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by Richard N. Aufmann, Vernon C. Barker and Joanne S. Lockwood

Edition: 3RD 04Copyright: 2004

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

Richard N. Aufmann, Vernon C. Barker and Joanne S. Lockwood

Edition: 3RD 04
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The Third Edition of Algebra: Introductory and Intermediate provides mathematically sound and comprehensive coverage of the topics considered essential in a combined introductory and intermediate algebra course. The text also includes new prep tests, updated applications, and a new design. Furthermore, the Instructor's Annotated Edition features a comprehensive selection of new instructor support material. The class-tested Aufmann Interactive Method, incorporated throughout the text, ensures that students interact with the math and master the concepts presented. This model is especially supportive for distance-learning and self-paced laboratory situations.

- New! The revised IAE, rich with new instructor support materials, features reduced student pages with support material in the margins. (Answers to exercises and transparency icons appear on the reduced student page.) Features include Instructor Notes; tips for introducing new or recycled vocabulary, symbols, formulas, rules, properties or equations; Discuss the Concepts prompts; Concept Check questions; Optional Student Activities; In-Class Examples to present with every objective; Suggested Assignments; Quick Quiz; and Answers to selected Writing Exercises, Focus on Problem Solving activities, and Projects and Group Activities.
- New! AIM for Success, a special preface for students, guides them in how to be successful using the text and the Aufmann Interactive Method (AIM). Suggestions for using the Preface as a lesson are featured in the Instructor's Resource Manual.
- New! Prep Tests at the beginning of each chapter highlight the prerequisite skills to be used in the chapter. The answers to these questions can be found in the Answer Appendix along with a reference to the objective from which the question was taken. Students who miss a question are encouraged to review the objective. The Go Figure problem that follows the Prep Test is a puzzle problem for interested students.
- The Aufmann Interactive Method (AIM), which accompanies every objective, features one or more sets of matched-pair examples that encourage students to interact with the text. The first example in each set is completely worked out; the second example, You Try It, prompts students to practice concepts as they are presented in the text. Complete worked-out solutions to these examples appear in an appendix at the end of the book, offering students immediate feedback, reinforcing the concept, helping to identify problem areas, and preventing frustration.
- An integrated learning system organized by objectives provides the main framework for the text. Each chapter begins with a list of learning objectives, which are woven throughout the text, in Exercises, Chapter Tests, and Cumulative Reviews, as well as through the print and multimedia ancillaries. The result is a seamless, easy-to-follow learning system.
- An extensive collection of contemporary application problems draws from real source data to show students the value of mathematics as a real-life tool. Chapter openers have been updated with new photos and captions illustrating and referencing a specific application from the chapter.
- Chapter-ending feature Focus on Problem Solving introduces students to various problem-solving strategies. Students are encouraged to write their own strategies and draw diagrams to find solutions. The use of some open-ended problems results in more than one right answer and strengthens problem-solving skills.
- Exercises following the presentation of a new operation require that students make a connection between a phrase and a mathematical process. To reinforce this skill, the authors present a verbal/mathematical connection each time they introduce a new topic or operation.
- Project and Group Activities, often at the end of each chapter, offer ideas for cooperative learning or extra credit projects in such areas as the use of calculators, collecting data from the Internet, data analysis, and extended applications.

