Understanding Elementary Algebra with Geometry: A Course for College Students / Edition 5

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Overview

Helping students grasp the "why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples-both numerical and algebraic-helps students compare and contrast related ideas and understand the sometimes-subtle distinctions among a wide variety of situations. This author team carefully prepares students to succeed in higher level mathematics.
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Product Details

  • ISBN-13: 9780534381240
  • Publisher: Brooks/Cole
  • Publication date: 11/28/2001
  • Edition description: 5TH BK&CDR
  • Edition number: 5
  • Pages: 578
  • Product dimensions: 8.56 (w) x 11.08 (h) x 1.09 (d)

Table of Contents

Chapter 1 The Integers 1
1.1 What Is Algebra? Introduction and Basic Notation 2
1.2 Integers 9
1.3 Adding Integers 16
1.4 Subtracting Integers 22
1.5 Multiplying and Dividing Integers 28
1.6 The Real Number System 36
Chapter 1 Summary 40
Chapter 1 Review Exercises 41
Chapter 1 Practice Test 42
Chapter 2 Algebraic Expressions 45
2.1 Variables and Exponents 46
2.2 Algebraic Substitution 53
2.3 The Distributive Property and Combining Like Terms 65
2.4 Simplifying Algebraic Expressions 72
2.5 Translating Phrases and Sentences Algebraically 78
Chapter 2 Summary 88
Chapter 2 Review Exercises 89
Chapter 2 Practice Test 91
Chapter 3 First-Degree Equations and Inequalities 93
3.1 Types of Equations 94
3.2 Solving First-Degree Equations in One Variable and Applications 98
3.3 More First-Degree Equations and Applications 109
3.4 Types of Inequalities and Basic Properties of Inequalities 123
3.5 Solving First-Degree Inequalities in One Variable and Applications 130
Chapter 3 Summary 138
Chapter 3 Review Exercises 140
Chapter 3 Practice Test 141
Chapters 1-3 Cumulative Review 141
Chapters 1-3 Cumulative Practice Test 142
Chapter 4 Rational Expressions 145
4.1 Fundamental Principle of Franctions 146
4.2 Multiplying and Dividing Rational Expressions 153
4.3 Adding and Subtracting Rational Expressions 162
4.4 Solving Fractional Equations and Inequalities 171
4.5 Ratio and Proportion 179
4.6 Applications 188
Chapter 4 Summary 198
Chapter 4 Review Exercises 200
Chapter 4 Practice Test 202
Chapter 5 Graphing Straight Lines 203
5.1 The Rectangular (Cartesian) Coordinate System 204
5.2 Graphing a Linear Equation in Two Variables 211
5.3 The Slope 225
5.4 The Equation of a Line 238
Chapter 5 Summary 250
Chapter 5 Review Exercises 251
Chapter 5 Practice Test 253
Chapter 6 Interpreting Graphs and Systems of Linear Equations 255
6.1 Interpreting Graphs 256
6.2 Solving Systems of Linear Equations: Graphical Method 266
6.3 Solving Systems of Linear Equations: Algebraic Methods 272
6.4 Applications 281
Chapter 6 Summary 288
Chapter 6 Review Exercises 289
Chapter 6 Practice Test 292
Chapters 4-6 Cumulative Review 293
Chapters 4-6 Cumulative Practice Test 295
Chapter 7 Exponents and Polynomials 297
7.1 Exponent Rules 298
7.2 Zero and Negative Exponents 305
7.3 Scientific Notation 314
7.4 Introduction to Polynomials 321
7.5 Multiplying Polynomials 328
7.6 Special Products 335
Chapter 7 Summary 340
Chapter 7 Review Exercises 342
Chapter 7 Practice Test 344
Chapter 8 Factoring 345
8.1 Common Factors 346
8.2 Factoring Trinomials 351
8.3 More Factoring 357
8.4 Solving Polynomial Equations by Factoring 364
8.5 Dividing Polynomials 372
Chapter 8 Summary 376
Chapter 8 Review Exercises 377
Chapter 8 Practice Test 378
Chapter 9 More Rational Expressions 381
9.1 Reducing Rational Expressions 382
9.2 Multiplying and Dividing Rational Expressions 387
9.3 Adding and Subtracting Rational Expressions 391
9.4 Fractional Equations 401
9.5 Literal Equations 409
9.6 Applications 413
Chapter 9 Summary 421
Chapter 9 Review Exercises 422
Chapter 9 Practice Test 424
Chapters 7-9 Cumulative Review 424
Chapters 7-9 Cumulative Practice Test 427
Chapter 10 Radical Expressions and Equations 429
10.1 Definitions and Basic Notation 430
10.2 Properties of Radicals and Simplest Radical Form 435
10.3 Adding and Subtracting Radical Expressions 444
10.4 Multiplying and Dividing Radical Expressions 449
10.5 Radical Equations 456
Chapter 10 Summary 462
Chapter 10 Review Exercises 463
Chapter 10 Practice Test 464
Chapter 11 Quadratic Equations 465
11.1 The Factoring and Square Root Methods 466
11.2 The Method of Completing the Square 474
11.3 The Quadratic Formula 479
11.4 Choosing a Method 487
11.5 Applications 491
11.6 Graphing Quadratic Equations 498
Chapter 11 Summary 507
Chapter 11 Review Exercises 509
Chapter 11 Practice Test 510
Chapters 10-11 Cumulative Review 510
Chapters 10-11 Cumulative Practice Test 511
Chapter G Geometry 513
G.1 Angles 514
G.2 Triangles 523
G.3 Congruence 530
G.4 Similarity 537
G.5 Quadrilaterals 549
G.6 Perimeter and Area 557
G.7 Circles 568
G.8 Solid Geometry 576
Chapter G Review Exercises 587
Chapter G Practice Test 593
Appendix A A Review of Arithmetic 595
A.1 Fractions 596
A.2 Multiplying and Dividing Fractions 600
A.3 Adding and Subtracting Fractions 604
A.4 Decimals 609
A.5 Percents 612
Appendix B Using a Scientific Calculator 617
Appendix C Using a Graphing Calculator 623
Appendix D Introduction to Functions 629
Answers to Selected Exercises and Chapter Tests 635
Index 663
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