Preparing for AdvAdvanced Algebraanced Algebras3.amazonaws.com/ecommerce-prod.mheducation.com/... · ii connectED.mcgraw-hill.comc Your Digital Math Portal Unit 1 | Linear Relations

i

connectED.mcgraw-hill.comccccc Your Digital Math Portal

Preparing for Preparing for Advanced AlgebraAdvanced Algebra

Personal Tutor

p. P6Multilingual

eGlossary

p. P2

Vocabulary

p. P4Foldables

p. P2

Table of ContentsEd

Fre

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/Sto

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es

Get Started On Chapter 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P2

Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P3

0-1 Representing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P4

0-2 FOIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P6

0-3 Factoring Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P7

0-4 Counting Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P9

0-5 Adding Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P13

0-6 Multiplying Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P16

0-7 Congruent and Similar Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P20

0-8 The Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P22

0-9 Measures of Center, Spread, and Position . . . . . . . . . . . . . . . . . . . . . . . . .P24

Posttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P29

Preparing for Advanced Algebra

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ii ii

Your Digital Math PortalconnectED.mcgraw-hill.comccccc

Unit 1 | Linear Relations and Functions

Personal Tutor

pp. 6, 63Multilingual

eGlossary

pp. 4, 60

Vocabulary

pp. 5, 69Animation

pp. 12, 84

Equations and Equations and InequalitiesInequalities

Jon Boyes/Photographer’s Choice/Getty Images

Equations and Inequalities

Get Ready for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1-1 Expressions and Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

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

1-3 Solving Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

1-4 Solving Absolute Value Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27

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

Explore: Algebra Lab Interval Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

1-6 Solving Compound and Absolute Value Inequalities . . . . . . . . . . . . . . . . . . . .41

Assessment

Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53

Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54

Standardized Test Practice, Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56

A.SSE.1.a, A.SSE.1.b

A.SSE.2

A.CED.1

A.SSE.1.b, A.CED.1

A.CED.1, A.CED.3

A.CED.1, A.CED.3

MathematicalContent

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iii iii


Self-Check

Practice

pp. 7, 127

Foldables

pp. 4, 60Graphing

Calculator

p. 90

Virtual

Manipulatives

pp. 28, 61

Linear Relations Linear Relations and Functionsand Functions

Roin

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es

Linear Relations and Functions

Get Ready for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2-1 Relations and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61

Extend: Algebra Lab Discrete and Continuous Functions . . . . . . . . . . . . . . . . . . . . . . . 68

2-2 Linear Relations and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69

Extend: Algebra Lab Roots of Equations and Zeros of Functions . . . . . . . . . . . . . . . . . . 75

2-3 Rate of Change and Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76

2-4 Writing Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83

Extend: Graphing Technology Lab Direct Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91

2-5 Scatter Plots and Lines of Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92

Extend: Algebra Lab Correlation and Causation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

2-6 Special Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101

Explore: Graphing Technology Lab Families of Lines. . . . . . . . . . . . . . . . . . . . . . . . . . 108

2-7 Parent Functions and Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109

2-8 Graphing Linear and Absolute Value Inequalities. . . . . . . . . . . . . . . . . . . . . .117

Assessment

Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127

Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128

Standardized Test Practice, Chapters 1–2 . . . . . . . . . . . . . . . . . . . . . . . . . .130

F.IF.4, F.IF.5

F.IF.4

F.IF.4, F.IF.9

F.IF.4

F.IF.4, F.IF.6

A.SSE.1.b, A.CED.2

F.IF.4

F.IF.4

F.IF.4

F.IF.4, F.IF.7.b

F.BF.3

F.IF.4, F.BF.3

A.CED.3

MathematicalContent

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iv iv



Personal Tutor


eGlossary

pp. 134, 218

Vocabulary

pp. 206, 290Animation

pp. 146, 247

Systems of Equations Systems of Equations and Inequalitiesand Inequalities

DreamPictures/Blend Im

ages/Getty Images

Systems of Equations and Inequalities

Get Ready for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Explore: Graphing Technology Lab Intersections of Graphs . . . . . . . . . . . . . . . . . . . . . 135

3-1 Solving Systems of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136

3-2 Solving Systems of Inequalities by Graphing . . . . . . . . . . . . . . . . . . . . . . . . .146