**1. Real Numbers and Variable Expressions**

Section 1.1 Integers

Section 1.2 Rational and Irrational Numbers

Section 1.3 The Order of Operations Agreement

Section 1.4 Variable Expressions

Section 1.5 Sets

**2. First-Degree Equations and Inequalities**

Section 2.1 Introduction to Equations

Section 2.2 General Equations

Section 2.3 Mixture, Investment, and Motion Problems

Section 2.4 Inequalities in One Variable

Section 2.5 Absolute Value Equations and Inequalities

**3. Geometry**

Section 3.1 Introduction to Geometry

Section 3.2 Plane Geometric Figures

Section 3.3 Solids

**4. Linear Equations and Inequalities in Two Variables**

Section 4.1 The Rectangular Coordinate System

Section 4.2 Introduction to Functions

Section 4.3 Linear Equations in Two Variables

Section 4.4 Slopes of Straight Lines

Section 4.5 Finding Equations of Lines

Section 4.6 Parallel and Perpendicular Lines

Section 4.7 Graphing Linear Inequalities

**5. Systems of Linear Equations and Inequalities**

Section 5.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method

Section 5.2 Solving Systems of Linear Equations by the Addition Method

Section 5.3 Solving Systems of Equations by Using Determinants

Section 5.4 Application Problems in Two Variables

Section 5.5 Solving Systems of Linear Inequalities

**6. Polynomials**

Section 6.1 Exponential Expressions

Section 6.2 Introduction to Polynomials

Section 6.3 Multiplication of Polynomials

Section 6.4 Division of Polynomials

**7. Factoring**

Section 7.1 Common Factors

Section 7.2 Factoring Polynomials of the Form x2 + bx + c

Section 7.3 Factoring Polynomials of the Form ax2 + bx + c

Section 7.4 Special Factoring

Section 7.5 Solving Equations

**8. Rational Expressions**

Section 8.1 Multiplication and Division of Rational Expressions

Section 8.2 Addition and Subtraction of Rational Expressions

Section 8.3 Complex Fractions

Section 8.4 Rational Equations

Section 8.5 Literal Equations

Section 8.6 Work and Uniform Motion Problems

Section 8.7 Variation

**9. Rational Exponents and Radicals**

Section 9.1 Rational Exponents and Radical Expressions

Section 9.2 Operations on Radical Expressions

Section 9.3 Complex Numbers

Section 9.4 Equations Containing Radical Expressions

**10. Quadratic Equations**

Section 10.1 Solving Quadratic Equations by Factoring or by Taking Square Roots

Section 10.2 Solving Quadratic Equations by Completing the Square

Section 10.3 Solving Quadratic Equations by Using the Quadratic Formula

Section 10.4 Solving Equations That Are Reducible to Quadratic Equations

Section 10.5 Applications of Quadratic Equations

Section 10.6 Quadratic Inequalities and Rational Inequalities

**11. Functions and Relations**

Section 11.1 Linear Functions

Section 11.2 Quadratic Functions

Section 11.3 Graphs of Functions

Section 11.4 Algebra of Functions

Section 11.5 One-to-One and Inverse Functions

Section 11.6 Conic Sections

**12. Exponential and Logarithmic Functions**

Section 12.1 Exponential Functions

Section 12.2 Introduction to Logarithms

Section 12.3 Graphs of Logarithmic Functions

Section 12.4 Solving Exponential and Logarithmic Equations

Section 12.5 Applications of Exponential and Logarithmic Functions

- Final Exam
- Review of Introductory Algebra Topics
- Section R.1 Variable Expressions
- Section R.2 Equations and Inequalities
- Section R.3 Linear Equations in Two Variables
- Section R.4 Polynomials
- Appendix: Calculator Guide for the TI-83 and TI83Plus; Proofs and Tables
- Solutions to You Try It
- Answers to Selected Exercises

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Summary

The Third Edition of Algebra: Introductory and Intermediate provides mathematically sound and comprehensive coverage of the topics considered essential in a combined introductory and intermediate algebra course. The text also includes new prep tests, updated applications, and a new design. Furthermore, the Instructor's Annotated Edition features a comprehensive selection of new instructor support material. The class-tested Aufmann Interactive Method, incorporated throughout the text, ensures that students interact with the math and master the concepts presented. This model is especially supportive for distance-learning and self-paced laboratory situations.

