today. Intermediate Algebra was written with these needs in mind. This textbook explains mathematics slowly, clearly, and in a way that is relevant to everyday life for the college student. As with previous editions, special attention has been given in the fourth edition to problem solving. This text is written to help students organize the information in any problem-solving situation, to reduce anxiety, and to provide a guide that enables students to become confident problem solvers.

One of the hallmark characteristics of Intermediate Algebra that makes the text easy to learn and teach from is the building block organization. Each section is written to stand on its own, and each homework set is completely self-testing. Exercises are paired and graded and are of varying levels and types to ensure that all skills and concepts are covered. As a result, the text offers students an effective and proven learning program suitable for a variety of course formats—including lecture-based classes; discussion-oriented classes; distance learning centers; modular, self-paced courses; mathematics laboratories; and computer-supported centers.

Intermediate Algebra is part of a series that includes the following:

  • Tobey/Slater, Basic College Mathematics, Fourth Edition
  • Blair/Tobey/Slater, Prealgebra, Second Edition
  • Tobey/Slater, Beginning Algebra, Fifth Edition
  • Tobey/Slater, Beginning and Intermediate Algebra

We have visited and listened to teachers across the country and have incorporated a number of their suggestions into this edition to help you with the particular learning delivery system at your school. The following pages describe the key continuing features and the key changes in the fourth edition.

Key Features and Changes in the Fourth Edition

Developing Problem-Solving Abilities

We are committed as authors to producing a textbook that emphasizes mathematical reasoning and problem-solving techniques as recommended by AMATYC, NCTM, AMS, NADE, MAA, and other groups. To this end, the exercise sets are built on a wealth of real-life and real-data applications. Unique exercises that help train students in data interpretation, mental mathematics, estimation, geometry and graphing, number sense, critical thinking, and decision making have been developed and incorporated into the exercise sets.

More Applied Exercises

The exercises and applications have been extensively revised. Numerous real-world and real-data application exercises show students the relevance of the math they are learning. The applications relate to everyday life, global issues beyond the borders of the United States, and other academic disciplines. Many include source citations. Nearly 50 percent of the applications are revised or new. The number of real-data applications has significantly increased. Many applications were contributed by actual students based on scenarios they encountered in their home or work lives.

Math in the Media

New Math in the Media applications appear at the end of each chapter to offer students yet another opportunity to see why developing mastery of mathematical concepts enhances their understanding of the world around them. The applications are based on information from familiar media sources. Students may interpret or verify information, perform calculations, make decisions or predictions, or provide a rationale for their responses.

Putting Your Skills to Work Applications

This highly successful feature has been revised in the fourth edition. There are eleven new Putting Your Skills to Work applications in the new edition. These nonroutine application exercises challenge students to synthesize the knowledge they have gained and apply it to a totally new area. Each exercise is specifically arranged for independent and cooperative learning or group investigation. Students are given the opportunity to help one another discover mathematical solutions to extended exercises. The investigations feature open-ended questions and extrapolation of data to areas beyond what is normally covered.

Internet Connections

As an integral part of each Putting Your Skills to Work exercise, students are exposed to an interesting application of the Internet and encouraged to continue their investigations. This use of technology inspires students' confidence in their abilities to successfully use mathematics. In the fourth edition, the Internet Connections have been completely revised and updated.

The companion Web site now features annotated links to help students navigate the sites more efficiently and to provide a more user-friendly experience.

Increased Integration and Emphasis on Geometry

Due to the emphasis on geometry in many statewide exams, geometry exercises are integrated throughout the text. The new edition contains approximately 20 percent more geometry exercises. Additionally, examples and exercises that incorporate a principle of geometry are now marked with a triangle icon for easy identification.

Developing Your Study Skills

This highly successful feature has been retained in the new edition. The boxed notes are integrated throughout the text to provide students with techniques for improving their study skills and succeeding in math courses.

