First-Degree Equations and Inequalities 2 Chapter Solving Equations and Inequalities 4 ... Graphing...

Prerequisite Skills• Getting Started 5

• Getting Ready for the Next Lesson10, 18, 27, 32, 39

Study Organizer 5

Reading and WritingMathematics • Reading Math Tips 11, 12, 34, 35

• Writing in Math 10, 17, 27, 31, 38,45

Standardized Test Practice• Multiple Choice 10, 17, 23, 24, 27,

31, 32, 39, 46, 51, 52

• Short Response/Grid In 46, 53

• Extended Response 53

Snapshots 17, 39

ix

First-Degree Equations andInequalities 2

Chapter Solving Equations and Inequalities 4

1-1 Expressions and Formulas................................................6

1-2 Properties of Real Numbers...........................................11

Practice Quiz 1: Lessons 1-1 and 1-2 ............................18

Algebra Activity: Investigating Polygons and Patterns..................................................................19

1-3 Solving Equations............................................................20

1-4 Solving Absolute Value Equations................................28

1-5 Solving Inequalities.........................................................33

Practice Quiz 2: Lessons 1-3 through 1-5....................39

1-6 Solving Compound and Absolute Value Inequalities....................................................................40

Study Guide and Review ..............................................47

Practice Test .....................................................................51

Standardized Test Practice...........................................52

Lesson 1-4, page 31

• Introduction 3

• Follow-Ups 27, 84, 120, 192

• Culmination 207

Unit 1Unit 1

Chapter Linear Relations and Functions 54

2-1 Relations and Functions..................................................56

2-2 Linear Equations..............................................................63

2-3 Slope...................................................................................68

Practice Quiz 1: Lessons 2-1 through 2-3 ....................74

2-4 Writing Linear Equations ...............................................75

2-5 Modeling Real-World Data: Using Scatter Plots .........81

Graphing Calculator Investigation:Lines of Regression ......................................................87

2-6 Special Functions .............................................................89

Practice Quiz 2: Lessons 2-4 through 2-6 ....................95

2-7 Graphing Inequalities .....................................................96

Study Guide and Review ............................................100

Practice Test ..................................................................105

Standardized Test Practice ........................................106

Snapshots 69, 84

Standardized Test Practice • Multiple Choice 62, 67, 74, 76, 78, 80, 86, 95, 99, 105,

106

• Short Response/Grid In 107

• Extended Response 107Study Organizer 55

Reading and Writing Mathematics • Reading Tips 56, 59, 71, 82

• Writing in Math 62, 67, 73, 80, 86, 94, 99

Prerequisite Skills • Getting Started 55

• Getting Ready for the Next Lesson 62, 67, 74, 80, 86, 95

Lesson 2-2, page 64

xx

Unit 1Unit 1

Chapter Systems of Equations andInequalities 108

3-1 Solving Systems of Equations by Graphing..............110

3-2 Solving Systems of Equations Algebraically.............116

Practice Quiz 1: Lessons 3-1 and 3-2 .........................122

3-3 Solving Systems of Inequalities by Graphing...........123

Graphing Calculator Investigation: Systems of Linear Inequalities ................................................128

3-4 Linear Programming.....................................................129


Algebra Activity: Graphing Equations in Three Variables ..........................................................136

3-5 Solving Systems of Equations in Three Variables ....138


Practice Test ..................................................................149



