# Algebra for College Students, 3rd edition

Published by Pearson (March 7, 2007) © 2008

**Allen R. Angel**Monroe Community College

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Angel's texts are a proven favorite among students and instructors alike. The Angel texts consistently receive praise for their readability - short, clear sentences are used to ensure the text is readable even for those with weak reading skills- and for the abundance of detailed, worked-out examples... more than any other text! In this revised, 3rd edition of *A lgebra *

*for College Students*, Angel continues to focus on the needs of the students taking this class and the instructors teaching them.

Angel's texts are a proven favorite among students and instructors alike. The Angel texts consistently receive praise for their readability - short, clear sentences are used to ensure the text is readable even for those with weak reading skills- and for the abundance of detailed, worked-out examples... more than any other text! In this revised, 3rdedition of *Algebra for College Students*, Angel continues to focus on the needs of the students taking this class and the instructors teaching them.

__INSTRUCTOR: __

**HOW DO YOU USE EXAMPLES? HOW DO YOUR STUDENTS?**

Angel hasmore examples than any other textbook!Anis now provided in the margin of your Annotated Instructor's Edition, next toInstructor Exampleeachstudent example. Your students really benefit from theAngel examplesbecause they’ve been worked-out, step-by-step, in great detail. With Angel, you can be sure that you will always have a relevant Angel Example to use in class, and your students will always have an example that matches the exercise they are working!

**WHAT DO YOU ASSIGN FOR HOMEWORK?**

Angel has more exercises than any other textbook!So you will always have plenty of exercises available to use in class and to assign students to work outside of class. Also notice that following every Angel example is a note to “Now Try” an odd-numbered end-of-section exercise. You could have your students work the Now Try exercise in class for immediate practice and reinforcement. The “Now Try” note and the exercise number are both in green. This is a cue to your students to know which Now Try exercises go with which examples. If you have them work the Now Try exercises for homework, they easily refer to an appropriate example when they need help.

**HOW MANY OF YOUR STUDENTS STRUGGLE JUST TO PASS THIS COURSE?**

The

MyMathLabprogram can help your students pass this course the first time! Use MyMathLab to assign, collect and grade homework, quizzes and/or tests. With MyMathLab — www.mymathlab.com — your students have access to unlimited practice, immediate feedback, examples, videos and a personalized study plan, all designed to help them pass this course on the first try! MyMathLab givesyouchoice of content as it’s currently available with more than 200 Pearson titles! View the success rates of MyMathLab at various schools inhttp://www.mymathlab.com/success_report.htmlMaking the Grade: A Report on the Success of MyMathLab in Higher Education Math Instruction (2005):

**WHEN ARE YOUR STUDENTS STUDYING FOR THEIR TESTS?**

Many students struggle to balance work, family and school commitments and that means many are studying late the night before their test when there is no one around to help them. Angel wants to help students during this time of need. Angel concludes every chapter with a practice test. Encourage your students to complete this

Chapter Testas practice and then direct them to the back of their text where they will find theChapter Test Prep Video CD. If your students get stuck on any of the problems from the chapter test, they can go to the Chapter Test Prep Video CD to view video of an Instructor working out the solution(s). It’s like having a tutor on-demand!Note:The Instructor’s Resource Manual includes several forms of each chapter test, so you have plenty for optional and required work.

**ARE YOUR STUDENT EASILY FRUSTRATED WHEN LEARNING MATH?**

Learning math is frustrating for many students, so Angel takes the time to offer your students encouragement and support when they are likely to need it most. Look for his “

Avoiding Common Errors”boxesthroughout the text as they point out some of the common mistakes students make, explain the error, and show the correct method for working the problem. See also Angel’s “Helpful Hints” and “Helpful Hint — Study Tips” boxes as they offer suggestions to enhance their math skills and study skills.

**HOW DO YOUR STUDENTS STUDY? WHAT DO THEY STUDY?**

Angel has taken extra steps to help your students study more efficiently and effectively. Encourage your students to read

Section 1.1of the text to find very practical advice on how to study better. You can easily create a Study Skills assignment using the exercises at the end of Section 1.1.See also how your students can use the

Newly EnhancedChapter Summariesthat conclude every chapter. They are designed to help students understand what material they need to study. The mathematical concept is highlighted in the left-hand column, and an example of the concept is then shown in the right-hand column.

**DO YOU ASSIGN PRACTICE TESTS?**

Angel offers 3 different types of practice tests that you can assign for optional or required work. There is a practice test found

and a one found at themid-waythrough each chapter. The answers to both tests are provided in the back of the text. Next to the answer, your students will find a reference to the section in the text where the concept is covered, so they’ll know exactly where to go to review the appropriate concepts! And beginning with Chapter 2, Angel also provides aendof every chapterCumulative Review Testthat you can assign to test your students’ knowledge of material from the beginning of the book to the end of that chapter.Note:The Instructor’s Resource Manual includes several forms of each chapter test, so you have plenty for optional and required work.