Extend: Graphing Technology Lab Systems of Linear Inequalities . . . . . . . . . . . . . . . . 153

3-3 Optimization with Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . .154

3-4 Systems of Equations in Three Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . .161

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168

Explore: Spreadsheet Lab Organizing Data with Matrices. . . . . . . . . . . . . . . . . . . . . . 169

3-5 Operations with Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .171

3-6 Multiplying Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .179

Extend: Graphing Technology Lab Operations with Matrices . . . . . . . . . . . . . . . . . . . 187

3-7 Solving Systems of Equations Using Cramer’s Rule . . . . . . . . . . . . . . . . . . . .189

3-8 Solving Systems of Equations Using Inverse Matrices. . . . . . . . . . . . . . . . . .198

Extend: Graphing Technology Lab Augmented Matrices . . . . . . . . . . . . . . . . . . . . . . . 205

Assessment


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .211



A.CED.3, A.REI.11

A.CED.3

A.CED.3

A.CED.3

A.CED.3

A.CED.3

MathematicalContent

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v v

Unit 2 | Quadratic, Polynomial, and Radical Functions and Relations

Quadratic Functions Quadratic Functions and Relationsand Relations

Virtual

Manipulatives

pp. 137, 219

Graphing

Calculator

pp. 205, 237

Foldables

pp. 134, 218Self-Check

Practice

pp. 183, 295

Blac

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4-1 Graphing Quadratic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .219

Extend: Graphing Technology Lab Modeling Real-World Data . . . . . . . . . . . . . . . . . . . 228

4-2 Solving Quadratic Equations by Graphing. . . . . . . . . . . . . . . . . . . . . . . . . . . .229

Extend: Graphing Technology Lab Solving Quadratic Equations by Graphing . . . . . . . . 237

4-3 Solving Quadratic Equations by Factoring . . . . . . . . . . . . . . . . . . . . . . . . . . .238

4-4 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .246

Extend: Algebra Lab The Complex Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255

4-5 Completing the Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256

Extend: Graphing Technology Lab Solving Quadratic Equations. . . . . . . . . . . . . . . . . . 263

4-6 The Quadratic Formula and the Discriminant . . . . . . . . . . . . . . . . . . . . . . . . .264

Explore: Graphing Technology Lab Families of Parabolas . . . . . . . . . . . . . . . . . . . . . . 273

4-7 Transformations of Quadratic Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .275

Extend: Algebra Lab Quadratics and Rate of Change . . . . . . . . . . . . . . . . . . . . . . . . . 281

4-8 Quadratic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .282

Extend: Graphing Technology Lab Modeling Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Assessment


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .295



Quadratic Functions and Relations

A.SSE.1.a, F.IF.9

F.IF.4

A.CED.2, F.IF.4

A.REI.11

A.SSE.2, F.IF.8.a

N.CN.1, N.CN.2

N.CN.7, F.IF.8.a

N.CN.7

N.CN.7, A.SSE.1.b

F.IF.4, F.BF.3

F.IF.8.a, F.BF.3

F.IF.4, F.IF.6

A.CED.1, A.CED.3

MathematicalContent

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vi vi

Unit 1 | Foundations for Functions



Personal Tutor


eGlossary

pp. 302, 384

Vocabulary


pp. 306, 387

Polynomials and Polynomial Functions5PPPPPP5PP

Photodisc/Getty Images

Polynomials and Polynomial Functions


5-1 Operations with Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .303

Extend: Algebra Lab Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

5-2 Dividing Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311

Extend: Graphing Technology Lab Dividing Polynomials . . . . . . . . . . . . . . . . . . . . . . . 318

Explore: Graphing Technology Lab Power Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 320

5-3 Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .322

5-4 Analyzing Graphs of Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . .330

Extend: Graphing Technology Lab Modeling Data Using Polynomial Functions . . . . . . 338

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .340

Explore: Graphing Technology Lab Solving Polynomial Equations by Graphing . . . . . . 341

5-5 Solving Polynomial Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .342

Extend: Graphing Technology Lab Polynomial Identities . . . . . . . . . . . . . . . . . . . . . . . 350

5-6 The Remainder and Factor Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .352