- New! The revised IAE, rich with new instructor support materials, features reduced student pages with support material in the margins. (Answers to exercises and transparency icons appear on the reduced student page.) Features include Instructor Notes; tips for introducing new or recycled vocabulary, symbols, formulas, rules, properties or equations; Discuss the Concepts prompts; Concept Check questions; Optional Student Activities; In-Class Examples to present with every objective; Suggested Assignments; Quick Quiz; and Answers to selected Writing Exercises, Focus on Problem Solving activities, and Projects and Group Activities.
- New! AIM for Success, a special preface for students, guides them in how to be successful using the text and the Aufmann Interactive Method (AIM). Suggestions for using the Preface as a lesson are featured in the Instructor's Resource Manual.
- New! Prep Tests at the beginning of each chapter highlight the prerequisite skills to be used in the chapter. The answers to these questions can be found in the Answer Appendix along with a reference to the objective from which the question was taken. Students who miss a question are encouraged to review the objective. The Go Figure problem that follows the Prep Test is a puzzle problem for interested students.
- The Aufmann Interactive Method (AIM), which accompanies every objective, features one or more sets of matched-pair examples that encourage students to interact with the text. The first example in each set is completely worked out; the second example, You Try It, prompts students to practice concepts as they are presented in the text. Complete worked-out solutions to these examples appear in an appendix at the end of the book, offering students immediate feedback, reinforcing the concept, helping to identify problem areas, and preventing frustration.
- An integrated learning system organized by objectives provides the main framework for the text. Each chapter begins with a list of learning objectives, which are woven throughout the text, in Exercises, Chapter Tests, and Cumulative Reviews, as well as through the print and multimedia ancillaries. The result is a seamless, easy-to-follow learning system.
- An extensive collection of contemporary application problems draws from real source data to show students the value of mathematics as a real-life tool. Chapter openers have been updated with new photos and captions illustrating and referencing a specific application from the chapter.
- Chapter-ending feature Focus on Problem Solving introduces students to various problem-solving strategies. Students are encouraged to write their own strategies and draw diagrams to find solutions. The use of some open-ended problems results in more than one right answer and strengthens problem-solving skills.
- Exercises following the presentation of a new operation require that students make a connection between a phrase and a mathematical process. To reinforce this skill, the authors present a verbal/mathematical connection each time they introduce a new topic or operation.
- Project and Group Activities, often at the end of each chapter, offer ideas for cooperative learning or extra credit projects in such areas as the use of calculators, collecting data from the Internet, data analysis, and extended applications.

