Elementary Algebra for College Students

by Angel, Allen R.

• ISBN13: 9780131400238
• ISBN10: 0131400231
• Edition: 6th
• Format: Hardcover
• Copyright: 2004-01-01
• Publisher: Prentice Hall

Summary

For freshman-level, one- or two- semester courses in Developmental Algebra. The Angel Series continues to offer proven pedagogy sound exercise sets and superior student support. An emphasis on the practical applications of algebra motivates students and encourages them to see algebra as an important part of their daily lives. The student-friendly writing style uses short, clear sentences and easy-to-understand language, and the outstanding pedagogical program makes the material easy to follow and comprehend. The new editions continue to place a strong emphasis on problem solving, incorporating it as a theme throughout the texts. Angel's solid exercise sets are recognized by reviewers as of the highest standard providing a large number of problems, paired exercises, and a broad and increasing range of difficulty.

Table of Contents

Preface	ix
To the Student	xxii
Real Numbers	1	(96)
Study Skills for Success in Mathematics	2	(6)
Problem Solving	8	(12)
Fractions	20	(11)
The Real Number System	31	(6)
Inequalities	37	(5)
Addition of Real Numbers	42	(10)
Subtraction of Real Numbers	52	(10)
Multiplication and Division of Real Numbers	62	(9)
Exponents, Parentheses, and the Order of Operations	71	(12)
Properties of the Real Number System	83	(14)
Chapter Summary	91	(1)
Chapter Review Exercises	92	(3)
Chapter Practice Test	95	(2)
Solving Linear Equations and Inequalities	97	(73)
Combining Like Terms	98	(9)
The Addition Property of Equality	107	(9)
The Multiplication Property of Equality	116	(7)
Solving Linear Equations with a Variable on Only One Side of the Equation	123	(10)
Solving Linear Equations with the Variable on Both Sides of the Equation	133	(10)
Ratios and Proportions	143	(15)
Inequalities in One Variable	158	(12)
Chapter Summary	165	(1)
Chapter Review Exercises	166	(2)
Chapter Practice Test	168	(1)
Cumulative Review Test	169	(1)
Formulas and Applications of Algebra	170	(71)
Formulas	171	(14)
Changing Application Problems into Equations	185	(14)
Solving Application Problems	199	(13)
Geometric Problems	212	(6)
Motion, Money, and Mixture Problems	218	(23)
Chapter Summary	234	(1)
Chapter Review Exercises	235	(3)
Chapter Practice Test	238	(1)
Cumulative Review Test	239	(2)
Exponents and Polynomials	241	(61)
Exponents	242	(10)
Negative Exponents	252	(8)
Scientific Notation	260	(12)
Addition and Subtraction of Polynomials	272	(8)
Multiplication of Polynomials	280	(10)
Division of Polynomials	290	(12)
Chapter Summary	297	(1)
Chapter Review Exercises	298	(2)
Chapter Practice Test	300	(1)
Cumulative Review Test	300	(2)
Factoring	302	(64)
Factoring a Monomial from a Polynomial	303	(7)
Factoring by Grouping	310	(6)
Factoring Trinomials of the form ax2 + bx + c, a = 1	316	(9)
Factoring Trinomials of the form ax2 + bx + c, a ≠ 1	325	(13)
Special Factoring Formulas and a General Review of Factoring	338	(8)
Solving Quadratic Equations Using Factoring	346	(6)
Applications of Quadratic Equations	352	(14)
Chapter Summary	361	(1)
Chapter Review Exercises	362	(2)
Chapter Practice Test	364	(1)
Cumulative Review Test	364	(2)
Rational Expressions and Equations	366	(73)
Simplifying Rational Expressions	367	(8)
Multiplication and Division of Rational Expressions	375	(7)
Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator	382	(8)
Addition and Subtraction of Rational Expressions	390	(9)
Complex Fractions	399	(5)
Solving Rational Equations	404	(9)
Rational Equations: Applications and Problem Solving	413	(13)
Variation	426	(13)
Chapter Summary	433	(1)
Chapter Review Exercises	434	(2)
Chapter Practice Test	436	(1)
Cumulative Review Test	437	(2)
Graphing Linear Equations	439	(69)
The Cartesian Coordinate System and Linear Equations in Two Variables	440	(10)
Graphing Linear Equations	450	(12)
Slope of a Line	462	(12)
Slope-Intercept and Point-Slope Forms of a Linear Equation	474	(13)
Graphing Linear Inequalities	487	(3)
Functions	490	(18)
Chapter Summary	501	(1)
Chapter Review Exercises	502	(3)
Chapter Practice Test	505	(1)
Cumulative Review Test	506	(2)
Systems of Linear Equations	508	(48)
Solving Systems of Equations Graphically	509	(11)
Solving Systems of Equations by Substitution	520	(6)
Solving Systems of Equations by the Addition Method	526	(9)
Systems of Equations: Applications and Problem Solving	535	(13)
Solving Systems of Linear Inequalities	548	(8)
Chapter Summary	551	(1)
Chapter Review Exercises	551	(2)
Chapter Practice Test	553	(1)
Cumulative Review Test	554	(2)
Roots and Radicals	556	(58)
Evaluating Square Roots	557	(8)
Simplifying Square Roots	565	(6)
Adding, Subtracting, and Multiplying Square Roots	571	(6)
Dividing Square Roots	577	(9)
Solving Radical Equations	586	(7)
Radicals: Applications and Problem Solving	593	(8)
Higher Roots and Rational Exponents	601	(13)
Chapter Summary	609	(1)
Chapter Review Exercises	609	(3)
Chapter Practice Test	612	(1)
Cumulative Review Test	612	(2)
Quadratic Equations	614	(1)
The Square Root Property	615	(5)
Solving Quadratic Equations by Completing the Square	620	(7)
Solving Quadratic Equations by the Quadratic Formula	627	(12)
Graphing Quadratic Equations	639	(10)
Complex Numbers	649	(9)
Chapter Summary	653	(1)
Chapter Review Exercises	654	(2)
Chapter Practice Test	656	(1)
Cumulative Review Test	656	(2)
Appendices
A Review of Decimals and Percents	658	(3)
B Finding the Greatest Common Factor and Least Common Denominator	661	(2)
C Geometry	663
Answers	1	(1)
Index	1	(1)
Photo Credits	1