• Getting Ready for the Next Lesson115, 122, 127, 135

Study Organizer 109

Reading and WritingMathematics • Reading Tips 124, 129

• Writing in Math 114, 121, 127,134, 144

Standardized Test Practice • Multiple Choice 115, 117, 120,

122, 127, 134, 144, 150


• Extended Response 127, 151

Snapshots 135

xi

Lesson 3-4, page 131

• XXX XXX

• XXX XXX

• XXX XXX

Unit 1Unit 1

xii


• Getting Ready for the Next Lesson158, 166, 174, 181, 188, 194, 201

Study Organizer 153

Reading and WritingMathematics• Reading Tips 154, 175, 182

• Writing in Math 158, 166, 173,181, 187, 193, 200, 207

Standardized Test Practice• Multiple Choice 158, 166, 173,

179, 181, 187, 194, 201, 207,215, 216

• Short Response/Grid In 176, 194,207, 217


Chapter Matrices 152

4-1 Introduction to Matrices...............................................154

Spreadsheet Investigation: Organizing Data .........159

4-2 Operations with Matrices.............................................160

4-3 Multiplying Matrices ....................................................167

Practice Quiz 1: Lessons 4-1 through 4-3 ..................174

4-4 Transformations with Matrices ...................................175

4-5 Determinants..................................................................182

4-6 Cramer’s Rule ................................................................189


4-7 Identity and Inverse Matrices .....................................195

4-8 Using Matrices to Solve Systems of Equations.........202

Graphing Calculator Investigation: Augmented Matrices ................................................208


Practice Test ..................................................................215


Snapshots 206


• Introduction 219

• Follow-Ups 227, 326, 369

• Culmination 399

Snapshots 228

Standardized Test Practice • Multiple Choice 228, 232, 234, 236, 238, 244, 249,

255, 262, 267, 275, 281, 282



Study Organizer 221

Reading and Writing Mathematics • Reading Tips 229, 246, 252, 270, 271, 273

• Writing in Math 227, 232, 238, 243, 249, 255, 262,267, 275


• Getting Ready for the Next Lesson 228, 232, 238, 244,249, 256, 262, 267

xiii

Polynomial and RadicalEquations and Inequalities 218

Chapter Polynomials 220

5-1 Monomials......................................................................222

5-2 Polynomials....................................................................229

5-3 Dividing Polynomials...................................................233


5-4 Factoring Polynomials..................................................239

5-5 Roots of Real Numbers.................................................245

5-6 Radical Expressions ......................................................250


5-7 Rational Exponents .......................................................257

5-8 Radical Equations and Inequalities ............................263

Graphing Calculator Investigation: Solving Radical Equations and Inequalities by Graphing.....................................................................268

5-9 Complex Numbers........................................................270


Practice Test ..................................................................281



Unit 2Unit 2

xiv

Chapter Quadratic Functions and Inequalities 284

6-1 Graphing Quadratic Functions ...................................286

6-2 Solving Quadratic Equations by Graphing...............294

Graphing Calculator Investigation: Modeling Real-World Data ........................................................300

6-3 Solving Quadratic Equations by Factoring ...............301


6-4 Completing the Square.................................................306

6-5 The Quadratic Formula and the Discriminant .........313

Graphing Calculator Investigation: Families of Parabolas ................................................320

6-6 Analyzing Graphs of Quadratic Functions ...............322


6-7 Graphing and Solving Quadratic Inequalities..........329


Practice Test ..................................................................341



• Getting Ready for the Next Lesson293, 299, 305, 312, 319, 328

Study Organizer 285

Standardized Test Practice • Multiple Choice 292, 293, 299,

302, 303, 305, 312, 319, 327,335, 341, 342



Snapshots 328

Reading and WritingMathematics • Reading Tips 294, 306, 313, 316,

323

• Writing in Math 292, 299, 305,312, 319, 327, 334


Unit 2Unit 2

xv

Chapter Polynomial Functions 344

7-1 Polynomial Functions...................................................346

7-2 Graphing Polynomial Functions.................................353

Graphing Calculator Investigation: Modeling Real-World Data......................................359

7-3 Solving Equations Using Quadratic Techniques ......360


7-4 The Remainder and Factor Theorems........................365

7-5 Roots and Zeros.............................................................371

7-6 Rational Zero Theorem.................................................378


7-7 Operations on Functions ..............................................383

7-8 Inverse Functions and Relations.................................390

7-9 Square Root Functions and Inequalities ....................395


Practice Test ..................................................................405



