© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

ContentsContentsContentsContentsContentsContentsContentsContentsContentsContentsContentsContentsContents

UNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS Planning the Unit 1a Unit 1 Overview 1 Getting Ready 2

Activity 1 Creating Equations—One to Two 3 Lesson 1-1 One-Variable Equations 3 Lesson 1-2 Two-Variable Equations 7 Lesson 1-3 Absolute Value Equations and Inequalities 11 Activity 1 Practice 15

Activity 2 Graphing to Find Solutions—Choices 17 Lesson 2-1 Graphing Two-Variable Equations 17 Lesson 2-2 Graphing Systems of Inequalities 21 Activity 2 Practice 27

Activity 3 Systems of Linear Equations—Monetary Systems Overload 29 Lesson 3-1 Solving Systems of Two Equations in Two Variables 29 Lesson 3-2 Solving Systems of Three Equations in Three Variables 36 Lesson 3-3 Matrix Operations 42 Lesson 3-4 Solving Matrix Equations 47 Activity 3 Practice 53

Embedded Assessment 1 Equations, Inequalities, and Systems—Gaming Systems 55

Activity 4 Piecewise-Defined Functions—Absolutely Piece-ful 57 Lesson 4-1 Introduction to Piecewise-Defined Functions 57 Lesson 4-2 Step Functions and Absolute Value Functions 61 Lesson 4-3 Transforming the Absolute Value Parent Function 65 Activity 4 Practice 71

Activity 5 Function Composition and Operations—New from Old 73 Lesson 5-1 Operations with Functions 73 Lesson 5-2 Function Composition 79 Lesson 5-3 More Function Composition 84 Activity 5 Practice 87

Activity 6 Inverse Functions—Old from New 89 Lesson 6-1 Finding Inverse Functions 89 Lesson 6-2 Graphs of Inverse Functions 93 Activity 6 Practice 97

Embedded Assessment 2 Piecewise-Defined, Composite, and Inverse Functions— Currency Conversion 99

UNIT 2 QUADRATIC FUNCTIONS Planning the Unit 101a Unit 2 Overview 101 Getting Ready 102

To the Teacher xi

Instructional Units

Contents v

v-x_SB_A2_TE_FM_TOC.indd Page 5 15/04/14 1:55 PM user-g-w-728 /103/SB00001_DEL/work/indd/TE/M02_High_School/FM/Application_files/TE_A2_FM

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

Contents continuedContents continuedContents Contents continuedcontinuedContents Contents Contents Contents Contents Contents continuedcontinuedcontinuedcontinuedcontinuedcontinued

Activity 7 Applications of Quadratic Functions—Fences 103 Lesson 7-1 Analyzing a Quadratic Function 103 Lesson 7-2 Factoring Quadratic Expressions 107 Lesson 7-3 Solving Quadratic Equations by Factoring 111 Lesson 7-4 More Uses for Factors 116 Activity 7 Practice 119

Activity 8 Introduction to Complex Numbers—Cardano’s Imaginary Numbers 121 Lesson 8-1 The Imaginary Unit, i 121 Lesson 8-2 Operations with Complex Numbers 126 Lesson 8-3 Factoring with Complex Numbers 132 Activity 8 Practice 135

Activity 9 Solving ax2 + bx + c = 0—Deriving the Quadratic Formula 137 Lesson 9-1 Completing the Square and Taking Square Roots 137 Lesson 9-2 The Quadratic Formula 141 Lesson 9-3 Solutions of Quadratic Equations 144 Activity 9 Practice 149

Embedded Assessment 1 Applications of Quadratic Functions and Equations— No Horsing Around 151

Activity 10 Writing Quadratic Equations—What Goes Up Must Come Down 153 Lesson 10-1 Parabolas and Quadratic Equations 153 Lesson 10-2 Writing a Quadratic Function Given Three Points 163 Lesson 10-3 Quadratic Regression 167 Activity 10 Practice 171