**HOW OFTEN DO YOUR STUDENTS GET "STUCK" WHEN TRYING TO SOLVE MATH PROBLEM?**

Angel can help you help your students learn how to solve problems with confidence! Early in the text your students are introduced to Angel’s

Five-Step Problem-Solving Procedurewhich is then incorporated throughout the text in appropriate examples.

__STUDENT: __

**HOW DO YOU USE YOUR MATH TEXTBOOK?**

If you answered “I use the examples” then Angel is the math text for you.

Angel hasmore examples than any other textbook! The Angel examples have been worked out step-by-step, in great detail so you will always have an example that matches the exercise you are working.Following every example you will see a note to “

Now Try” an odd-numbered exercise at the end of the section. The “Now Try” exercise number is in green and is your cue to know which Now Try exercises go with which examples. So you can practice and easily refer to the right example when you need help.

**DO YOU WANT TO PASS THIS COURSE?**

MyMathLabis a program that can help you pass this course the first time. With MyMathLab — www.mymathlab.com — you have access to unlimited practice, immediate feedback, examples, practice tests, videos and a personalized study plan, all designed to help you pass this course now! It’s like having a tutor available to you around the clock!Please talk with your instructor if MyMathLab wasn’t available with your textbook at time of purchase.

**WHEN DO YOU STUDY FOR YOUR QUIZZES AND TESTS?**

If you answered “the night before the quiz or test” then you are not alone. Angel wants you to study more effectively, regardless of when you do it, so that you can get the best results possible. Before your quiz or test, be sure to complete the practice test found

and the practice test at themid-waythrough the chapter. The answers to both tests are provided in the back of the text. Next to the answer you will find a reference to the section in the text where the concept is covered, so you’ll know exactly where to go to review the concepts you didn’t get right!endof the chapterWhen you take the end-of-chapter practice tests you also get extra help with video solutions! In the back of your text you will find the

Chapter Test Prep Video CD. When you are studying for your test, even if it’s late the night before, and you get stuck on any of the problems go to the CD to see a video of an Instructor working out the solution(s). It’s like having a tutor on-demand!

**WANT TO KNOW WHAT YOU SHOULD STUDY?**

If you are like many other students, you are struggling to balance the demands of school, work and family. Angel understands this and has taken extra steps to help you learn how to study more efficiently and effectively. Read

Section 1.1of the text to find very practical advice on how to study better. And use the detailedChapter Summarythat concludes every chapter to help you organize the material you need to study. The key concepts are highlighted in the left-hand column, and an example of those concepts is shown in the right-hand column. This design will make it easy for you to review the important concepts covered within the chapter.

**DO YOU FIND YOURSELF EASILY FRUSTRATED WITH MATH?**

Angel understands that learning math can be frustrating, so he takes the time to offer you encouragement and support when you’ll need it most. Look for his “

Avoiding Common Errors”boxesthroughout the text as they point out some of the common mistakes people make, explain the error, and show you the correct method for working the problem. See also Angel’s “Helpful Hints” and “Helpful Hint — Study Tips” as they offer suggestions that will enhance both your math skills and your study skills.

**HOW OFTEN DO YOU GET "STUCK" WHEN TRYING TO SOLVE A MATH PROBLEM?**

Angel will help you learn to solve problems with confidence! Early in the text you’ll be introduced to his

Five-Step Problem-Solving Procedure.See how it isincorporated throughout the text in appropriate examples and follow the 5-Step Problem Solving Procedure as you solve equations on your own.

In this revised, 3rd edition of *Algebra for College Students*, Angel remains committed to making this a text that students can read and truly understand. Here’s how Angel accomplishes this with the new edition:

ENHANCED!Angel is frequently praised for thereadabilityof his texts. He is mindful to use short, clear sentences to ensure the text is readable for even those students with the weakest reading skills.In this 3rd edition, the design of the textbook was carefully reviewed to enhance its clarity and readability.The basic colors in the textbook have been softened and art/photos have been added where appropriate to aid comprehension and peak interest in the material being presented.

ENHANCED!Students and Instructors love Angel’sExamples!Not only are the examples worked-out, step-by-step, in great detail but there are more than any other textbook!This 3rd edition now guaranteesAdditionally, aneveryexercise has a corresponding example andeveryexample has a correspondingNow Tryexercise.is now provided in the margin of the Annotated Instructor's Edition, next toInstructor Exampleeachstudent example. This 7th edition ensures Instructors will always have a relevant Angel Example to use in class and students will always have a corresponding example for the exercise they are working.

