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## Overview

###### ADVERTISEMENT

## Product Details

ISBN-13: | 9780130328434 |
---|---|

Publisher: | Prentice Hall Professional Technical Reference |

Publication date: | 12/28/2001 |

Pages: | 1022 |

## Read an Excerpt

*Introductory and Intermediate Algebra for College Students* provides comprehensive, in-depth coverage of the topics required in a course combining the study of introductory and intermediate algebra. The primary goals of the book are to help students acquire a solid foundation in introductory and intermediate algebra, without the repetition of topics in two separate texts, and to show how algebra can model and solve authentic real-world problems.

A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:

- "I cannot follow the explanations."
- "The applications are not interesting."

I thought about both of these objections in writing every page of this book.

**"I can't follow the explanations."** For many of my students, textbook explanations are too compressed. The chapters in *Introductory and Intermediate Algebra for College Students* have been written to make them extremely accessible. Every section contains a range of simple, intermediate, and challenging examples. Voice balloons allow for specific annotations in examples, further clarifying procedures and concepts.

**"The applications are not interesting."** One of the things I enjoy most about teaching in a large urban community college is the diversity of who my students are and what interests them. Real-world data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all up-to-date real-world data to be interesting and intriguing tostudents. By connecting algebra to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.

### Key Pedagogical Features

*Introductory and Intermediate Algebra for College Students* is part of a series of four texts that include *Introductory Algebra for College Students,* Third Edition, *Intermediate Algebra for College Students,* Third Edition, and *Algebra for College Students,* Fourth Edition. The following features are found throughout the series.

**Chapter-Opening and Section-Opening Scenarios.**Every chapter*and every section*opens with a compelling image that supports a scenario presenting a unique application of algebra in students' lives outside the classroom:. Each scenario is revisited later in the chapter or section.**Section Objectives.**Learning objectives open every section. The objective are stated in the margin at their point of use.**Detailed Illustrative Examples.**Each illustrative example is titled, making; clear the purpose of the example. Examples are clearly written and provide students with detailed step-by-step solutions. No steps are omitted and each step is explained.**Check Point Examples.**Each worked example is followed by a similar matched problem for the student to work while reading the material. This actively involves the student in the learning process and gives students the opportunity to work with a concept as soon as they have learned it. Answers to all Check Points are given in the answer section.**Graphing.**Chapter 1 contains an introduction to graphing, a topic that is integrated throughout the book. Line, bar, circle, and rectangular coordinate graphs that use real data appear in nearly every section and exercise set. Many examples and exercises use graphs to explore relationships between data and to provide ways of visualizing a problem's solution.**Geometric Problem Solving.**Section 2.6 on problem solving in geometry teaches geometric concepts that are important to a student's understanding of algebra. There is frequent emphasis on problem solving in geometric situations, as well as on geometric models that allow students to visualize algebraic formulas.**Functions.**Functions are introduced in Chapter 8, with functions emphasized throughout the second half of the book.**Thorough, Yet Optional Technology.**Although the use of graphing utilities is optional, they are utilized in Using Technology boxes to enable students to visualize algebraic concepts. The use of graphing utilities is also reinforced in the technology exercises appearing in the exercise sets for those who want this option. With the book's early introduction to graphing, students can look at the calculator screens in the Using Technology boxes and gain an increased understanding of an example's solution even if they are not using a graphing utility in the course.**Enrichment Essays.**Enrichment essays provide historical, interdisciplinary, and otherwise interesting connections throughout the text.**Study Tips.**Study Tip boxes offer suggestions for problem solving, point out common student errors, and provide informal tips and suggestions. These invaluable hints appear in abundance throughout the book.**Discovery.**Discover for Yourself boxes, found throughout the text, encourage students to further explore algebraic concepts. These explorations are optional and their omission does not interfere with the continuity of the topic under consideration.**Exercise Sets.**An extensive collection of exercises is included in an exercise set at the end of each section. The text organizes exercises by level within six category types: Practice Exercises, Application Exercises, Writing in Mathematics, Technology Exercises, Critical Thinking Exercises, and Review Exercises. This format makes it easy to create well-rounded homework assignments. Writing exercises offer students the opportunity to write about every objective covered in each section, as well as to discuss, interpret, and give opinions about data. Each review exercise contains the section number and example number of a similar worked-out example.**Chapter Projects.**At the end of each chapter are collaborative activities that give students the opportunity to work cooperatively as they think and talk about mathematics. Many of these exercises should result in interesting group, discussions.**Chapter Review Grids.**Each chapter contains a review chart that summarizes the definitions and concepts in every section of the chapter. Examples that illustrate these key concepts are also included in the chart. Like the summary grid, review exercises are organized by each section of the chapter.**End-of-Chapter Materials.**The review grids provide a focused summary and illustrative examples for each section in the chapter. A comprehensive collection of review exercises for each of the chapter's sections follows the review grid. This is followed by a chapter test. Beginning with Chapter 2, each chapter concludes with a comprehensive collection of cumulative review exercises.**A Review of Introductory Algebra.**Appendix A, entitled*Are You Prepared for Intermediate Algebra?*, provides students with a fast way to review introductory algebra topics before starting the intermediate algebra portion of the book.**Supplements Package.**This text is supported by a wealth of supplements designed for added effectiveness and efficiency. These items are described on pages xiii through xv.