5-7 Roots and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .358

Extend: Graphing Technology Lab Analyzing Polynomial Functions . . . . . . . . . . . . . . . 366

5-8 Rational Zero Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .367


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .377



A.APR.1

A.APR.6

A.APR.6

F.IF.4

F.IF.4, F.IF.7.c

F.IF.4, F.IF.7.c

F.IF.4, F.IF.7.c

A.CED.1

A.REI.11

A.APR.2, F.IF.7.c

N.CN.9, A.APR.3

A.APR.4

MathematicalContent

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vii vii


Self-Check

Practice

pp. 326, 443

Foldables

pp. 302, 384Graphing

Calculator

pp. 338, 436

Virtual

Manipulatives

p. 331

Inverses and Radical Functions and Relations6III6FF

Stoc

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Inverses and Radical Functions and Relations


6-1 Operations on Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .385

6-2 Inverse Functions and Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .393

Extend: Graphing Technology Lab Inverse Functions and Relations. . . . . . . . . . . . . . . 399

6-3 Square Root Functions and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .400

6-4 nth Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .407

Extend: Graphing Technology Lab Graphing nth Root Functions . . . . . . . . . . . . . . . . . 413

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .414

6-5 Operations with Radical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .415

6-6 Rational Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .422

6-7 Solving Radical Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . .429

Extend: Graphing Technology Lab Solving Radical Equations and Inequalities . . . . . . . 436

Assessment


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .443



F.IF.9, F.BF.1.b

F.IF.4, F.BF.4.a

F.IF.7.b, F.BF.3

A.SSE.2

F.IF.7.b, F.BF.3

A.SSE.2

A.REI.2

A.REI.2, A.REI.11

MathematicalContent

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viii viii



Unit 3 | Advanced Functions and Relations

Personal Tutor


eGlossary

pp. 450, 528

Vocabulary


pp. 453, 532

Exponential and Exponential and Logarithmic Functions Logarithmic Functions and Relationsand Relations

Purestock/Getty Images

Exponential and Logarithmic Functions and Relations


7-1 Graphing Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .451

Explore: Graphing Technology Lab Solving Exponential Equations and Inequalities . . . 459

7-2 Solving Exponential Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . .461

7-3 Logarithms and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .468

Extend: Graphing Technology Lab Choosing the Best Model . . . . . . . . . . . . . . . . . . . . 476

7-4 Solving Logarithmic Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . .478

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .484

7-5 Properties of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .485

7-6 Common Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .492

Extend: Graphing Technology Lab Solving Logarithmic Equations and Inequalities . . . 499

7-7 Base e and Natural Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .501

Explore: Spreadsheet Lab Compound Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

7-8 Using Exponential and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . .509

Extend: Graphing Technology Lab Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516

Assessment


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .521



F.IF.7.e, F.IF.8.b

A.REI.11

A.CED.1, F.LE.4

F.IF.7.e, F.BF.3

A.SSE.2, A.CED.1

A.CED.1

A.CED.1

A.REI.11

A.SSE.2

F.IF.8.b, F.LE.4

F.BF.1.b

MathematicalContent

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ix ix


Self-Check

Practice

pp. 464, 585

Foldables


Calculator

pp. 516, 579

Virtual

Manipulatives

pp. 451, 557

Rational Functions Rational Functions and Relationsand Relations

Imag

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urce

/Mas

terfi

le

Rational Functions and Relations


8-1 Multiplying and Dividing Rational Expressions . . . . . . . . . . . . . . . . . . . . . . .529

8-2 Adding and Subtracting Rational Expressions . . . . . . . . . . . . . . . . . . . . . . . .538

8-3 Graphing Reciprocal Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .545

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .552

8-4 Graphing Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .553

Extend: Graphing Technology Lab Graphing Rational Functions . . . . . . . . . . . . . . . . . 561

8-5 Variation Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .562

8-6 Solving Rational Equations and Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . .570

Extend: Graphing Technology Lab Solving Rational Equations and Inequalities . . . . . . 579