ENHANCED!Instructors love Angel'sExercises!In this 3rd edition, special attention was made to ensure every exercise set provides a gradual, yet continuous increase in difficulty-level.Application exercises were reviewed for relevancy and interest to today's students. Also, variables other thanxandyare now used more frequently in the examples and exercises. You can have confidence in Angel's exercise sets - plenty of exercises available to use in class and to assign to your students to work outside of class.

NEW!Many students struggle just to pass this course and that's whyMyMathLab is being offered with this 3rd edition!MyMathLab can help you help your students pass this course the first time. 1600 schools presently use MyMathLab to assign, collect and grade homework, quizzes and/or tests. With MyMathLab - www.mymathlab.com - your students have access to unlimited practice, immediate feedback, examples, videos and a personalized study plan, all designed to help them them pass this course on the first try! MyMathLab gives Instructors choice of content as it's currently available with more than 200 Pearson texts! View the success rates of MyMathLab at various schools inhttp://www.mymathlab.com/success_report.html.Making the Grade: A Report on the Success of MyMathLab in Higher Education Math Instruction (2005):

NEW!Many students are struggling to balance work, family and school commitments. This means that many are studying for their tests late the night before when there is no one around to help them. Angel wants to help students during this time of need!In this revised, 3rd edition, students will benefit from theEncourage your students to complete the end-of-chapter practice test in their text. If they get stuck on any of the problems from the chapter test, even if it is late the night before, they can go to theChapter Test Prep Video CDavailable in the back of their textbook.Chapter Test Prep Video CDto view video of an Instructor working out the solution(s). For the student it's like having a tutor on-demand!

ENHANCED!Many students struggle with what to study and how to study.In this 3rd edition, Angel provides new ways to improve on what your students study and how.Thehave been rewritten to include the important facts and concepts covered in the chapter. They've also been redesigned in a concise, clear, column-format. The left hand column highlights the fact or concept and the right hand column offers an example of that fact or concept.Chapter Summaries

NEW!Angel has also included. Use theseMid-ChapterTestsin every chapter of this 3rd editionMid-Chapter Teststo see how well your students are understanding the topcis covered in the first part of the chapter. The answers to theMid-Chapter Testscan be found in the back of the text. Next to the answer, your students will find a reference to the section in the text where the concept is covered, so they'll know exactly where to go to review!Note:The Instructor's Resource Manual includes several test forms of each chapter test, so you have plenty available for optional and required work.

ENHANCED!Learning math is very frustrating for many students, so Angel takes the time to offer your students encouragement and support when they are likely to need it the most.That's why Angel is providing moreAvoiding Common Errorsboxes andmoreTheHelpful Hintsin this 3rd edition!Avoiding Common Errorsboxes point out some of the common mistakes that students make, explain the error, and show the correct method for working the problem.Helpful HintsandHelpful Hints-Study Tipsoffer suggestions to enhance students math skills and study skills throughout the course.

REVISED! In this 3rd edition,TheGoals of This Chapterhave replacedA Look Ahead.Goals of This Chapterappear at the beginning of each chapter to give students an overview of what they will see and are expected to learn in that chapter.

UPDATED! In this 3rd edition, theUsing Your Graphing Calculatorboxes now show keystrokes for the TI-84 Plus calculator. Note:The same keystrokes are appropriate for the TI-83 Plus calculator.

REMOVED - TheMathematics in Actionfeature has been removed to conserve space.

**Note: Each chapter concludes with Chapter Summary, Chapter Review Exercises, and Chapter Practice Test and after Chapter 1, Cumulative Review Test.**