Snapshots 368

Standardized Test Practice• Multiple Choice 352, 358, 364, 370, 377, 382, 389,

394, 399, 405, 406

• Short Response/Grid In 370, 374, 375, 407


Study Organizer 345

Reading and Writing Mathematics• Reading Tips 354, 372, 384, 391

• Writing in Math 352, 357, 364, 370, 377, 382, 389,394, 399



Advanced Functions andRelations 408

Chapter Conic Sections 410

8-1 Midpoint and Distance Formulas...............................412

Algebra Activity: Midpoint and Distance Formulas in Three Dimensions ...............................417

8-2 Parabolas .........................................................................419

8-3 Circles..............................................................................426


Algebra Activity: Investigating Ellipses....................432

8-4 Ellipses ............................................................................433

8-5 Hyperbolas .....................................................................441


8-6 Conic Sections................................................................449

Algebra Activity: Conic Sections ................................453

8-7 Solving Quadratic Systems..........................................455


Practice Test ..................................................................467


xvi



Study Organizer 411

Reading and WritingMathematics• Reading Tips 442, 449

• Writing in Math 416, 425, 430,439, 447, 452, 459

Standardized Test Practice• Multiple Choice 413, 414, 416, 425,

431, 439, 440, 447, 452, 459, 467,468



Snapshots 448


• Follow-Ups 429, 502, 529

• Culmination 565


Unit 3Unit 3

xvii


• Getting Ready for the Next Lesson478, 484, 490, 498, 504

Study Organizer 471

Reading and WritingMathematics• Writing in Math 477, 484, 490,

498, 503, 511

Standardized Test Practice• Multiple Choice 473, 476, 478, 484,

490, 498, 503, 504, 511, 517, 518



Snapshots 492

Chapter Rational Expressions and Equations 470

9-1 Multiplying and Dividing Rational Expressions......472

9-2 Adding and Subtracting Rational Expressions.........479


9-3 Graphing Rational Functions ......................................485

Graphing Calculator Investigation: Graphing Rational Functions ..................................491

9-4 Direct, Joint, and Inverse Variation ............................492


9-5 Classes of Functions .....................................................499

9-6 Solving Rational Equations and Inequalities ............505

Graphing Calculator Investigation: Solving Rational Equations by Graphing ..............512


Practice Test ..................................................................517




Unit 3Unit 3

Chapter Exponential and LogarithmicRelations 520

Algebra Activity: Investigating ExponentialFunctions ....................................................................522

10-1 Exponential Functions ..................................................523

10-2 Logarithms and Logarithmic Functions ....................531

Practice Quiz 1: Lessons 10-1 and 10-2 .....................538

Graphing Calculator Investigation: Modeling Real-World Data: Curve Fitting ............539

10-3 Properties of Logarithms ..............................................541

10-4 Common Logarithms....................................................547

Graphing Calculator Investigation: Solving Exponential and Logarithmic Equations and Inequalities ......................................552

10-5 Base e and Natural Logarithms...................................554

Practice Quiz 2: Lessons 10-3 through 10-5 ..............559

10-6 Exponential Growth and Decay..................................560


Practice Test ..................................................................571


xviii

Snapshots 535, 565


563, 564, 571, 572

• Short Response/Grid In 530, 546, 559, 564, 573


Study Organizer 521

Reading and Writing Mathematics • Writing in Math 530, 537, 546, 551, 559, 564


• Getting Ready for the Next Lesson 530, 538, 546, 551,559

Discrete Mathematics 574

Chapter Sequences and Series 576

11-1 Arithmetic Sequences ...................................................578

11-2 Arithmetic Series ...........................................................583

11-3 Geometric Sequences ....................................................588


Graphing Calculator Investigation: Limits .............593

11-4 Geometric Series............................................................594

11-5 Infinite Geometric Series ..............................................599

Spreadsheet Investigation: Amortizing Loans ......605

11-6 Recursion and Special Sequences ...............................606

Algebra Activity: Fractals ............................................611

11-7 The Binomial Theorem .................................................612


11-8 Proof and Mathematical Induction .............................618


Practice Test ..................................................................627