## Supplements for the Instructor

### Printed Resources

*Annotated Instructor's Edition (0-13-032843-X)*

• Answers to exercises on the same text page or in Graphing Answer Section.

• Graphing Answer Section contains answers to exercises requiring graphical solutions.

*Instructor's Solutions Manual (0-13-034328-5)*

• Step-by-step solutions for every even-numbered section exercise.

• Step-by-step solutions for every (even and odd) Check Point exercise, Chapter Review exercise, Chapter Test and Cumulative Review exercise.

*Instructor's Resource Manual (0-13-034319-6)*

• Notes to the Instructor

• Eight Chapter Tests per chapter (5 free response, 3 multiple choice)

• Eight Final Exams ( 4 free response, 4 multiple choice)

• Twenty additional exercises per section for added test exercises or worksheets.

• Answers to all items

### Media Resources

*TestGen-EQ with QuizMaster-EQ (CD-ROM for IBM and Macintosh 0-13-034324-2)*

• Algorithmically driven, text specific testing program.

• Networkable for administering tests and capturing grades on-line.

• Edit or add your own questions to create a nearly unlimited number of tests and worksheets.

• Use the new "Function Plotter" to create graphs.

• Tests can be easily exported to HTML so they can be posted to the Web.

*Computerized Tutorial Software Course Management System*

MathPro Explorer 4.0

• Network version for IBM and Macintosh

• Enables instructors to create either customized or algorithmically generated practice quizzes from any section of a chapter.

• Includes an e-mail function for networked users, enabling instructors toy send a message to a specific student or to an entire group.

• Network based reports and summaries for a class or student and for cumulative or selected scores are available.

*MathPro 5*

• Anytime. Anywhere.

• Online tutorial with enhanced class and student management features.

• Integration of TestGen-EQ allows for testing to operate within the tutorial environment.

• Course management tracking of both tutorial and testing activity.

*Online Options for Distance Learning*

WebCT/Blackboard/CourseCompass

• Prentice Hall offers three different on-line interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text.

## Supplements for the Student

### Printed Resource

*Student Solutions Manual (0-13-034327-7)*

• Step-by-step solutions for every odd-numbered section exercise.

• Step-by-step solutions for every (even and odd) Check Point exercise, Chapter Review exercise, Chapter Test and Cumulative Review exercise.

*How to Study Mathematics*

• Have your instructor contact the local Prentice Hall sales representative.

*Math on the Internet: A Student's Guide*

• Have your instructor contact the local Prentice Hall sales representative.

### Media Resources

*Computerized Tutorial Software*

MathPro Explorer 4.0

• Keyed to each section of the text for text-specific tutorial exercises and instruction.

• Warm-up exercises and graded Practice Problems.

• Video clips show a problem being explained and worked out on the board.

• Algorithmically generated exercises. On-line help, glossary and summary of scores.

MathPro 5-Anytime. Anywhere.

• Enhanced, Internet-based version of Prentice Hall's popular tutorial software.

*Lecture Videos*

• Keyed to each section of the text.

*Digitized Lecture Videos on CD.*

• Have your instructor contact the local Prentice Hall sales representative.

*Prentice Hall Tutoring Center*

• Provides one-on-one tutorial assistance by phone, e-mail, or fax.

*Companion Website*

• Offers Warm-ups, Real World Activities and Chapter Quizzes.

• E-mail results to your instructor.

• Destination links provide additional opportunities to explore other related sites.