Activity 11 Transformations of y = x2—Parent Parabola 173 Lesson 11-1 Translations of Parabolas 173 Lesson 11-2 Shrinking, Stretching, and Reflecting Parabolas 178 Lesson 11-3 Vertex Form 186 Activity 11 Practice 189

Embedded Assessment 2 Writing and Transforming Quadratic Functions— The Safari Experience 191

Activity 12 Graphing Quadratics and Quadratic Inequalities—Calendar Art 193 Lesson 12-1 Key Features of Quadratic Functions 193 Lesson 12-2 More Key Features of Quadratic Functions 197 Lesson 12-3 Graphing Quadratic Functions 200 Lesson 12-4 The Discriminant 204 Lesson 12-5 Graphing Quadratic Inequalities 206 Activity 12 Practice 209

Activity 13 Systems of Linear and Nonlinear Equations—Supply and Demand 211 Lesson 13-1 Solving a System Graphically 211 Lesson 13-2 Solving a System Algebraically 217 Activity 13 Practice 221

Embedded Assessment 3 Graphing Quadratic Functions and Solving Systems— The Green Monster 223

vi SpringBoard® Mathematics Algebra 2

v-x_SB_A2_TE_FM_TOC.indd Page 6 15/04/14 1:55 PM user-g-w-728 /103/SB00001_DEL/work/indd/TE/M02_High_School/FM/Application_files/TE_A2_FM

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

UNIT 3 POLYNOMIALS Planning the Unit 225a Unit 3 Overview 225 Getting Ready 226

Activity 14 Introduction to Polynomials—Postal Service 227 Lesson 14-1 Polynomials 227 Lesson 14-2 Some Attributes of Polynomial Functions 231 Lesson 14-3 Even and Odd Functions 237 Activity 14 Practice 239

Activity 15 Polynomial Operations—Polly’s Pasta 241 Lesson 15-1 Adding and Subtracting Polynomials 241 Lesson 15-2 Multiplying Polynomials 245 Lesson 15-3 Dividing Polynomials 248 Activity 15 Practice 253

Activity 16 Binomial Theorem—Pascal’s Triangle 255 Lesson 16-1 Introduction to Pascal’s Triangle 255 Lesson 16-2 Applying the Binomial Theorem 259 Activity 16 Practice 263

Embedded Assessment 1 Polynomial Operations—This Test is Square 265

Activity 17 Factors of Polynomials—How Many Roots? 267 Lesson 17-1 Algebraic Methods 267 Lesson 17-2 The Fundamental Theorem of Algebra 271 Activity 17 Practice 275

Activity 18 Graphs of Polynomials—Getting to the End Behavior 277 Lesson 18-1 Graphing Polynomial Functions 277 Lesson 18-2 Finding the Roots of a Polynomial Function 281 Lesson 18-3 Comparing Polynomial Functions 287 Activity 18 Practice 289

Embedded Assessment 2 Factoring and Graphing Polynomials—Sketch Artist 291

UNIT 4 SERIES, EXPONENTIAL AND LOGARITHMIC FUNCTIONS Planning the Unit 293a Unit 4 Overview 293 Getting Ready 294

Activity 19 Arithmetic Sequences and Series—Arithmetic Alkanes 295 Lesson 19-1 Arithmetic Sequences 295 Lesson 19-2 Arithmetic Series 299 Lesson 19-3 Sigma Notation 303 Activity 19 Practice 305

Activity 20 Geometric Sequences and Series—Squares with Patterns 307 Lesson 20-1 Geometric Sequences 307 Lesson 20-2 Geometric Series 312 Lesson 20-3 Convergence of Series 317 Activity 20 Practice 319

Contents vii

v-x_SB_A2_TE_FM_TOC.indd Page 7 15/04/14 1:55 PM user-g-w-728 /103/SB00001_DEL/work/indd/TE/M02_High_School/FM/Application_files/TE_A2_FM