• Getting Ready for the Next Lesson582, 587, 592, 598, 604, 610, 617

Study Organizer 577

Reading and WritingMathematics• Reading Tips 606, 619

• Writing in Math 582, 587, 592,598, 603, 610, 616, 621


591, 592, 598, 603, 610, 616,621, 627, 628



Snapshots 604


• Follow-Ups 616, 635

• Culmination 685


xix

Unit 4Unit 4

xx

Chapter Probability and Statistics 630

12-1 The Counting Principle ................................................632

12-2 Permutations and Combinations ................................638

12-3 Probability ......................................................................644


12-4 Multiplying Probabilities .............................................651

12-5 Adding Probabilities.....................................................658

12-6 Statistical Measures.......................................................664


12-7 The Normal Distribution ..............................................671

12-8 Binomial Experiments ..................................................676

Algebra Activity: Simulations.....................................681

12-9 Sampling and Error.......................................................682

Algebra Activity: Testing Hypotheses .......................686


Practice Test ..................................................................693



Snapshots 658

Standardized Test Practice • Multiple Choice 633, 634, 636, 642, 649, 657, 662,

669, 675, 680, 685, 693, 694



Study Organizer 631

Reading and Writing Mathematics • Reading Tips 633, 638, 644, 646, 665, 669

• Writing in Math 636, 642, 649, 657, 662, 669, 675,679, 685



xxi

Trigonometry 696

Chapter Trigonometric Functions 698

Spreadsheet Investigation: Special Right Triangles .............................................700

13-1 Right Triangle Trigonometry .......................................701

13-2 Angles and Angle Measure .........................................709

Practice Quiz 1: Lessons 13-1 and 13-2 .....................715

Algebra Activity: Investigating Regular Polygons Using Trigonometry..................................................716

13-3 Trigonometric Functions of General Angles .............717

13-4 Law of Sines ....................................................................725

13-5 Law of Cosines ..............................................................733


13-6 Circular Functions.........................................................739

13-7 Inverse Trigonometric Functions ................................746


Practice Test ..................................................................757




Study Organizer 699

Reading and WritingMathematics• Reading Tips 701, 709, 711, 718,

740

• Writing in Math 708, 714, 724,732, 737, 744, 751


714, 724, 732, 737, 738, 745,751, 757, 758

• Short Response/Grid In 708, 724,732, 745, 751, 759


Snapshots 715


• Follow-Ups 708, 775

• Culmination 804


Unit 5Unit 5

xxii

Chapter Trigonometric Graphs and Identities 760

Snapshots 797


796, 804, 809, 810



Study Organizer 761

Reading and Writing Mathematics• Reading Tips 786, 788

• Writing in Math 768, 776, 781, 785, 790, 796, 804


• Getting Ready for the Next Lesson 768, 776, 781, 785,790, 797

14-1 Graphing Trigonometric Functions ............................762

14-2 Translations of Trigonometric Graphs .......................769

14-3 Trigonometric Identities ...............................................777


14-4 Verifying Trigonometric Identities ..............................782

14-5 Sum and Difference of Angles Formulas...................786

14-6 Double-Angle and Half-Angle Formulas ..................791


Graphing Calculator Investigation: Solving Trigonometric Equations ...........................798

14-7 Solving Trigonometric Equations ...............................799


Practice Test ..................................................................809


Student Handbook

SkillsPrerequisite Skills..................................................................................814Extra Practice .........................................................................................828Mixed Problem Solving........................................................................862Preparing for Standardized Tests .......................................................876

ReferenceEnglish-Spanish Glossary ......................................................................R1Selected Answers ..................................................................................R20Photo Credits.........................................................................................R86Index .......................................................................................................R87Symbols and Formulas ..............................................Inside Back Cover


First-Degree Equations and Inequalities 2 Chapter Solving Equations and Inequalities 4 ... Graphing...

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Transcript of First-Degree Equations and Inequalities 2 Chapter Solving Equations and Inequalities 4 ... Graphing...