**Preface**

**To the Student**

**CHAPTER 1: Basic Concepts**

1.1 Study Skills for Success in Mathematics, and Using a Calculator

1.2 Sets and Other Basic Concepts

1.3 Properties of and Operations with Real Numbers

1.4 Order of Operations

*Mid-Chapter Test: Sections 1.1—1.4*

1.5 Exponents

1.6 Scientific Notation

**CHAPTER 2: Equations and Inequalities **

2.1 Solving Linear Equations

2.2 Problem Solving and Using Formulas

2.3 Applications of Algebra

*Mid-Chapter Test: Sections 2.1—2.3*

2.4 Additional Application Problems

2.5 Solving Linear Inequalities

2.6 Solving Equations and Inequalities Containing Absolute Values

**CHAPTER 3: Graphs and Functions**

3.1 Graphs

3.2 Functions

3.3 Linear Functions: Graphs and Applications

3.4 The Slope-Intercept Form of a Linear Equation

*Mid-Chapter Test: Sections 3.1—3.4*

3.5 The Point-Slope Form of a Linear Equation

3.6 The Algebra of Functions

3.7 Graphing Linear Inequalities

**CHAPTER 4: Systems of Equations and Inequalities **

4.1 Solving Systems of Linear Equations in Two Variables

4.2 Solving Systems of Linear Equations in Three Variables

4.3 Systems of Linear Equations: Applications and Problem Solving

*Mid-Chapter Test: Sections 4.1—4.3*

4.4 Solving Systems of Equations Using Matrices

4.5 Solving Systems of Equations Using Determinants and Cramer’s Rule

4.6 Solving Systems of Linear Inequalities

** **

**CHAPTER 5: Polynomials and Polynomial Functions**

5.1 Addition and Subtraction of Polynomials

5.2 Multiplication of Polynomials

5.3 Division of Polynomials and Synthetic Division

5.4 Factoring a Monomial from a Polynomial and Factoring by Grouping

*Mid-Chapter Test: Sections 5.1—5.4*

5.5 Factoring Trinomials

5.6 Special Factoring Formulas

5.7 A General Review of Factoring

5.8 Polynomial Equations

**CHAPTER 6: Rational Expressions and Equations**

6.1 The Domains of Rational Functions and Multiplication and Division of Rational Expressions

6.2 Addition and Subtraction of Rational Expressions

6.3 Complex Fractions

6.4 Solving Rational Equations

*Mid-Chapter Test: Sections 6.1—6.4*

6.5 Rational Equations: Applications and Problem Solving

6.6 Variation**CHAPTER 7: Roots, Radicals, and Complex Numbers**

7.1 Roots and Radicals

7.2 Rational Exponents

7.3 Simplifying Radicals

7.4 Adding, Subtracting, and Multiplying Radicals

*Mid-Chapter Test: Sections 7.1—7.4*

7.5 Dividing Radicals

7.6 Solving Radical Equations

7.7 Complex Numbers

** **

**CHAPTER 8: Quadratic Functions**

8.1 Solving Quadratic Equations by Completing the Square

8.2 Solving Quadratic Equations by the Quadratic Formula

8.3 Quadratic Equations: Applications and Problem Solving

*Mid-Chapter Test: Sections 8.1—8.3*

8.4 Writing Equations in Quadratic Form

8.5 Graphing Quadratic Functions

8.6 Quadratic and Other Inequalities in One Variable

**CHAPTER** **9: Exponential and Logarithmic Functions**

9.1 Composite and Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

*Mid-Chapter Test: Sections 9.1—9.4*

9.5 Common Logarithms

9.6 Exponential and Logarithmic Equations

9.7 Natural Exponential and Natural Logarithmic Functions

**CHAPTER** **10: Characteristics of Functions and Their Graphs**

10.1 Continuous and Discontinuous Functions

10.2 Characteristics of Graphs of Polynomial Functions

*Mid-Chapter Test: Sections 10.1—10.2*

10.3 Finding the Rational Zeros of a Polynomial Function

10.4 Finding the Real Zeros of a Polynomial Function

10.5 Characteristics of Graphs of Rational Functions

** **

**CHAPTER** **11: Conic Sections**

11.1 T he Parabola and the Circle

11.2 The Ellipse

*Mid-Chapter Test: Sections 11.1—11.2*

11.3 The Hyperbola

11.4 Nonlinear Systems of Equations and Their Applications

11.5 Nonlinear Systems of Inequalities

**CHAPTER** **12: Sequences, Series, and Probability**

12.1 Sequences and Series

12.2 Arithmetic Sequences and Series

12.3 Geometric Sequences and Series

*Mid-Chapter Test: Sections 12.1—12.3*

12.4 Mathematical Induction

12.5 The Binomial Theorem

12.6 The Counting Principle, Permutations, and Combinations

12.7 Probability

**APPENDIX Geometric Formulas**

**Answers**

**Graphing Answer Section ***found only in the Annotated Instructor's Edition

**Applications Index**

**Index**

**Photo Credits**

Allen R. Angel received his AAS in Electrical Technology from New York City Community College. He then received his BS in Physics and his MS in Mathematics from SUNY at New Paltz, and he took additional graduate work at Rutgers University. He is Professor Emeritus at Monroe Community College in Rochester, New York where he served for many years as the chair of the Mathematics Department. He also served as the Assistant Director of the National Science Foundation Summer Institutes at Rutgers University from 1967—73. He served as the President of the New York State Mathematics Association of Two Year Colleges (NYSMATYC) and the Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). He is the recipient of many awards including a number of NISOD Excellence in Teaching Awards, NYSMATYC's Outstanding Contributions to Mathematics Education Award, and AMATYC's President Award. Allen enjoy tennis, worldwide travel, and visiting with his children and granddaughter.

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