Intermediate Algebra

Cover Page......Page 1
Title Page......Page 4
Copyright Page......Page 5
About the Authors......Page 6
Preface......Page 14
Guided Tour: Features and Supplements......Page 22
Applications Index......Page 32
Contents......Page 8
The Human Side of Algebra......Page 36
1.1 Numbers and Their Properties......Page 37
1.2 Operations and Properties of Real Numbers......Page 52
1.3 Properties of Exponents......Page 72
1.4 Algebraic Expressions and the Order of Operations......Page 86
Collaborative Learning 1B......Page 99
Research Question......Page 100
Summary......Page 101
Review Exercises......Page 103
Practice Test 1......Page 106
The Human Side of Algebra......Page 110
2.1 Linear Equations in One Variable......Page 111
2.2 Formulas, Geometry, and Problem Solving......Page 124
2.3 Problem Solving: Integers and Geometry......Page 137
2.4 Problem Solving: Percent, Investment, Motion, and Mixture Problems......Page 148
2.5 Linear and Compound Inequalities......Page 160
2.6 Absolute-Value Equations and Inequalities......Page 179
Collabortive Learning 2A......Page 191
Research Questions......Page 192
Summary......Page 193
Review Exercises......Page 195
Practice Test 2......Page 199
Cumulative Review Chapters 1–2......Page 201
The Human Side of Algebra......Page 204
3.1 Graphs......Page 205
3.2 Using Slopes to Graph Lines......Page 223
3.3 Equations of Lines......Page 238
3.4 Linear Inequalities in Two Variables......Page 249
3.5 Introduction to Functions......Page 262
3.6 Linear Functions......Page 281
Collaborative Learning 3B......Page 301
Research Questions......Page 302
Summary......Page 303
Review Exercises......Page 306
Practice Test 3......Page 311
Cumulative Review Chapters 1–3......Page 320
The Human Side of Algebra......Page 326
4.1 Systems with Two Variables......Page 327
4.2 Systems with Three Variables......Page 348
4.3 Coin, Distance-Rate-Time, Investment, and Geometry Problems......Page 358
4.4 Systems of Linear Inequalities......Page 370
Collaborative Learning 4A......Page 377
Collaborative Learning 4B......Page 378
Summary......Page 379
Review Exercises......Page 381
Practice Test 4......Page 384
Cumulative Review Chapters 1–4......Page 388
The Human Side of Algebra......Page 394
5.1 Polynomials: Addition and Subtraction......Page 395
5.2 Multiplication of Polynomials......Page 406
5.3 The Greatest Common Factor and Factoring by Grouping......Page 417
5.4 Factoring Trinomials......Page 426
5.5 Special Factoring......Page 435
5.6 General Methods of Factoring......Page 445
5.7 Solving Equations by Factoring: Applications......Page 451
Collaborative Learning 5B......Page 464
Research Questions......Page 465
Summary......Page 466
Review Exercises......Page 468
Practice Test 5......Page 470
Cumulative Review Chapters 1–5......Page 472
The Human Side of Algebra......Page 476
6.1 Rational Expressions......Page 477
6.2 Multiplication and Division of Rational Expressions......Page 489
6.3 Addition and Subtraction of Rational Expressions......Page 497
6.4 Complex Fractions......Page 509
6.5 Division of Polynomials and Synthetic Division......Page 519
6.6 Equations Involving Rational Expressions......Page 530
6.7 Applications: Problem Solving......Page 544
6.8 Variation......Page 554
Collaborative Learning 6A......Page 562
Collaborative Learning 6B......Page 563
Summary......Page 564
Review Exercises......Page 566
Practice Test 6......Page 569
Cumulative Review Chapters 1–6......Page 571
The Human Side of Algebra......Page 576
7.1 Rational Exponents and Radicals......Page 577
7.2 Simplifying Radicals......Page 588
7.3 Operations with Radicals......Page 599
7.4 Solving Equations Containing Radicals......Page 610
7.5 Complex Numbers......Page 618
Collaborative Learning 7B......Page 629
Research Questions......Page 630
Summary......Page 631
Review Exercises......Page 632
Practice Test 7......Page 635
Cumulative Review Chapters 1–7......Page 639
The Human Side of Algebra......Page 644
8.1 Solving Quadratics by Completing the Square......Page 645
8.2 The Quadratic Formula: Applications......Page 658
8.3 The Discriminant and Its Applications......Page 670
8.4 Solving Equations in Quadratic Form......Page 679
8.5 Nonlinear Inequalities......Page 688
Collaborative Learning 8A......Page 700
Research Questions......Page 701
Summary......Page 702
Review Exercises......Page 703
Practice Test 8......Page 706
Cumulative Review Chapters 1–8......Page 708
The Human Side of Algebra......Page 712
9.1 Quadratic Functions (Parabolas) and Their Graphs......Page 713
9.2 Circles and Ellipses......Page 735
9.3 Hyperbolas and Identification of Conics......Page 753
9.4 Nonlinear Systems of Equations......Page 767
9.5 Nonlinear Systems of Inequalities......Page 779
Collaborative Learning 9B......Page 786
Research Questions......Page 787
Summary......Page 788
Review Exercises......Page 789
Practice Test 9......Page 794
Cumulative Review Chapters 1–9......Page 800
The Human Side of Algebra......Page 805
10.1 The Algebra of Functions......Page 806
10.2 Inverse Functions......Page 818
10.3 Exponential Functions......Page 831
10.4 Logarithmic Functions and Their Properties......Page 842
10.5 Common and Natural Logarithms......Page 854
10.6 Exponential and Logarithmic Equations and Applications......Page 870
Collaborative Learning 10A......Page 882
Research Questions......Page 883
Summary......Page 884
Review Exercises......Page 885
Practice Test 10......Page 889
Cumulative Review Chapters 1–10......Page 894
 Selected Answers......Page 901
Appendix......Page 953
Photo Credits......Page 989
Index......Page 991