Graphs, Charts, and Tables

When students find mathematics in real-world publications, they often see data represented in a graph, chart, or table and are asked to make a reasonable conclusion based on the data presented. This emphasis on graphical interpretation is a continuing trend with the expanding technology of our day. Therefore, the number of mathematical exercises based on charts, graphs, and tables has been significantly increased in this edition.

New Design

The fourth edition has a new design and art program that enhances the accessible, student-friendly writing style. See the walk-through of features in the preface.

Mastering Mathematical Concepts

Text features that develop the mastery of concepts include the following:

Learning Objectives

Concise learning objectives listed at the beginning of each section allow students to preview the goals of that section.

Examples and Exercises

The examples and exercises in this text have been carefully chosen to guide students through Intermediate Algebra. We have incorporated several different types of exercises and examples to assist your students in retaining the content of this course.

Chapter Pretests

Each chapter opens with a concise pretest to familiarize students with the learning objectives for that particular chapter. The exercises are keyed to the appropriate sections of the chapter. All answers appear in the back of the book.

Practice Problems

Practice Problems are found throughout the chapter after the examples and are designed to provide students with immediate practice of the skills presented in the examples. The complete worked-out solution to each Practice Problem appears in the back of the book.

To Think About

These critical thinking questions follow some of the examples in the text and also appear in the exercise sets. They extend the concept being taught, providing the opportunity for students to stretch their minds, to look for patterns, and to make conclusions based on previous experience. The new edition includes approximately 30 percent more of these exercises.

Exercise Sets

Exercise sets are paired and graded. This design helps ease the students into the exercises, and the answers provide students with immediate feedback.

Cumulative Review Problems

Each exercise set concludes with a section of Cumulative Review Problems. These exercises review topics previously covered and are designed to assist students in retaining the material. Many additional applied exercises have been added to these sections.

Graphing and Scientific Calculator Exercises

Calculator boxes are placed in the margins of the text to alert students to a scientific or graphing calculator application. In the exercise sections, icons indicate exercises that are designed for solving with a graphing or scientific calculator.

Reviewing Mathematical Concepts

At the end of each chapter, we have included exercises and tests that provide students with several different formats to help them review and reinforce the ideas that they have learned. This not only assists the students with the present chapter but also reviews previously covered topics.

Chapter Organizers

The concepts and mathematical procedures covered in each chapter are reviewed at the end of the chapter in a unique Chapter Organizer. This device has been extremely popular with faculty and students alike. It not only lists concepts and methods but also provides a completely worked-out example for each type of exercise. Students often find that preparing a similar chapter organizer on their own in higher-level math courses becomes an invaluable way to master the content of a chapter of material.

Verbal and Writing Skills

These exercises provide students with the opportunity to extend a mathematical concept by allowing them to use their own words, to clarify their thinking, and to become familiar with mathematical terms.

Chapter Review Problems

These exercises serve as a quick refresher at the end of each chapter. They can also be used by the student as a quiz of the chapter material.

Tests

Found at the end of each chapter, the Chapter Test is a representative review of the material from that particular chapter and simulates an actual testing format.

Cumulative Tests

At the end of each chapter is a Cumulative Test. One-half of the content of each Cumulative Test is based on the math skills learned in previous chapters. By completing these tests, students build confidence that they have mastered the concepts of the present chapter as well as concepts from previous chapters.

Additional Content Changes in the Fourth Edition

In addition to the improvements listed previously, the new edition contains the following changes.

  • Throughout the text, explanations, definitions, and procedures have been carefully revised for greater clarity and precision.
  • The discussion in Chapter 2 of solving linear equations now includes coverage of equations with no solution and equations with infinitely many solutions.
  • To help prepare students better for college algebra, the concept of a function (first discussed in Chapter 3) is now integrated into Chapters 5, 6, and 7, where we discuss polynomial, rational, and radical functions. As in the previous edition, functions are also discussed in Chapters 8 and 10.
  • The sections on determinants and Cramer's rule have been moved from Chapter 4 to Appendix B. This material can be covered with ease after Section 4.3.