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

Contents continuedContents continuedContents Contents continuedcontinuedContents Contents Contents Contents Contents Contents continuedcontinuedcontinuedcontinuedcontinuedcontinued

Embedded Assessment 1 Sequences and Series—The Chessboard Problem 321

Activity 21 Exponential Functions and Graphs—Sizing Up the Situation 323 Lesson 21-1 Exploring Exponential Patterns 323 Lesson 21-2 Exponential Functions 326 Lesson 21-3 Exponential Graphs and Asymptotes 329 Lesson 21-4 Transforming Exponential Functions 331 Lesson 21-5 Natural Base Exponential Functions 336 Activity 21 Practice 341

Activity 22 Logarithms and Their Properties—Earthquakes and Richter Scale 343 Lesson 22-1 Exponential Data 343 Lesson 22-2 The Common Logarithm Function 348 Lesson 22-3 Properties of Logarithms 350 Lesson 22-4 More Properties of Logarithms 353 Activity 22 Practice 355

Embedded Assessment 2 Exponential Functions and Common Logarithms— Whether or Not 357

Activity 23 Inverse Functions: Exponential and Logarithmic Functions— Undoing It All 359 Lesson 23-1 Logarithms in Other Bases 359 Lesson 23-2 Properties of Logarithms and the Change of Base Formula 362 Lesson 23-3 Graphs of Logarithmic Functions 365 Activity 23 Practice 369

Activity 24 Logarithmic and Exponential Equations and Inequalities— College Costs 371 Lesson 24-1 Exponential Equations 371 Lesson 24-2 Solving Equations by Using Logarithms 373 Lesson 24-3 Logarithmic Equations 376 Lesson 24-4 Exponential and Logarithmic Inequalities 379 Activity 24 Practice 381

Embedded Assessment 3 Exponential and Logarithmic Equations— Evaluating Your Interest 383

UNIT 5 RADICAL AND RATIONAL FUNCTIONS Planning the Unit 385a Unit 5 Overview 385 Getting Ready 386

Activity 25 Square Root and Cube Root Functions—Go, Boat, Go! 387 Lesson 25-1 Square Root Functions 387 Lesson 25-2 Solving Square Root Equations 391 Lesson 25-3 Cube Root Functions 394 Lesson 25-4 Solving Cube Root Equations 397 Activity 25 Practice 399

viii SpringBoard® Mathematics Algebra 2

v-x_SB_A2_TE_FM_TOC.indd Page 8 15/04/14 1:55 PM user-g-w-728 /103/SB00001_DEL/work/indd/TE/M02_High_School/FM/Application_files/TE_A2_FM

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

Activity 26 Inverses: Roots, Squares, and Cubes—Swing, Swing, Swing 401 Lesson 26-1 Square Root Functions and Regressions 401 Lesson 26-2 Square Root and Quadratic Functions 406 Lesson 26-3 Cube Root and Cubic Functions 410 Activity 26 Practice 413

Embedded Assessment 1 Radical Functions: Square Roots, Cube Roots, and Their Inverses—How Big is That Ball? 415

Activity 27 Introduction to Rational Functions—Planning a Summer Camp 417 Lesson 27-1 Formulating and Graphing a Rational Function 417 Lesson 27-2 Formulating and Graphing More Rational Functions 421 Lesson 27-3 Identifying Asymptotes 425 Activity 27 Practice 429

Activity 28 Inverse Variation and Rational Functions—Stream Survival 431 Lesson 28-1 Inverse Variation and Combined Variation 431 Lesson 28-2 Transformations of the Parent Rational Function 435 Activity 28 Practice 441

Embedded Assessment 2 Rational Functions and Variation—A Condo for My Cat 443

Activity 29 Simplifying Rational Expressions—It’s All Rational 445 Lesson 29-1 Multiplying and Dividing Rational Expressions 445 Lesson 29-2 Adding and Subtracting Rational Expressions 449 Lesson 29-3 Finding Horizontal and Vertical Asymptotes 453 Lesson 29-4 Graphing Rational Functions 457 Activity 29 Practice 461

