Understanding Intermediate Algebra

by Hirsch, Lewis; Goodman, Arthur

• ISBN13: 9780534381257
• ISBN10: 0534381251
• Edition: CD
• Format: Hardcover
• Copyright: 2002-11-01
• Publisher: Brooks/Cole Pub Co

Summary

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 variety of situations. This author team carefully prepares students to succeed in higher level mathematics.

Table of Contents

The Fundamental Concepts	p. 1
Basic Definitions: The Real Numbers and the Real Number Line	p. 2
Operations with Real Numbers	p. 14
Algebraic Expressions	p. 28
Translating Phrases and Sentences into Algebraic Form	p. 36
First-Degree Equations and Inequalities	p. 46
Chapter 1 Summary	p. 55
Chapter 1 Review Exercises	p. 57
Chapter 1 Practice Test	p. 61
Equations and Inequalities	p. 63
Equations as Mathematical Models	p. 64
First-Degree Equations and Applications	p. 74
First-Degree Inequalities and Applications	p. 87
Absolute-Value Equations and Inequalities	p. 99
Chapter 2 Summary	p. 107
Chapter 2 Review Exercises	p. 110
Chapter 2 Practice Test	p. 113
Graphing Straight Lines and Functions	p. 115
The Rectangular Coordinate System and Graphing Straight Lines	p. 116
Graphs and Equations	p. 128
Relations and Functions: Basic Concepts	p. 141
Function Notation	p. 158
Interpreting Graphs	p. 166
Chapter 3 Summary	p. 178
Chapter 3 Review Exercises	p. 181
Chapter 3 Practice Test	p. 186
Chapters 1-3 Cumulative Review	p. 188
Chapters 1-3 Cumulative Practice Test	p. 192
Equations of a Line and Linear Systems in Two Variables	p. 195
Straight Lines and Slope	p. 196
Equations of a Line and Linear Functions as Mathematical Models	p. 214
Linear Systems in Two Variables	p. 228
Graphing Linear Inequalities in Two Variables	p. 243
Chapter 4 Summary	p. 249
Chapter 4 Review Exercises	p. 252
Chapter 4 Practice Test	p. 255
Polynomial Expressions and Functions	p. 257
Polynomial Functions as Mathematical Models	p. 258
Polynomials: Sums, Differences, and Products	p. 265
General Forms and Special Products	p. 271
Factoring Out the Greatest Common Factor	p. 279
Factoring Trinomials	p. 284
Solving Polynomial Equations by Factoring	p. 293
Polynomial Division	p. 301
Chapter 5 Summary	p. 304
Chapter 5 Review Exercises	p. 305
Chapter 5 Practice Test	p. 307
Rational Expressions and Functions	p. 309
Rational Functions	p. 310
Equivalent Fractions	p. 315
Multiplication and Division of Rational Expressions	p. 320
Sums and Differences of Rational Expressions	p. 324
Mixed Operations and Complex Fractions	p. 332
Fractional Equations and Inequalities	p. 337
Literal Equations	p. 343
Applications: Rational Functions and Equations as Mathematical Models	p. 347
Chapter 6 Summary	p. 362
Chapter 6 Review Exercises	p. 364
Chapter 6 Practice Test	p. 368
Chapters 4-6 Cumulative Review	p. 369
Chapters 4-6 Cumulative Practice Test	p. 373
Exponents and Radicals	p. 375
Natural Number and Integer Exponents	p. 376
Scientific Notation	p. 388
Rational Exponents and Radical Notation	p. 393
Simplifying Radical Expressions	p. 404
Adding and Subtracting Radical Expressions	p. 411
Multiplying and Dividing Radical Expressions	p. 414
Radical Functions and Equations	p. 418
Complex Numbers	p. 425
Chapter 7 Summary	p. 433
Chapter 7 Review Exercises	p. 436
Chapter 7 Practice Test	p. 438
Quadratic Functions and Equations	p. 441
Quadratic Functions as Mathematical Models	p. 442
Solving Quadratic Equations: The Factoring and Square Root Methods	p. 450
Solving Quadratic Equations: Completing the Square	p. 462
Solving Quadratic Equations: The Quadratic Formula	p. 466
Equations Reducible to Quadratic Form (and More Radical Equations)	p. 473
Graphing Quadratic Functions	p. 480
Quadratic and Rational Inequalities	p. 498
The Distance Formula: Circles	p. 508
Chapter 8 Summary	p. 519
Chapter 8 Review Exercises	p. 525
Chapter 8 Practice Test	p. 529
More on Functions	p. 531
More on Function Notation: Split Functions	p. 532
Composition and the Algebra of Functions	p. 539
Types of Functions	p. 544
Inverse Functions	p. 551
Variation	p. 559
Chapter 9 Summary	p. 567
Chapter 9 Review Exercises	p. 570
Chapter 9 Practice Test	p. 573
Chapters 7-9 Cumulative Review	p. 575
Chapters 7-9 Cumulative Practice Test	p. 578
Exponential and Logarithmic Functions	p. 581
Exponential Functions	p. 582
Logarithms and Logarithmic Functions	p. 592
Properties of Logarithms	p. 598
Common Logarithms, Natural Logarithms, and Change of Base	p. 603
Exponential and Logarithmic Equations	p. 608
Applications: Exponential and Logarithmic Functions as Mathematical Models	p. 616
Chapter 10 Summary	p. 624
Chapter 10 Review Exercises	p. 626
Chapter 10 Practice Test	p. 628
More Systems of Equations and Systems of Inequalities	p. 631
3 X 3 Linear Systems	p. 632
Solving Linear Systems Using Augmented Matrices	p. 641
The Algebra of Matrices	p. 651
Solving Linear Systems Using Matrix Inverses	p. 659
Determinants and Cramer's Rule	p. 668
Systems of Linear Inequalities	p. 676
Nonlinear Systems of Equations	p. 683
Chapter 11 Summary	p. 690
Chapter 11 Review Exercises	p. 695
Chapter 11 Practice Test	p. 697
Chapters 10-11 Cumulative Review	p. 698
Chapters 10-11 Cumulative Practice Test	p. 701
Sets	p. 703
Conic Sections	p. 707
Sequences and Series: The Binomial Theorem	p. 727
Sequences	p. 728
Series and Sigma Notation	p. 733
Arithmetic Sequences and Series	p. 737
Geometric Sequences and Series	p. 746
The Binomial Theorem	p. 757
Appendix C Summary	p. 765
Appendix C Review Exercises	p. 767
Appendix C Practice Test	p. 770
Answers to Selected Exercises and Chapter Tests	p. 771
Index	p. 823
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