Expanded and Enhanced Supplements Resource Package

The fourth edition is supported by a wealth of new supplements designed for added effectiveness and efficiency. New items include: MathPro 4.0 Explorer tutorial software; MathPro 5—the new online version of the popular tutorial program—providing online access anytime and anywhere with assessment and enhanced course management; TestGen-EQ with Quizmaster-EQ; all-new lecture videos; lecture videos digitized on CD-ROM; Prentice Hall Tutor Center; and options for online and distance learning courses. Please see the list of supplements for their descriptions.

Options for Online and Distance Learning

For maximum convenience, Prentice Hall offers online interactivity and delivery options for a variety of distance learning needs.

Companion Web Site


The companion Web site includes basic distance learning access to links to the text's Internet Connections activities. For the fourth edition, the Internet Connections activities have been completely revised and updated. The Web site now features annotated links to facilitate student navigation of the sites associated with the exercises.

This text-specific site offers students online self-quizzes. Questions are graded, and students can e-mail their results to the instructor. Syllabus Manager gives professors the option of creating their own online custom syllabus. Visit the Web site to learn more.

WebCT


WebCT includes distance learning access to content found in the Tobey/Slater companion Web site and more. WebCT provides tools to create, manage, and use online course materials. Contact your local Prentice Hall sales representative for details.

BlackBoard

BlackBoard includes distance learning access to content and features from the Tobey/Slater companion Web site and more. BlackBoard provides simple templates and tools to create, manage, and use online course materials. Instructors can take advantage of items such as online help, course management tools, communication tools, and access to instructor and student manuals. Contact your local Prentice Hall sales representative for details.

CourseCompass™ Powered by BlackBoard

This program includes distance learning access to content and features from the Tobey/Slater companion Web site and more. Prentice Hall content is preloaded in a customized version of BlackBoard 5. CourseCompass™ provides all BlackBoard 5's powerful course management tools to create, manage, and use online course materials. Contact your local Prentice Hall sales representative for details.

Supplements for the Instructor

Printed Resources

Annotated Instructor's Edition (ISBN: 0-13-032838-3)
• Complete student text
• Answers in place on the same text page as the exercises
• Teaching Tips at key points where students historically need extra help
• Answers to all exercises in pretests, review problems, tests, cumulative tests, diagnostic pretest, and practice final

Instructor's Solutions Manual (ISBN: 0-13-034204-1)
• Detailed step-by-step solutions to the even-numbered exercises
• Solutions to every exercise (odd and even) in the diagnostic pretest, pretests, review problems, tests, cumulative tests, and practice final
• Solution methods that reflect those emphasized in the text

Instructor's Resource Manual with Tests (ISBN: 0-13-034203-3)
• Nine test forms per chapter-six free response, three multiple choice. Two of the free-response tests are cumulative in nature.
• Two forms of pretests per chapter
• Eight forms of final examination
• Twenty additional exercises per section
• Answers to all tests and additional exercises

Media Resources

New TestGen-EQ with QuizMaster-EQ (Windows/Macintosh) (ISBN: 0-13-060023-7)
• Algorithmically driven, text-specific testing program
• Networkable for administering tests and capturing grades online
• The built-in Question Editor allows you to edit or add your own questions to create a nearly unlimited number of tests and worksheets.
• Use the Function Plotter to create graphs.
• Side-by-side "Testbank" window and "Test" window show your test as you build it and as it will be printed.
• Extensive symbol palettes and expression templates to assist in writing questions that include specialized tables and notation
• QuizMaster-EQ tests can be used for practice and graded tests. Instructors can set preferences to determine test availability, time limits, and number of tries. It provides detailed exam reports for individual students, classes, or the course.