Activity 30 Rational Equations and Inequalities—A Rational Pastime 463 Lesson 30-1 Solving Rational Equations 463 Lesson 30-2 Solving Rational Inequalities 467 Activity 30 Practice 471

Embedded Assessment 3 Rational Expressions, Equations, and Inequalities— Work It Out! 473

UNIT 6 TRIGONOMETRY Planning the Unit 475a Unit 6 Overview 475 Getting Ready 476

Activity 31 Understanding Radian Measure—Revolving Restaurant 477 Lesson 31-1 Radian Measure 477 Lesson 31-2 Applying Radian Measure 482 Activity 31 Practice 485

Activity 32 Trigonometric Functions—Which Angle is Up? 487 Lesson 32-1 Placing the Unit Circle on the Coordinate Plane 487 Lesson 32-2 Special Right Triangles and the Unit Circle 494 Activity 32 Practice 499

Contents ix

v-x_SB_A2_TE_FM_TOC.indd Page 9 15/04/14 1:55 PM user-g-w-728 /103/SB00001_DEL/work/indd/TE/M02_High_School/FM/Application_files/TE_A2_FM

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

© 2

015

Colle

ge B

oard

. All

righ

ts re

serv

ed.

Contents continuedContents continuedContents Contents continuedcontinuedContents Contents Contents Contents Contents Contents continuedcontinuedcontinuedcontinuedcontinuedcontinued

Activity 33 Trigonometric Identities: Pythagorean Connection—More Than Just Triangles 501 Lesson 33-1 The Pythagorean Identity 501 Lesson 33-2 Other Trigonometric Identities 504 Activity 33 Practice 507

Embedded Assessment 1 Radians, Unit Circles, and Trigonometry—A Floral Clock 509

Activity 34 Graphs of Trigonometric Functions—Creation of a Mural 511 Lesson 34-1 Periodic Functions 511 Lesson 34-2 The Sine Function 515 Lesson 34-3 The Cosine Function 521 Lesson 34-4 The Tangent Function 527 Lesson 34-5 Translating Trigonometric Functions 533 Activity 34 Practice 539

Activity 35 Choosing Functions to Model Periodic Phenomena—The Sky Wheel 541 Lesson 35-1 Modeling Periodic Phenomena 541 Activity 35 Practice 547

Embedded Assessment 2 Trigonometric Functions—Totally Tires 549

UNIT 7 PROBABILITY AND STATISTICS Planning the Unit 551a Unit 7 Overview 551 Getting Ready 552

Activity 36 Normal Distribution—Take Me Out to the Ballgame 553 Lesson 36-1 Shapes of Distributions 553 Lesson 36-2 Characteristics of the Normal Distribution 558 Lesson 36-3 z-Scores and their Probabilities 562 Lesson 36-4 Modeling with the Normal Distribution 568 Activity 36 Practice 573

Activity 37 Random Sampling—Part-Time Jobs 577 Lesson 37-1 Surveys 577 Lesson 37-2 Experiments 582 Lesson 37-3 Observational Studies 586 Activity 37 Practice 589

Embedded Assessment 1 Normal Models, Surveys, and Experiments— Researching Readers 591

Activity 38 Simulations—Is Martin Improving? 593 Lesson 38-1 Devising Simulations 593 Lesson 38-2 Confirming Data with Simulations 600 Activity 38 Practice 604

Activity 39 Margin of Error—Can't Get No Satisfaction 605 Lesson 39-1 Introduction to Margin of Error 605 Lesson 39-2 Computing Margin of Error 611 Activity 39 Practice 618

x SpringBoard® Mathematics Algebra 2

v-x_SB_A2_TE_FM_TOC.indd Page 10 15/04/14 1:55 PM user-g-w-728 /103/SB00001_DEL/work/indd/TE/M02_High_School/FM/Application_files/TE_A2_FM