Table of Contents

**1. Real Numbers and Variable Expressions**

Section 1.1 Integers

Section 1.2 Rational and Irrational Numbers

Section 1.3 The Order of Operations Agreement

Section 1.4 Variable Expressions

Section 1.5 Sets

**2. First-Degree Equations and Inequalities**

Section 2.1 Introduction to Equations

Section 2.2 General Equations

Section 2.3 Mixture, Investment, and Motion Problems

Section 2.4 Inequalities in One Variable

Section 2.5 Absolute Value Equations and Inequalities

**3. Geometry**

Section 3.1 Introduction to Geometry

Section 3.2 Plane Geometric Figures

Section 3.3 Solids

**4. Linear Equations and Inequalities in Two Variables**

Section 4.1 The Rectangular Coordinate System

Section 4.2 Introduction to Functions

Section 4.3 Linear Equations in Two Variables

Section 4.4 Slopes of Straight Lines

Section 4.5 Finding Equations of Lines

Section 4.6 Parallel and Perpendicular Lines

Section 4.7 Graphing Linear Inequalities

**5. Systems of Linear Equations and Inequalities**

Section 5.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method

Section 5.2 Solving Systems of Linear Equations by the Addition Method

Section 5.3 Solving Systems of Equations by Using Determinants

Section 5.4 Application Problems in Two Variables

Section 5.5 Solving Systems of Linear Inequalities

**6. Polynomials**

Section 6.1 Exponential Expressions

Section 6.2 Introduction to Polynomials

Section 6.3 Multiplication of Polynomials

Section 6.4 Division of Polynomials

**7. Factoring**

Section 7.1 Common Factors

Section 7.2 Factoring Polynomials of the Form x2 + bx + c

Section 7.3 Factoring Polynomials of the Form ax2 + bx + c

Section 7.4 Special Factoring

Section 7.5 Solving Equations

**8. Rational Expressions**

Section 8.1 Multiplication and Division of Rational Expressions

Section 8.2 Addition and Subtraction of Rational Expressions

Section 8.3 Complex Fractions

Section 8.4 Rational Equations

Section 8.5 Literal Equations

Section 8.6 Work and Uniform Motion Problems

Section 8.7 Variation

**9. Rational Exponents and Radicals**

Section 9.1 Rational Exponents and Radical Expressions

Section 9.2 Operations on Radical Expressions

Section 9.3 Complex Numbers

Section 9.4 Equations Containing Radical Expressions

**10. Quadratic Equations**

Section 10.1 Solving Quadratic Equations by Factoring or by Taking Square Roots

Section 10.2 Solving Quadratic Equations by Completing the Square

Section 10.3 Solving Quadratic Equations by Using the Quadratic Formula

Section 10.4 Solving Equations That Are Reducible to Quadratic Equations

Section 10.5 Applications of Quadratic Equations

Section 10.6 Quadratic Inequalities and Rational Inequalities

**11. Functions and Relations**

Section 11.1 Linear Functions

Section 11.2 Quadratic Functions

Section 11.3 Graphs of Functions

Section 11.4 Algebra of Functions

Section 11.5 One-to-One and Inverse Functions

Section 11.6 Conic Sections

**12. Exponential and Logarithmic Functions**

Section 12.1 Exponential Functions

Section 12.2 Introduction to Logarithms

Section 12.3 Graphs of Logarithmic Functions

Section 12.4 Solving Exponential and Logarithmic Equations

Section 12.5 Applications of Exponential and Logarithmic Functions

- Final Exam
- Review of Introductory Algebra Topics
- Section R.1 Variable Expressions
- Section R.2 Equations and Inequalities
- Section R.3 Linear Equations in Two Variables
- Section R.4 Polynomials
- Appendix: Calculator Guide for the TI-83 and TI83Plus; Proofs and Tables
- Solutions to You Try It
- Answers to Selected Exercises

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

Published: 2004

International: No

The Third Edition of Algebra: Introductory and Intermediate provides mathematically sound and comprehensive coverage of the topics considered essential in a combined introductory and intermediate algebra course. The text also includes new prep tests, updated applications, and a new design. Furthermore, the Instructor's Annotated Edition features a comprehensive selection of new instructor support material. The class-tested Aufmann Interactive Method, incorporated throughout the text, ensures that students interact with the math and master the concepts presented. This model is especially supportive for distance-learning and self-paced laboratory situations.

- New! The revised IAE, rich with new instructor support materials, features reduced student pages with support material in the margins. (Answers to exercises and transparency icons appear on the reduced student page.) Features include Instructor Notes; tips for introducing new or recycled vocabulary, symbols, formulas, rules, properties or equations; Discuss the Concepts prompts; Concept Check questions; Optional Student Activities; In-Class Examples to present with every objective; Suggested Assignments; Quick Quiz; and Answers to selected Writing Exercises, Focus on Problem Solving activities, and Projects and Group Activities.
- New! AIM for Success, a special preface for students, guides them in how to be successful using the text and the Aufmann Interactive Method (AIM). Suggestions for using the Preface as a lesson are featured in the Instructor's Resource Manual.
- New! Prep Tests at the beginning of each chapter highlight the prerequisite skills to be used in the chapter. The answers to these questions can be found in the Answer Appendix along with a reference to the objective from which the question was taken. Students who miss a question are encouraged to review the objective. The Go Figure problem that follows the Prep Test is a puzzle problem for interested students.
- The Aufmann Interactive Method (AIM), which accompanies every objective, features one or more sets of matched-pair examples that encourage students to interact with the text. The first example in each set is completely worked out; the second example, You Try It, prompts students to practice concepts as they are presented in the text. Complete worked-out solutions to these examples appear in an appendix at the end of the book, offering students immediate feedback, reinforcing the concept, helping to identify problem areas, and preventing frustration.
- An integrated learning system organized by objectives provides the main framework for the text. Each chapter begins with a list of learning objectives, which are woven throughout the text, in Exercises, Chapter Tests, and Cumulative Reviews, as well as through the print and multimedia ancillaries. The result is a seamless, easy-to-follow learning system.
- An extensive collection of contemporary application problems draws from real source data to show students the value of mathematics as a real-life tool. Chapter openers have been updated with new photos and captions illustrating and referencing a specific application from the chapter.
- Chapter-ending feature Focus on Problem Solving introduces students to various problem-solving strategies. Students are encouraged to write their own strategies and draw diagrams to find solutions. The use of some open-ended problems results in more than one right answer and strengthens problem-solving skills.
- Exercises following the presentation of a new operation require that students make a connection between a phrase and a mathematical process. To reinforce this skill, the authors present a verbal/mathematical connection each time they introduce a new topic or operation.
- Project and Group Activities, often at the end of each chapter, offer ideas for cooperative learning or extra credit projects in such areas as the use of calculators, collecting data from the Internet, data analysis, and extended applications.