New MathPro Explorer 4.0 Network Version for Windows/Macintosh (ISBN: 0-13-060010-5)
• Enables instructors to create either customized or algorithmically generated practice tests from any section of a chapter or a test of random items
• Includes an e-mail function for network users, enabling instructors to send a message to a specific student or an entire group
• Provides network-based reports and summaries for a class or student and for cumulative or selected scores

New MathPro 5 Anytime. Anywhere. With Assessment.
• The popular MathPro tutorial program available over the Internet
• Online tutorial access-anytime and anywhere
• Enhanced course management tools

Companion Web Site

• Internet Connections activities have been completely revised and updated. Annotated finks facilitate student navigation.
• Site provides online self-quizzes. Questions are graded, and students can e-mail their results to the instructor.
• Syllabus Manager gives professors the option of creating their own online custom syllabus. Visit the Web site to learn more.

Supplements for Students

Printed Resources

Student Solutions Manual (ISBN: 0-13-034201-7)
• Solutions to all odd-numbered exercises
• Solutions to every (odd and even) exercise found in pretests, chapter tests, reviews, and cumulative reviews
• Solution methods that reflect those emphasized in the textbook
• Ask your bookstore about ordering.

Media Resources

New MathPro Explorer 4.0 CD-ROM (Student version: 0-13-060022-9)
• Keyed to each section of the text for text-specific tutorial exercises and instruction
• Warm-up exercises and graded Practice Problems
• Video clips solve in detail an exercise similar to one being attempted.
• Algorithmically generated exercises; includes bookmark, online help, glossary, and summary of scores for the exercises tried
• Explorations enable students to explore concepts in more detail.

New MathPro 5 Anytime. Anywhere. With Assessment.
• The popular MathPro, tutorial program available over the Internet
• Online tutorial access-anytime and anywhere

New Lecture Videos (ISBN: 0-13-060018-0)
• All new videotapes accompany the fourth edition.
• Videos are keyed to each section of the text.
• Key concepts are explained step-by-step.

New Digitized Lecture Videos on CD-ROM (ISBN: 0-13-060019-9)
• The entire set of Intermediate Algebra, Fourth Edition lecture videotapes in digital form
• Convenient access to video tutorial support from home or campus computer
• Available shrink-wrapped with the text or stand-alone

New Prentice Hall Tutor Center
• Staffed by qualified math instructors and open 5 days a week, 7 hours a day
• Text specific tutoring provided via toll-free telephone, fax, or e-mail.
• The Prentice Hall Tutor Center is accessed through a registration number that may be bundled with a new textbook or purchased separately.

Companion Web Site
• Internet Connections activities have been completely revised and updated.
• Site provides an online study guide via self-quizzes. Questions are graded, and students can e-mail their results to the instructor.

Additional Printed Material

Have your instructor contact the local Prentice Hall sales representative about the following resources.
• How to Study Mathematics
• Math on the Internet: A Student's Guide
• Prentice Hall/New York Times, Theme of the Times Newspaper Supplement

To the Student

This book was written with your needs and interests in mind. The original manuscript and the first three editions of this book have been class-tested with students all across the country. Based on the suggestions of many students, the book has been refined and improved to maximize your learning while using this text.

We realize that some students who enter college have never enjoyed math or done well in a math course. You may find that you are anxious about taking this course. We want you to know that this book has been written to help you overcome those difficulties. Literally thousands of students across the country have found an amazing ability to learn math in using previous editions of this book. We have incorporated several learning tools and various types of exercises and examples to assist you in learning this material.

It helps to know that learning mathematics is going to help you in life. Perhaps you have entered this course feeling that little or no mathematics will be necessary in your future job. However, elementary school teachers, bus drivers, laboratory technicians, nurses, telephone operators, cable TV repair personnel, photographers, pharmacists, salespeople, doctors, architects, inspectors, counselors, and custodians who once believed that they needed little if any mathematics are finding that the mathematical skills presented in this course can help them. Mathematics, you will find, can help you too. In this book, a great number of examples and exercises come from everyday life. You will be amazed at the number of ways mathematics is used in the world each day.

Our greatest wish is that you will find success and personal satisfaction in your mathematics course. We have written this book to help you accomplish that very goal.