## Table of Contents

**CONTENTS**

A Brief Guide to Getting the Most from This Book

Preface

To The Student

About the Author

**Chapter 1: The Real Number System**

1.1 Fractions

1.2 The Real Numbers

1.3 Ordered Pairs and Graphs

1.4 Basic Rules of Algebra

Mid-Chapter Check Point

1.5 Addition of Real Numbers

1.6 Subtraction of Real Numbers

1.7 Multiplication and Division of Real Numbers

1.8 Exponents, Order of Operations, and Mathematical Models

Chapter 1 Group Project

Summary

Review Exercises

Chapter 1 Test

**Chapter 2: Linear Equations and Inequalities in One Variable**

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 Solving Linear Equations

2.4 Formulas and Percents

Mid-Chapter Check Point

2.5 An Introduction to Problem Solving

2.6 Problem Solving in Geometry

2.7 Solving Linear Inequalities

Chapter 2 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 2)

Chapter 2 Test

**Chapter**

**3: Linear Equations in Two Variables**

3.1 Graphing Equations in Two Variables

3.2 Graphing Linear Equations Using Intercepts

3.3 Slope

3.4 The Slope-Intercept Form of the Equations of a Line

Mid-Chapter Check Point

3.5 The Point-Slope Form of the Equation of a Line

Chapter 3 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 3)

Chapter 3 Test

**Chapter**

**4: Systems of Linear Equations**

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by the Substitution Method

4.3 Solving Systems of Linear Equations by the Addition Method

Mid-Chapter Check Point

4.4 Problem Solving Using Systems of Equations

4.5 Systems of Linear Equations in Three Variables

Chapter 4 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 4)

Chapter 4 Test

**Chapter**

**5: Exponents and Polynomials**

5.1 Adding and Subtracting Polynomials

5.2 Multiplying Polynomials

5.3 Special Products

5.4 Polynomials in Several Variables

Mid-Chapter Check Point

5.5 Dividing Polynomials

5.6 Long Division of Polynomials; Synthetic Division

5.7 Negative Exponents and Scientific Notation

Chapter 5 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 5)

Chapter 5 Test

**Chapter**

**6: Factoring Polynomials**

6.1 The Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials Whose Leading Coefficient is One

6.3 Factoring Trinomials Whose Leading Coefficient Is Not One

Mid-Chapter Check Point

6.4 Factoring Special Forms

6.5 A General Factoring Strategy

6.6 Solving Quadratic Equations by Factoring

Chapter 6 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 6)

Chapter 6 Test

**Chapter 7: Rational Expressions**

7.1 Radical Expressions and Their Simplification

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same Denominators

7.4 Adding and Subtracting Rational Expressions with Different Denominators

Mid-Chapter Check Point

7.5 Complex Rational Expressions

7.6 Solving Rational Equations

7.7 Applications Using Rational Equations and Proportions

7.8 Modeling Using Variation

Chapter 7 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 7)

Chapter 7 Test

**Mid-Textbook Check Point**

**Chapter 8: Basics of Functions**

8.1 Introduction to Functions

8.2 The Algebra of Functions

Mid-Chapter Check Point

8.3 Composite and Inverse Functions

Chapter 8 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 8)

Chapter 8 Test

**Chapter 9: Inequalities and Problem Solving**

9.1 Interval Notation and Business Applications Using Linear Inequalities

9.2 Compound Inequalities

9.3 Equations and Inequalities Involving Absolute Value

Mid-Chapter Check Point

9.4 Linear Inequalities in Two Variables

9.5 Linear Programming

Chapter 9 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 9)

Chapter 9 Test

**Chapter 10: Radicals, Radical Functions, and Rational Exponents**

10.1 Radical Expressions and Functions

10.2 Rational Expressions

10.3 Multiplying and Simplifying Radical Expressions

10.4 Adding, Subtracting, and Dividing Radical Expressions

Mid-Chapter Check Point

10.5 Multiplying with More Than One Term and Rationalizing Denominators

10.6 Radical Equalities

10.7 Complex Numbers

Chapter 10 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 10)

Chapter 10 Test

**Chapter 11: Quadratic Equations and Functions**

11.1 The Square Root Property and Completing the Square

11.2 The Quadratic Formula

11.3 Quadratic Functions and Their Graphs

Mid-Chapter Check Point

11.4 Equations Quadratic in Form

11.5 Polynomial and Rational Inequalities

Chapter 11 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 11)

Chapter 11 Test

**Chapter 12: Exponential and Logarithmic Functions**

12.1 Exponential Functions

12.2 Logarithmic Functions

12.3 Properties of Logarithms

Mid-Chapter Check Point

12.4 Exponential and Logarithmic Equations

12.5 Exponential Growth and Decay; Modeling Data

Chapter 12 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 12)

Chapter 12 Test

**Chapter 13: Conic Sections and Systems of Nonlinear Equations**

13.1 The Circle

13.2 The Ellipse

13.3 The Hyperbola

Mid-Chapter Check Point

13.4 The Parabola; Identifying Conic Sections

13.5 Systems of Nonlinear Equations in Two Variables

Chapter 13 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 13)

