First-Degree Equations and Inequalities 2 Chapter Solving Equations and Inequalities 4 Introduction 3 Follow-Ups 27, 84, 120, 192 Culmination 207 Getting Started 5 Getting Ready for the Next Lesson 10, 18, 27, 32, 39 Study Organizer 5 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...52 Reading Math Tips 11, 12, 34, 35 Writing in Math 10, 17, 27, 31, 38, 45 Lesson 1-4, page 31 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
Unit 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 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...106 Getting Started 55 Getting Ready for the Next Lesson 62, 67, 74, 80, 86, 95 Study Organizer 55 Multiple Choice 62, 67, 74, 76, 78, 80, 86, 95, 99, 105, 106 Short Response/Grid In 107 Extended Response 107 Reading Tips 56, 59, 71, 82 Writing in Math 62, 67, 73, 80, 86, 94, 99 Snapshots 69, 84 Lesson 2-2, page 64 x
Unit 1 Chapter Getting Started 109 Getting Ready for the Next Lesson 115, 122, 127, 135 Study Organizer 109 Reading Tips 124, 129 Writing in Math 114, 121, 127, 134, 144 Systems of Equations and Inequalities 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 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...150 Multiple Choice 115, 117, 120, 122, 127, 134, 144, 150 Short Response/Grid In 149, 151 Extended Response 127, 151 Snapshots 135 Lesson 3-4, page 131 xi
Unit 1 Chapter Matrices 152 Getting Started 153 XXX Getting XXXReady for the Next Lesson 158, 166, 174, 181, 188, 194, 201 XXX XXX XXX XXX Study Organizer 153 Reading Tips 154, 175, 182 Writing in Math 158, 166, 173, 181, 187, 193, 200, 207 Multiple Choice 158, 166, 173, 179, 181, 187, 194, 201, 207, 215, 216 Short Response/Grid In 176, 194, 207, 217 Extended Response 217 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 Augmented Matrices...208 Study Guide and Review...209 Practice Test...215...216 Snapshots 206 Lesson 4-6, page 193 xii
Polynomial and Radical Equations and Inequalities 218 Chapter Polynomials 220 Introduction 219 Follow-Ups 227, 326, 369 Culmination 399 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 Solving Radical Equations and Inequalities by Graphing...268 5-9 Complex Numbers...270 Study Guide and Review...276 Practice Test...281...282 Lesson 5-7, page 259 Getting Started 221 Getting Ready for the Next Lesson 228, 232, 238, 244, 249, 256, 262, 267 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 Tips 229, 246, 252, 270, 271, 273 Writing in Math 227, 232, 238, 243, 249, 255, 262, 267, 275 Snapshots 228 xiii
Unit 2 Chapter Getting Started 285 Getting Ready for the Next Lesson 293, 299, 305, 312, 319, 328 Study Organizer 285 Reading Tips 294, 306, 313, 316, 323 Writing in Math 292, 299, 305, 312, 319, 327, 334 Multiple Choice 292, 293, 299, 302, 303, 305, 312, 319, 327, 335, 341, 342 Short Response/Grid In 343 Extended Response 343 Quadratic Functions and Inequalities 284 6-1 Graphing Quadratic Functions...286 6-2 Solving Quadratic Equations by Graphing...294 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 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...342 Lesson 6-4, page 311 Snapshots 328 xiv
Unit 2 Chapter Polynomial Functions 344 7-1 Polynomial Functions...346 7-2 Graphing Polynomial Functions...353 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...406 Lesson 7-1, page 346 Getting Started 345 Getting Ready for the Next Lesson 352, 358, 364, 370, 377, 382, 389, 394 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 Tips 354, 372, 384, 391 Writing in Math 352, 357, 364, 370, 377, 382, 389, 394, 399 Snapshots 368 xv
Advanced Functions and Relations 408 Chapter Conic Sections 410 Introduction 409 Follow-Ups 429, 502, 529 Culmination 565 Getting Started 411 Getting Ready for the Next Lesson 416, 425, 431, 440, 448, 452 Study Organizer 411 Reading Tips 442, 449 Writing in Math 416, 425, 430, 439, 447, 452, 459 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...468 Multiple Choice 413, 414, 416, 425, 431, 439, 440, 447, 452, 459, 467, 468 Short Response/Grid In 469 Extended Response 469 Snapshots 448 Lesson 8-4, page 435 xvi
Unit 3 Getting Started 471 Getting Ready for the Next Lesson 478, 484, 490, 498, 504 Study Organizer 471 Chapter Writing in Math 477, 484, 490, 498, 503, 511 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 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 Solving Rational Equations by Graphing...512 Study Guide and Review...513 Practice Test...517...518 Multiple Choice 473, 476, 478, 484, 490, 498, 503, 504, 511, 517, 518 Short Response/Grid In 519 Extended Response 519 Snapshots 492 Lesson 9-5, page 503 xvii
Unit 3 Chapter Lesson 10-6, page 564 Exponential and Logarithmic Relations 520 Algebra Activity: Investigating Exponential Functions...522 10-1 Exponential Functions...523 10-2 Logarithms and Logarithmic Functions...531 Practice Quiz 1: Lessons 10-1 and 10-2...538 Modeling Real-World Data: Curve Fitting...539 10-3 Properties of Logarithms...541 10-4 Common Logarithms...547 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...572 Getting Started 521 Getting Ready for the Next Lesson 530, 538, 546, 551, 559 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 Writing in Math 530, 537, 546, 551, 559, 564 Snapshots 535, 565 xviii
Discrete 574 Chapter Sequences and Series 576 Introduction 575 Follow-Ups 616, 635 Culmination 685 Getting Started 577 Getting Ready for the Next Lesson 582, 587, 592, 598, 604, 610, 617 Study Organizer 577 Reading Tips 606, 619 Writing in Math 582, 587, 592, 598, 603, 610, 616, 621 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 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...628 Multiple Choice 582, 587, 588, 591, 592, 598, 603, 610, 616, 621, 627, 628 Short Response/Grid In 629 Extended Response 629 Snapshots 604 Lesson 11-5, page 603 xix
Unit 4 Chapter Probability and Statistics 630 Lesson 12-3, page 648 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...694 Getting Started 631 Getting Ready for the Next Lesson 637, 643, 650, 657, 663, 670, 675, 680 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 Tips 633, 638, 644, 646, 665, 669 Writing in Math 636, 642, 649, 657, 662, 669, 675, 679, 685 Snapshots 658 xx
Trigonometry 696 Chapter Trigonometric Functions 698 Introduction 697 Follow-Ups 708, 775 Culmination 804 Getting Started 699 Getting Ready for the Next Lesson 708, 715, 724, 732, 738, 745 Study Organizer 699 Reading Tips 701, 709, 711, 718, 740 Writing in Math 708, 714, 724, 732, 737, 744, 751 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...758 Lesson 13-6, page 744 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 xxi
Unit 5 Lesson 14-7, page 803 Chapter Trigonometric Graphs and Identities 760 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 Solving Trigonometric Equations...798 14-7 Solving Trigonometric Equations...799 Study Guide and Review...805 Practice Test...809...810 Student Handbook Skills...814 Extra Practice...828 Mixed Problem Solving...862 Preparing for Standardized Tests...876 Reference English-Spanish Glossary...R1 Selected Answers...R20 Photo Credits...R86 Index...R87 Symbols and Formulas...Inside Back Cover Getting Started 761 Getting Ready for the Next Lesson 768, 776, 781, 785, 790, 797 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 Tips 786, 788 Writing in Math 768, 776, 781, 785, 790, 796, 804 Snapshots 797 xxii