Suggestions for Students

  1. Be sure to take the time to read the boxes marked Developing Your Study Skills. These ideas come from faculty and students throughout the United States, who have found ways to succeed in mathematics, and they want to share those ideas with you.
  2. Read through each section of the book that is assigned by your instructor. You will be amazed at how much information you will learn as you read. It will "fill in the pieces" of mathematical knowledge. Reading a math book is a key part of learning math.
  3. Study carefully each example. Then work out the related practice problem. Direct involvement in doing exercises and not just thinking about them is one of the greatest guarantees of success in this course.
  4. Work out all assigned homework exercises. Verify your answers in the back of the book. Ask questions when you don't understand or when you are not sure of an answer.
  5. Be sure to take advantage of end-of-chapter helps. Study the Chapter Organizers. Do the chapter review exercises and the practice test exercises.
  6. If you need help, remember that teachers and tutors can assist you. The Student Solutions Manual for this textbook is most valuable. This manual shows worked-out solutions for all the odd-numbered exercises as well as diagnostic pretest, chapter review, chapter test, and cumulative test exercises in this book. (If your college bookstore does not carry the Student Solutions Manual, ask them to order a copy for you. ISBN: 0-13-034201-7)
  7. Watch the videotapes or digitized videos on CD-ROM, where every section of this text is explained in detail. The work is solved using the same methods explained in the text.
  8. Use MathPro. MathPro Explorer 4.0 is a tutorial software package that allows you to be tutored in any section of the book. It also allows you to test yourself on your mastery of any section of the text. Practice problem solving using the resources available to you. MathPro 5 is the online version of this comprehensive tutorial program.
  9. Remember that learning mathematics takes time. However, the time spent is well worth the effort. Take the time to study, do homework, review, ask questions, and just reflect over what you have learned. The time you invest in learning mathematics will reap dividends in your future courses and in your future life.

We encourage you to look over your textbook carefully. Many important features have been designed to make learning mathematics a more enjoyable activity. Some special features, unique to this textbook, are those that students throughout the country have told us that they found especially helpful.

Four Key Textbook features to Help You

  1. Practice problems with worked-out solutions. Immediately following every example is a similar exercise called the Practice Problem. If you can work it out correctly by following the example as a general point of reference, you will likely be able to do the homework exercises. If you encounter some difficulty, you will find helpful the completely worked-out solutions to the Practice Problems that appear at the end of the text.
  2. Student-friendly application exercises. In every chapter of this book you will find application exercises that are realistic and interesting. Many of the exercises were actually written or suggested by students. As you develop your problem-solving and reasoning skills in this course, you will encounter a number of real-world situations that show you how very helpful mathematical skills are in today's complex world.
  3. Putting Your Skills to Work exercises. In each chapter unique exercise sets ask you to analyze in depth some mathematical aspect of daily life. You will be asked to extend your knowledge, to do some creative thinking, and to work in small groups in a cooperative learning situation. You will even have a chance to explore some Web sites and see how the Internet can assist you in learning. These sections will awaken some new interests and help you develop the critical thinking skills so necessary both in college and after you graduate.
  4. The Chapter Organizer. Everything you need to learn in any one chapter of this book is readily available at your fingertips in the Chapter Organizer. This very popular chart summarizes all methods covered in the chapter, gives page references, and shows an example completely worked out for every major topic covered. Students have found this tool very helpful in mastering the content of any chapter of the book.
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Introduction

To the Instructor

We share a partnership with you. For over thirty years we have taught mathematics courses at North Shore Community College. Each semester we join you in the daily task of sharing the knowledge of mathematics with students who often struggle with this subject. We enjoy teaching and helping students—and we are confident that you share these joys with us.

Mathematics instructors and students face many challenges today. Intermediate Algebra was written with these needs in mind. This textbook explains mathematics slowly, clearly, and in a way that is relevant to everyday life for the college student. As with previous editions, special attention has been given in the fourth edition to problem solving. This text is written to help students organize the information in any problem-solving situation, to reduce anxiety, and to provide a guide that enables students to become confident problem solvers.