Chapter 13 Test

**Chapter 14 Sequences, Induction, and Probability**

14.1 Sequences and Summation Notation

14.2 Arithmetic Sequences

14.3 Geometric Sequences and Series

Mid-Chapter Check Points

14.4 The Binomial Theorem

14.5 Counting Principles, Permutations, and Combinations

14.6 Probability

Chapter 14 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 14)

Chapter 14 Test

Appendices

A: Matrix Solutions to Systems of Linear Equations

B: Determinants and Cramer’s Rule

C: Where Did That Come From? Selected Proofs

Answers to Selected Exercises

Graphing Answer Section

Applications Index

Subject Index

Photo Credits

## Preface

*Introductory and Intermediate Algebra for College Students* provides comprehensive, in-depth coverage of the topics required in a course combining the study of introductory and intermediate algebra. The primary goals of the book are to help students acquire a solid foundation in introductory and intermediate algebra, without the repetition of topics in two separate texts, and to show how algebra can model and solve authentic real-world problems.

A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:

- "I cannot follow the explanations."
- "The applications are not interesting."

I thought about both of these objections in writing every page of this book.

*"I can't follow the explanations."* For many of my students, textbook explanations are too compressed. The chapters in *Introductory and Intermediate Algebra for College Students* have been written to make them extremely accessible. Every section contains a range of simple, intermediate, and challenging examples. Voice balloons allow for specific annotations in examples, further clarifying procedures and concepts.

*"The applications are not interesting."* One of the things I enjoy most about teaching in a large urban community college is the diversity of who my students are and what interests them. Real-world data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all up-to-date real-world data to be interesting and intriguing to students. Byconnecting algebra to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.

### Key Pedagogical Features

*Introductory and Intermediate Algebra for College Students* is part of a series of four texts that include *Introductory Algebra for College Students,* Third Edition, *Intermediate Algebra for College Students,* Third Edition, and *Algebra for College Students,* Fourth Edition. The following features are found throughout the series.

*Chapter-Opening and Section-Opening Scenarios.*Every chapter*and every section*opens with a compelling image that supports a scenario presenting a unique application of algebra in students' lives outside the classroom:. Each scenario is revisited later in the chapter or section.*Section Objectives.*Learning objectives open every section. The objective are stated in the margin at their point of use.*Detailed Illustrative Examples.*Each illustrative example is titled, making; clear the purpose of the example. Examples are clearly written and provide students with detailed step-by-step solutions. No steps are omitted and each step is explained.*Check Point Examples.*Each worked example is followed by a similar matched problem for the student to work while reading the material. This actively involves the student in the learning process and gives students the opportunity to work with a concept as soon as they have learned it. Answers to all Check Points are given in the answer section.*Graphing.*Chapter 1 contains an introduction to graphing, a topic that is integrated throughout the book. Line, bar, circle, and rectangular coordinate graphs that use real data appear in nearly every section and exercise set. Many examples and exercises use graphs to explore relationships between data and to provide ways of visualizing a problem's solution.*Geometric Problem Solving.*Section 2.6 on problem solving in geometry teaches geometric concepts that are important to a student's understanding of algebra. There is frequent emphasis on problem solving in geometric situations, as well as on geometric models that allow students to visualize algebraic formulas.*Functions.*Functions are introduced in Chapter 8, with functions emphasized throughout the second half of the book.*Thorough, Yet Optional Technology.*Although the use of graphing utilities is optional, they are utilized in Using Technology boxes to enable students to visualize algebraic concepts. The use of graphing utilities is also reinforced in the technology exercises appearing in the exercise sets for those who want this option. With the book's early introduction to graphing, students can look at the calculator screens in the Using Technology boxes and gain an increased understanding of an example's solution even if they are not using a graphing utility in the course.*Enrichment Essays.*Enrichment essays provide historical, interdisciplinary, and otherwise interesting connections throughout the text.*Study Tips.*Study Tip boxes offer suggestions for problem solving, point out common student errors, and provide informal tips and suggestions. These invaluable hints appear in abundance throughout the book.*Discovery.*Discover for Yourself boxes, found throughout the text, encourage students to further explore algebraic concepts. These explorations are optional and their omission does not interfere with the continuity of the topic under consideration.*Exercise Sets.*An extensive collection of exercises is included in an exercise set at the end of each section. The text organizes exercises by level within six category types: Practice Exercises, Application Exercises, Writing in Mathematics, Technology Exercises, Critical Thinking Exercises, and Review Exercises. This format makes it easy to create well-rounded homework assignments. Writing exercises offer students the opportunity to write about every objective covered in each section, as well as to discuss, interpret, and give opinions about data. Each review exercise contains the section number and example number of a similar worked-out example.*Chapter Projects.*At the end of each chapter are collaborative activities that give students the opportunity to work cooperatively as they think and talk about mathematics. Many of these exercises should result in interesting group, discussions.*Chapter Review Grids.*Each chapter contains a review chart that summarizes the definitions and concepts in every section of the chapter. Examples that illustrate these key concepts are also included in the chart. Like the summary grid, review exercises are organized by each section of the chapter.*End-of-Chapter Materials.*The review grids provide a focused summary and illustrative examples for each section in the chapter. A comprehensive collection of review exercises for each of the chapter's sections follows the review grid. This is followed by a chapter test. Beginning with Chapter 2, each chapter concludes with a comprehensive collection of cumulative review exercises.*A Review of Introductory Algebra.*Appendix A, entitled*Are You Prepared for Intermediate Algebra?*, provides students with a fast way to review introductory algebra topics before starting the intermediate algebra portion of the book.*Supplements Package.*This text is supported by a wealth of supplements designed for added effectiveness and efficiency. These items are described on pages xiii through xv.