Excerpts

This book was written for college students and other adults who have never been exposed to algebra or those who have been exposed but need a refresher course. My primary goal was to write a book that students can read, understand, and enjoy. To achieve this goal I have used short sentences, clear explanations, and many detailed, worked-out examples. I have tried to make the book relevant to college students by using practical applications of algebra throughout the text. Features of the Text Full-Color Format.Color is used pedagogically in the following ways: Important definitions and procedures are color screened. Color screening or color type is used to make other important items stand out. Artwork is enhanced and clarified with use of multiple colors. The full-color format allows for easy identification of important features by students. The full-color format makes the text more appealing and interesting to students. Readability.One of the most important features of the text is its readability. The book is very readable, even for those with .weak reading skills. Short, clear sentences are used and more easily recognized, and easy-to-understand language is used whenever possible. Accuracy.Accuracy in a mathematics text is essential. To ensure accuracy in this book, mathematicians from around the country have read the pages carefully for typographical errors and have checked all the answers. Connections.Many of our students do not thoroughly grasp new concepts the first time they are presented. In this text we encourage students to make connections. That is, we introduce a concept, then later in the text briefly reintroduce it and build upon it. Often an important concept is used in many sections of the text. Students are reminded where the material was seen before, or where it will be used again. This also serves to emphasize the importance of the concept. Important concepts are also reinforced throughout the text in the Cumulative Review Exercises and Cumulative Review Tests. Chapter Opening Application.Each chapter begins with a real-life application related to the material covered in the chapter. By the time students complete the chapter, they should have the knowledge to work the problem. A Look Ahead.This feature at the beginning of each chapter gives students a preview of the chapter and also indicates where this material will be used again in other chapters of the book. This material helps students see the connections between various topics in the book and the connection to realworld situations. The Use of Icons.At the beginning of each chapter and of each section, a variety of icons are illustrated. These icons are provided to tell students where they may be able to get extra help if needed. There are icons for theStudent's Solution Manual;theStudent's Study Guide); CDs and videotapes; Math Pro the Prentice Hall Tutor Center;and theAngel Website.Each of these items will be discussed shortly. Keyed Section Objectives.Each section opens with a list of skills that the student should learn in that section. The objectives are then keyed to the appropriate portions of the sections with red numbers such as1. Problem Solving.Polya's five-step problem-solving procedure is discussed in Section 1.2. Throughout the book problem solving and Polya's problem-solving procedure are emphasized. Practical Applications.Practical applications of algebra are stressed throughout the text. Students need to learn how to translate application problems into algebraic symbols. The problem-solving approach used throughout this text gives students ample practice in setting up and solving application problems. The use of practical applications motivates students. Detailed. Worked-Out Examples.A wealth of examples have been wo