One of the hallmark characteristics of Intermediate Algebra that makes the text easy to learn and teach from is the building block organization. Each section is written to stand on its own, and each homework set is completely self-testing. Exercises are paired and graded and are of varying levels and types to ensure that all skills and concepts are covered. As a result, the text offers students an effective and proven learning program suitable for a variety of course formats—including lecture-based classes; discussion-oriented classes; distance learning centers; modular, self-paced courses; mathematics laboratories; and computer-supported centers.

Intermediate Algebra is part of a series that includes thefollowing:

  • Tobey/Slater, Basic College Mathematics, Fourth Edition
  • Blair/Tobey/Slater, Prealgebra, Second Edition
  • Tobey/Slater, Beginning Algebra, Fifth Edition
  • Tobey/Slater, Beginning and Intermediate Algebra

We have visited and listened to teachers across the country and have incorporated a number of their suggestions into this edition to help you with the particular learning delivery system at your school. The following pages describe the key continuing features and the key changes in the fourth edition.

Key Features and Changes in the Fourth Edition

Developing Problem-Solving Abilities

We are committed as authors to producing a textbook that emphasizes mathematical reasoning and problem-solving techniques as recommended by AMATYC, NCTM, AMS, NADE, MAA, and other groups. To this end, the exercise sets are built on a wealth of real-life and real-data applications. Unique exercises that help train students in data interpretation, mental mathematics, estimation, geometry and graphing, number sense, critical thinking, and decision making have been developed and incorporated into the exercise sets.

More Applied Exercises

The exercises and applications have been extensively revised. Numerous real-world and real-data application exercises show students the relevance of the math they are learning. The applications relate to everyday life, global issues beyond the borders of the United States, and other academic disciplines. Many include source citations. Nearly 50 percent of the applications are revised or new. The number of real-data applications has significantly increased. Many applications were contributed by actual students based on scenarios they encountered in their home or work lives.

Math in the Media

New Math in the Media applications appear at the end of each chapter to offer students yet another opportunity to see why developing mastery of mathematical concepts enhances their understanding of the world around them. The applications are based on information from familiar media sources. Students may interpret or verify information, perform calculations, make decisions or predictions, or provide a rationale for their responses.

Putting Your Skills to Work Applications

This highly successful feature has been revised in the fourth edition. There are eleven new Putting Your Skills to Work applications in the new edition. These nonroutine application exercises challenge students to synthesize the knowledge they have gained and apply it to a totally new area. Each exercise is specifically arranged for independent and cooperative learning or group investigation. Students are given the opportunity to help one another discover mathematical solutions to extended exercises. The investigations feature open-ended questions and extrapolation of data to areas beyond what is normally covered.

Internet Connections

As an integral part of each Putting Your Skills to Work exercise, students are exposed to an interesting application of the Internet and encouraged to continue their investigations. This use of technology inspires students' confidence in their abilities to successfully use mathematics. In the fourth edition, the Internet Connections have been completely revised and updated.

Developing Your Study Skills

This highly successful feature has been retained in the new edition. The boxed notes are integrated throughout the text to provide students with techniques for improving their study skills and succeeding in math courses.

Graphs, Charts, and Tables

When students find mathematics in real-world publications, they often see data represented in a graph, chart, or table and are asked to make a reasonable conclusion based on the data presented. This emphasis on graphical interpretation is a continuing trend with the expanding technology of our day. Therefore, the number of mathematical exercises based on charts, graphs, and tables has been significantly increased in this edition.

New Design

The fourth edition has a new design and art program that enhances the accessible, student-friendly writing style. See the walk-through of features in the preface.

Mastering Mathematical Concepts

Text features that develop the mastery of concepts include the following:

Learning Objectives

Concise learning objectives listed at the beginning of each section allow students to preview the goals of that section.