## Supplements for the Instructor

### Printed Resources

*Annotated Instructor's Edition (0-13-032843-X)*

• Answers to exercises on the same text page or in Graphing Answer Section.

• Graphing Answer Section contains answers to exercises requiring graphical solutions.

*Instructor's Solutions Manual (0-13-034328-5)*

• Step-by-step solutions for every even-numbered section exercise.

• Step-by-step solutions for every (even and odd) Check Point exercise, Chapter Review exercise, Chapter Test and Cumulative Review exercise.

*Instructor's Resource Manual (0-13-034319-6)*

• Notes to the Instructor

• Eight Chapter Tests per chapter (5 free response, 3 multiple choice)

• Eight Final Exams ( 4 free response, 4 multiple choice)

• Twenty additional exercises per section for added test exercises or worksheets.

• Answers to all items

### Media Resources

*TestGen-EQ with QuizMaster-EQ (CD-ROM for IBM and Macintosh 0-13-034324-2)*

• Algorithmically driven, text specific testing program.

• Networkable for administering tests and capturing grades on-line.

• Edit or add your own questions to create a nearly unlimited number of tests and worksheets.

• Use the new "Function Plotter" to create graphs.

• Tests can be easily exported to HTML so they can be posted to the Web.

*Computerized Tutorial Software Course Management System*

MathPro Explorer 4.0

• Network version for IBM and Macintosh

• Enables instructors to create either customized or algorithmically generated practice quizzes from any section of a chapter.

• Includes an e-mail function for networked users, enabling instructors toy send a message to a specific student or to an entire group.

• Network based reports and summaries for a class or student and for cumulative or selected scores are available.

*MathPro 5*

• Anytime. Anywhere.

• Online tutorial with enhanced class and student management features.

• Integration of TestGen-EQ allows for testing to operate within the tutorial environment.

• Course management tracking of both tutorial and testing activity.

*Online Options for Distance Learning*

WebCT/Blackboard/CourseCompass

• Prentice Hall offers three different on-line interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text.

## Supplements for the Student

### Printed Resource

*Student Solutions Manual (0-13-034327-7)*

• Step-by-step solutions for every odd-numbered section exercise.

• Step-by-step solutions for every (even and odd) Check Point exercise, Chapter Review exercise, Chapter Test and Cumulative Review exercise.

*How to Study Mathematics*

• Have your instructor contact the local Prentice Hall sales representative.

*Math on the Internet: A Student's Guide*

• Have your instructor contact the local Prentice Hall sales representative.

### Media Resources

*Computerized Tutorial Software*

MathPro Explorer 4.0

• Keyed to each section of the text for text-specific tutorial exercises and instruction.

• Warm-up exercises and graded Practice Problems.

• Video clips show a problem being explained and worked out on the board.

• Algorithmically generated exercises. On-line help, glossary and summary of scores.

MathPro 5-Anytime. Anywhere.

• Enhanced, Internet-based version of Prentice Hall's popular tutorial software.

*Lecture Videos*

• Keyed to each section of the text.

*Digitized Lecture Videos on CD.*

• Have your instructor contact the local Prentice Hall sales representative.

*Prentice Hall Tutoring Center*

• Provides one-on-one tutorial assistance by phone, e-mail, or fax.

*Companion Website*

• Offers Warm-ups, Real World Activities and Chapter Quizzes.

• E-mail results to your instructor.

• Destination links provide additional opportunities to explore other related sites.