Elementary and Intermediate Algebra

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2004-01-01
  • Publisher: Prentice Hall
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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

Prefacep. xi
To the Studentp. xxiii
Real Numbersp. 1
Study Skills for Success in Mathematicsp. 2
Problem Solvingp. 9
Fractionsp. 21
The Real Number Systemp. 33
Inequalitiesp. 38
Addition of Real Numbersp. 43
Subtraction of Real Numbersp. 51
Multiplication and Division of Real Numbersp. 59
Exponents, Parentheses, and the Order of Operationsp. 67
Properties of the Real Number Systemp. 80
Summaryp. 85
Review Exercisesp. 87
Practice Testp. 89
Solving Linear Equationsp. 91
Combining Like Termsp. 92
The Addition Property of Equalityp. 101
The Multiplication Property of Equalityp. 111
Solving Linear Equations with a Variable on Only One Side of the Equationp. 120
Solving Linear Equations with the Variable on Both Sides of the Equationp. 127
Ratios and Proportionsp. 135
Summaryp. 149
Review Exercisesp. 150
Practice Testp. 151
Cumulative Review Testp. 152
Formulas and Applications of Algebrap. 153
Formulasp. 154
Changing Application Problems into Equationsp. 167
Solving Application Problemsp. 179
Geometric Problemsp. 195
Motion and Mixture Problemsp. 200
Summaryp. 214
Review Exercisesp. 215
Practice Testp. 217
Cumulative Review Testp. 218
Graphing Linear Equationsp. 221
The Cartesian Coordinate System and Linear Equations in Two Variablesp. 222
Graphing Linear Equationsp. 232
Slope of a Linep. 244
Slope-Intercept and Point-Slope Forms of a Linear Equationp. 251
Summaryp. 265
Review Exercisesp. 266
Practice Testp. 268
Cumulative Review Testp. 269
Exponents and Polynomialsp. 271
Exponentsp. 272
Negative Exponentsp. 281
Scientific Notationp. 288
Addition and Subtraction of Polynomialsp. 296
Multiplication of Polynomialsp. 303
Division of Polynomialsp. 314
Summaryp. 324
Review Exercisesp. 325
Practice Testp. 327
Cumulative Review Testp. 328
Factoringp. 329
Factoring a Monomial from a Polynomialp. 330
Factoring by Groupingp. 338
Factoring Trinomials of the from ax[superscript 2] + bx + c, a = 1p. 343
Factoring Trinomials of the form ax[superscript 2] + bx + c, a [not equal] 1p. 352
Special Factoring Formulas and a General Review of Factoringp. 365
Solving Quadratic Equations Using Factoringp. 372
Summaryp. 382
Review Exercisesp. 383
Practice Testp. 385
Cumulative Review Testp. 385
Rational Expressions and Equationsp. 387
Simplifying Rational Expressionsp. 388
Multiplication and Division of Rational Expressionsp. 395
Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominatorp. 402
Addition and Subtraction of Rational Expressionsp. 410
Complex Fractionsp. 419
Solving Rational Equationsp. 424
Rational Equations: Applications and Problem Solvingp. 433
Variationp. 444
Summaryp. 453
Review Exercisesp. 453
Practice Testp. 456
Cumulative Review Testp. 457
Functions and Their Graphsp. 459
More on Graphsp. 460
Functionsp. 468
Linear Functionsp. 468
Slope, Modeling, and Linear Relationshipsp. 497
The Algebra of Functionsp. 514
Summaryp. 523
Review Exercisesp. 524
Practice Testp. 526
Cumulative Review Testp. 528
Systems of Linear Equationsp. 529
Solving Systems of Equations Graphicallyp. 530
Solving Systems of Equations by Substitutionp. 540
Solving Systems of Equations by the Addition Methodp. 546
Solving Systems of Linear Equations in Three Variablesp. 554
Systems of Linear Equations: Applications and Problem Solvingp. 561
Solving Systems of Equations Using Matricesp. 574
Solving Systems of Equations Using Determinants and Cramer's Rulep. 582
Summaryp. 590
Review Exercisesp. 592
Practice Testp. 594
Cumulative Review Testp. 595
Inequalities in One and Two Variablesp. 597
Solving Linear Inequalities in One Variablep. 598
Solving Equations and Inequalities Containing Absolute Valuep. 613
Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalitiesp. 623
Summaryp. 631
Review Exercisesp. 631
Practice Testp. 633
Cumulative Review Testp. 634
Roots, Radicals, and Complex Numbersp. 637
Roots and Radicalsp. 638
Rational Exponentsp. 646
Multiplying and Simplifying Radicalsp. 654
Dividing and Simplifying Radicalsp. 662
Adding and Subtracting Radicalsp. 672
Solving Radical Equationsp. 678
Complex Numbersp. 690
Summaryp. 698
Review Exercisesp. 699
Practice Testp. 702
Cumulative Review Testp. 703
Quadratic Functionsp. 705
Solving Quadratic Equations by Completing the Squarep. 706
Solving Quadratic Equations by the Quadratic Formulap. 716
Quadratic Equations: Applications and Problem Solvingp. 730
Factoring Expressions and Solving Equations that are Quadratic in Formp. 737
Graphing Quadratic Functionsp. 745
Quadratic and Other Inequalities in One Variablep. 766
Summaryp. 775
Review Exercisesp. 776
Practice Testp. 778
Cumulative Review Testp. 779
Exponential and Logarithmic Functionsp. 781
Composite and Inverse Functionsp. 782
Exponential Functionsp. 794
Logarithmic Functionsp. 801
Properties of Logarithmsp. 807
Common Logarithmsp. 813
Exponential and Logarithmic Equationsp. 819
Natural Exponential and Natural Logarithmic Functionsp. 826
Summaryp. 838
Review Exercisesp. 839
Practice Testp. 841
Cumulative Review Testp. 842
Conic Sectionsp. 843
The Parabola and the Circlep. 844
The Ellipsep. 856
The Hyperbolap. 861
Nonlinear Systems of Equations and Their Applicationsp. 867
Summaryp. 875
Review Exercisesp. 876
Practice Testp. 878
Cumulative Review Testp. 879
Sequences, Series, and the Binomial Theoremp. 881
Sequences and Seriesp. 882
Arithmetic Sequences and Seriesp. 890
Geometric Sequences and Seriesp. 896
The Binomial Theoremp. 907
Summaryp. 913
Review Exercisesp. 914
Practice Testp. 916
Cumulative Review Testp. 917
Appendicesp. 919
Review of Decimals and Percentsp. 919
Finding the Greatest Common Factor and Least Common Denominatorp. 922
Geometry Concepts and Formulasp. 924
Review of Exponents, Polynomials, and Factoringp. 931
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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 appeal ing 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 real-world situations. The Use of Icons.At the beginning of each chapter and 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 4/5 Software;thePrentice Hall Tutor Center,and theAngel Website,be discussed shortly. 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 Exam

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