Examples and Exercises

The examples and exercises in this text have been carefully chosen to guide students through Intermediate Algebra. We have incorporated several different types of exercises and examples to assist your students in retaining the content of this course.

Chapter Pretests

Each chapter opens with a concise pretest to familiarize students with the learning objectives for that particular chapter. The exercises are keyed to the appropriate sections of the chapter. All answers appear in the back of the book.

Practice Problems

Practice Problems are found throughout the chapter after the examples and are designed to provide students with immediate practice of the skills presented in the examples. The complete worked-out solution to each Practice Problem appears in the back of the book.

To Think About

These critical thinking questions follow some of the examples in the text and also appear in the exercise sets. They extend the concept being taught, providing the opportunity for students to stretch their minds, to look for patterns, and to make conclusions based on previous experience. The new edition includes approximately 30 percent more of these exercises.

Exercise Sets

Exercise sets are paired and graded. This design helps ease the students into the exercises, and the answers provide students with immediate feedback.

Cumulative Review Problems

Each exercise set concludes with a section of Cumulative Review Problems. These exercises review topics previously covered and are designed to assist students in retaining the material. Many additional applied exercises have been added to these sections.

Graphing and Scientific Calculator Exercises

Calculator boxes are placed in the margins of the text to alert students to a scientific or graphing calculator application. In the exercise sections, icons indicate exercises that are designed for solving with a graphing or scientific calculator.

Reviewing Mathematical Concepts

At the end of each chapter, we have included exercises and tests that provide students with several different formats to help them review and reinforce the ideas that they have learned. This not only assists the students with the present chapter but also reviews previously covered topics.

Chapter Organizers

The concepts and mathematical procedures covered in each chapter are reviewed at the end of the chapter in a unique Chapter Organizer. This device has been extremely popular with faculty and students alike. It not only lists concepts and methods but also provides a completely worked-out example for each type of exercise. Students often find that preparing a similar chapter organizer on their own in higher-level math courses becomes an invaluable way to master the content of a chapter of material.

Verbal and Writing Skills

These exercises provide students with the opportunity to extend a mathematical concept by allowing them to use their own words, to clarify their thinking, and to become familiar with mathematical terms.

Chapter Review Problems

These exercises serve as a quick refresher at the end of each chapter. They can also be used by the student as a quiz of the chapter material.

Tests

Found at the end of each chapter, the Chapter Test is a representative review of the material from that particular chapter and simulates an actual testing format.

Cumulative Tests

At the end of each chapter is a Cumulative Test. One-half of the content of each Cumulative Test is based on the math skills learned in previous chapters. By completing these tests, students build confidence that they have mastered the concepts of the present chapter as well as concepts from previous chapters.

Additional Content Changes in the Fourth Edition

In addition to the improvements listed previously, the new edition contains the following changes.

  • Throughout the text, explanations, definitions, and procedures have been carefully revised for greater clarity and precision.
  • The discussion in Chapter 2 of solving linear equations now includes coverage of equations with no solution and equations with infinitely many solutions.
  • To help prepare students better for college algebra, the concept of a function (first discussed in Chapter 3) is now integrated into Chapters 5, 6, and 7, where we discuss polynomial, rational, and radical functions. As in the previous edition, functions are also discussed in Chapters 8 and 10.
  • The sections on determinants and Cramer's rule have been moved from Chapter 4 to Appendix B. This material can be covered with ease after Section 4.3.

Expanded and Enhanced Supplements Resource Package

The fourth edition is supported by a wealth of new supplements designed for added effectiveness and efficiency. New items include: MathPro 4.0 Explorer tutorial software; MathPro 5—the new online version of the popular tutorial program—providing online access anytime and anywhere with assessment and enhanced course management; TestGen-EQ with Quizmaster-EQ; all-new lecture videos; lecture videos digitized on CD-ROM; Prentice Hall Tutor Center; and options for online and distance learning courses. Please see the list of supplements for their descriptions.

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