Page 1
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
Page 2
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
Page 3
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
Practice Quiz 2: Lessons 3-3 and 3-4 .........................135
Algebra Activity: Graphing Equations in Three Variables ..........................................................136
3-5 Solving Systems of Equations in Three Variables ....138
Study Guide and Review ............................................145
Practice Test ..................................................................149
Standardized Test Practice ........................................150
Prerequisite Skills• Getting Started 109
• 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
• Short Response/Grid In 149, 151
• Extended Response 127, 151
Snapshots 135
xi
Lesson 3-4, page 131
Page 4
• XXX XXX
• XXX XXX
• XXX XXX
Unit 1Unit 1
xii
Prerequisite Skills• Getting Started 153
• 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
• Extended Response 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
Practice Quiz 2: Lessons 4-4 through 4-6 ..................194
4-7 Identity and Inverse Matrices .....................................195
4-8 Using Matrices to Solve Systems of Equations.........202
Graphing Calculator Investigation: Augmented Matrices ................................................208
Study Guide and Review ............................................209
Practice Test ..................................................................215
Standardized Test Practice ........................................216
Snapshots 206
Lesson 4-6, page 193
Page 5
• 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
• Short Response/Grid In 283
• Extended Response 283
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
Prerequisite Skills • Getting Started 221
• 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
Practice Quiz 1: Lessons 5-1 through 5-3 ..................238
5-4 Factoring Polynomials..................................................239
5-5 Roots of Real Numbers.................................................245
5-6 Radical Expressions ......................................................250
Practice Quiz 2: Lessons 5-4 through 5-6 ..................256
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
Study Guide and Review ............................................276
Practice Test ..................................................................281
Standardized Test Practice ........................................282
Lesson 5-7, page 259
Page 6
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
Practice Quiz 1: Lessons 6-1 through 6-3 ..................305
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
Practice Quiz 2: Lessons 6-4 through 6-6 ..................328
6-7 Graphing and Solving Quadratic Inequalities..........329
Study Guide and Review ............................................336
Practice Test ..................................................................341
Standardized Test Practice ........................................342
Prerequisite Skills • Getting Started 285
• 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
• Short Response/Grid In 343
• Extended Response 343
Snapshots 328
Reading and WritingMathematics • Reading Tips 294, 306, 313, 316,
323
• Writing in Math 292, 299, 305,312, 319, 327, 334
Lesson 6-4, page 311
Page 7
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
Practice Quiz 1: Lessons 7-1 through 7-3 ..................364
7-4 The Remainder and Factor Theorems........................365
7-5 Roots and Zeros.............................................................371
7-6 Rational Zero Theorem.................................................378
Practice Quiz 2: Lessons 7-4 through 7-6 ..................382
7-7 Operations on Functions ..............................................383
7-8 Inverse Functions and Relations.................................390
7-9 Square Root Functions and Inequalities ....................395
Study Guide and Review ............................................400
Practice Test ..................................................................405
Standardized Test Practice ........................................406
Lesson 7-1, page 346
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
• Extended Response 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
Prerequisite Skills• Getting Started 345
• Getting Ready for the Next Lesson 352, 358, 364, 370,377, 382, 389, 394
Page 8
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
Practice Quiz 1: Lessons 8-1 and 8-3 .........................431
Algebra Activity: Investigating Ellipses....................432
8-4 Ellipses ............................................................................433
8-5 Hyperbolas .....................................................................441
Practice Quiz 2: Lessons 8-4 and 8-5 .........................448
8-6 Conic Sections................................................................449
Algebra Activity: Conic Sections ................................453
8-7 Solving Quadratic Systems..........................................455
Study Guide and Review ............................................461
Practice Test ..................................................................467
Standardized Test Practice ........................................468
xvi
Prerequisite Skills• Getting Started 411
• Getting Ready for the Next Lesson416, 425, 431, 440, 448, 452
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
• Short Response/Grid In 469
• Extended Response 469
Snapshots 448
• Introduction 409
• Follow-Ups 429, 502, 529
• Culmination 565
Lesson 8-4, page 435
Page 9
Unit 3Unit 3
xvii
Prerequisite Skills• Getting Started 471
• 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
• Short Response/Grid In 519
• Extended Response 519
Snapshots 492
Chapter Rational Expressions and Equations 470
9-1 Multiplying and Dividing Rational Expressions......472
9-2 Adding and Subtracting Rational Expressions.........479