**1. Real Numbers and Variable Expressions**

Section 1.1 Integers

Section 1.2 Rational and Irrational Numbers

Section 1.3 The Order of Operations Agreement

Section 1.4 Variable Expressions

Section 1.5 Sets

**2. First-Degree Equations and Inequalities**

Section 2.1 Introduction to Equations

Section 2.2 General Equations

Section 2.3 Mixture, Investment, and Motion Problems

Section 2.4 Inequalities in One Variable

Section 2.5 Absolute Value Equations and Inequalities

**3. Geometry**

Section 3.1 Introduction to Geometry

Section 3.2 Plane Geometric Figures

Section 3.3 Solids

**4. Linear Equations and Inequalities in Two Variables**

Section 4.1 The Rectangular Coordinate System

Section 4.2 Introduction to Functions

Section 4.3 Linear Equations in Two Variables

Section 4.4 Slopes of Straight Lines

Section 4.5 Finding Equations of Lines

Section 4.6 Parallel and Perpendicular Lines

Section 4.7 Graphing Linear Inequalities

**5. Systems of Linear Equations and Inequalities**

Section 5.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method

Section 5.2 Solving Systems of Linear Equations by the Addition Method

Section 5.3 Solving Systems of Equations by Using Determinants

Section 5.4 Application Problems in Two Variables

Section 5.5 Solving Systems of Linear Inequalities

**6. Polynomials**

Section 6.1 Exponential Expressions

Section 6.2 Introduction to Polynomials

Section 6.3 Multiplication of Polynomials

Section 6.4 Division of Polynomials

**7. Factoring**

Section 7.1 Common Factors

Section 7.2 Factoring Polynomials of the Form x2 + bx + c

Section 7.3 Factoring Polynomials of the Form ax2 + bx + c

Section 7.4 Special Factoring

Section 7.5 Solving Equations

**8. Rational Expressions**

Section 8.1 Multiplication and Division of Rational Expressions

Section 8.2 Addition and Subtraction of Rational Expressions

Section 8.3 Complex Fractions

Section 8.4 Rational Equations

Section 8.5 Literal Equations

Section 8.6 Work and Uniform Motion Problems

Section 8.7 Variation

**9. Rational Exponents and Radicals**

Section 9.1 Rational Exponents and Radical Expressions

Section 9.2 Operations on Radical Expressions

Section 9.3 Complex Numbers

Section 9.4 Equations Containing Radical Expressions

**10. Quadratic Equations**

Section 10.1 Solving Quadratic Equations by Factoring or by Taking Square Roots

Section 10.2 Solving Quadratic Equations by Completing the Square

Section 10.3 Solving Quadratic Equations by Using the Quadratic Formula

Section 10.4 Solving Equations That Are Reducible to Quadratic Equations

Section 10.5 Applications of Quadratic Equations

Section 10.6 Quadratic Inequalities and Rational Inequalities

**11. Functions and Relations**

Section 11.1 Linear Functions

Section 11.2 Quadratic Functions

Section 11.3 Graphs of Functions

Section 11.4 Algebra of Functions

Section 11.5 One-to-One and Inverse Functions

Section 11.6 Conic Sections

**12. Exponential and Logarithmic Functions**

Section 12.1 Exponential Functions

Section 12.2 Introduction to Logarithms

Section 12.3 Graphs of Logarithmic Functions

Section 12.4 Solving Exponential and Logarithmic Equations

Section 12.5 Applications of Exponential and Logarithmic Functions

- Final Exam
- Review of Introductory Algebra Topics
- Section R.1 Variable Expressions
- Section R.2 Equations and Inequalities
- Section R.3 Linear Equations in Two Variables
- Section R.4 Polynomials
- Appendix: Calculator Guide for the TI-83 and TI83Plus; Proofs and Tables
- Solutions to You Try It
- Answers to Selected Exercises