Practice Quiz 1: Lessons 9-1 and 9-2 .........................484
9-3 Graphing Rational Functions ......................................485
Graphing Calculator Investigation: Graphing Rational Functions ..................................491
9-4 Direct, Joint, and Inverse Variation ............................492
Practice Quiz 2: Lessons 9-3 and 9-4 .........................498
9-5 Classes of Functions .....................................................499
9-6 Solving Rational Equations and Inequalities ............505
Graphing Calculator Investigation: Solving Rational Equations by Graphing ..............512
Study Guide and Review ............................................513
Practice Test ..................................................................517
Standardized Test Practice ........................................518
Lesson 9-5, page 503
Page 10
Lesson 10-6, page 564
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
Study Guide and Review ............................................566
Practice Test ..................................................................571
Standardized Test Practice ........................................572
xviii
Snapshots 535, 565
Standardized Test Practice• Multiple Choice 530, 537, 538, 546, 551, 559, 562,
563, 564, 571, 572
• Short Response/Grid In 530, 546, 559, 564, 573
• Extended Response 573
Study Organizer 521
Reading and Writing Mathematics • Writing in Math 530, 537, 546, 551, 559, 564
Prerequisite Skills • Getting Started 521
• Getting Ready for the Next Lesson 530, 538, 546, 551,559
Page 11
Discrete Mathematics 574
Chapter Sequences and Series 576
11-1 Arithmetic Sequences ...................................................578
11-2 Arithmetic Series ...........................................................583
11-3 Geometric Sequences ....................................................588
Practice Quiz 1: Lessons 11-1 through 11-3 ..............592
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
Practice Quiz 2: Lessons 11-4 through 11-7 ..............617
11-8 Proof and Mathematical Induction .............................618
Study Guide and Review ............................................622
Practice Test ..................................................................627
Standardized Test Practice ........................................628
Prerequisite Skills• Getting Started 577
• 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
Standardized Test Practice• Multiple Choice 582, 587, 588,
591, 592, 598, 603, 610, 616,621, 627, 628
• Short Response/Grid In 629
• Extended Response 629
Snapshots 604
• Introduction 575
• Follow-Ups 616, 635
• Culmination 685
Lesson 11-5, page 603
xix
Page 12
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
Practice Quiz 1: Lessons 12-1 through 12-3 ..............650
12-4 Multiplying Probabilities .............................................651
12-5 Adding Probabilities.....................................................658
12-6 Statistical Measures.......................................................664
Practice Quiz 2: Lessons 12-4 through 12-6 ..............670
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
Study Guide and Review ............................................687
Practice Test ..................................................................693
Standardized Test Practice ........................................694
Lesson 12-3, page 648
Snapshots 658
Standardized Test Practice • Multiple Choice 633, 634, 636, 642, 649, 657, 662,
669, 675, 680, 685, 693, 694
• Short Response/Grid In 680, 695
• Extended Response 695
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
Prerequisite Skills • Getting Started 631
• Getting Ready for the Next Lesson 637, 643, 650, 657,663, 670, 675, 680
Page 13
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
Practice Quiz 2: Lessons 13-3 through 13-5 ..............738
13-6 Circular Functions.........................................................739
13-7 Inverse Trigonometric Functions ................................746
Study Guide and Review ............................................752
Practice Test ..................................................................757
Standardized Test Practice ........................................758
Prerequisite Skills• Getting Started 699
• Getting Ready for the Next Lesson708, 715, 724, 732, 738, 745
Study Organizer 699
Reading and WritingMathematics• Reading Tips 701, 709, 711, 718,
740
• Writing in Math 708, 714, 724,732, 737, 744, 751
Standardized Test Practice• Multiple Choice 702, 706, 708,
714, 724, 732, 737, 738, 745,751, 757, 758
• Short Response/Grid In 708, 724,732, 745, 751, 759
• Extended Response 759
Snapshots 715
• Introduction 697
• Follow-Ups 708, 775
• Culmination 804
Lesson 13-6, page 744
Page 14
Unit 5Unit 5
xxii
Chapter Trigonometric Graphs and Identities 760
Snapshots 797
Standardized Test Practice• Multiple Choice 768, 776, 781, 783, 784, 785, 790,
796, 804, 809, 810
• Short Response/Grid In 811
• Extended Response 811
Study Organizer 761
Reading and Writing Mathematics• Reading Tips 786, 788
• Writing in Math 768, 776, 781, 785, 790, 796, 804
Prerequisite Skills• Getting Started 761
• 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
Practice Quiz 1: Lessons 14-1 through 14-3 ..............781
14-4 Verifying Trigonometric Identities ..............................782
14-5 Sum and Difference of Angles Formulas...................786
14-6 Double-Angle and Half-Angle Formulas ..................791
Practice Quiz 2: Lessons 14-4 through 14-6 ..............797
Graphing Calculator Investigation: Solving Trigonometric Equations ...........................798
14-7 Solving Trigonometric Equations ...............................799
Study Guide and Review ............................................805
Practice Test ..................................................................809
Standardized Test Practice ........................................810
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
Lesson 14-7, page 803