Assessment


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .585



A.APR.7

A.APR.7

A.CED.2, F.BF.3

A.CED.2, F.IF.9

A.CED.2

A.CED.1, A.REI.2

A.REI.2, A.REI.11

MathematicalContent

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x x




Personal Tutor


eGlossary

pp. 592, 658

Vocabulary


pp. 641, 659

Conic SectionsConic Sections

Brand X Pictures/PunchStock

Conic Sections


9-1 Midpoint and Distance Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .593

9-2 Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .599

Explore: Graphing Technology Lab Equations of Circles . . . . . . . . . . . . . . . . . . . . . 606

9-3 Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .607

Explore: Algebra Lab Investigating Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614

9-4 Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .615

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .623

9-5 Hyperbolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .624

9-6 Identifying Conic Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .632

Extend: Graphing Technology Lab Analyzing Quadratic Relations . . . . . . . . . . . . . . 637

Explore: Graphing Technology Lab Linear-Nonlinear Systems . . . . . . . . . . . . . . . . . 639

9-7 Solving Linear-Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .640

Assessment

Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .646

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .651

Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .652

Standardized Test Practice, Chapters 1–9 . . . . . . . . . . . . . . . . . . . . . . . .654

A.CED.4

A.SSE.1.b, A.CED.2

A.SSE.1.b, A.CED.4

A.SSE.1.b, A.CED.2

A.SSE.1.b, A.CED.2

A.SSE.1.b, F.IF.9

A.REI.11

MathematicalContent

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xi xi

Unit 4 | Discrete Mathematics

Self-Check

Practice

pp. 603, 715

Foldables


Calculator

pp. 639, 690

Virtual

Manipulatives

pp. 594, 681

Sequences and Sequences and SeriesSeries

Mar

tin C

hild

/Pho

todi

sc/G

etty

Imag

es

Sequences and Series

Get Ready for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657

10-1 Sequences as Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .659

10-2 Arithmetic Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .666

10-3 Geometric Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .674

Explore: Algebra Lab Area Under a Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681

10-4 Infinite Geometric Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .683

Extend: Graphing Technology Lab Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .691

10-5 Recursion and Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .692

Extend: Spreadsheet Lab Amortizing Loans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698

10-6 The Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .699

Extend: Algebra Lab Combinations and Pascal’s Triangle . . . . . . . . . . . . . . . . . . . . 704

10-7 Proof by Mathematical Induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .705

Assessment


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .715


Standardized Test Practice, Chapters 1–10 . . . . . . . . . . . . . . . . . . . . . . .718

F.IF.4

A.CED.4

A.SSE.4

A.APR.5

A.APR.5

A.SSE.1.b, A.APR.5

MathematicalContent

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xii xii



Personal Tutor


eGlossary

pp. 722, 788

Vocabulary


pp. 720, 799

Unit 4 | Discrete Mathematics

Statistics Statistics and Probabilityand Probability

MIXA/Getty Im

ages

Statistics and Probability


11-1 Designing a Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .723

Extend: Graphing Technology Lab Simulations and Margin of Error . . . . . . . . . . . . . 731

11-2 Distributions of Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .733

11-3 Probability Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .742

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .751

11-4 The Binomial Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .752

11-5 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .760

Extend: Spreadsheet Lab Normal Approximation of Binomial Distributions . . . . . . . 767

11-6 Confidence Intervals and Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . .769

Assessment


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .781



S.IC.3, S.IC.5

S.IC.4, S.IC.6

S.IC.1

S.MD.7

S.MD.6, S.MD.7

S.ID.4

S.ID.4

S.IC.1, S.IC.4

MathematicalContent

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xiii xiii

Self-Check

Practice

pp. 738, 865

Foldables


Calculator

pp. 731, 844

Virtual

Manipulatives

pp. 737, 822

Unit 5 | Trigonometry

Trigonometric Trigonometric FunctionsFunctions

Denn

is W

elsh

/Upp

erCu

t Im

ages

/Get

ty Im

ages

Trigonometric Functions


Explore: Spreadsheet Lab Investigating Special Right Triangles . . . . . . . . . . . . . . . 789

12-1 Trigonometric Functions in Right Triangles. . . . . . . . . . . . . . . . . . . . . . . . .790

12-2 Angles and Angle Measure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .799

Extend: Geometry Lab Areas of Parallelograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . 806

12-3 Trigonometric Functions of General Angles . . . . . . . . . . . . . . . . . . . . . . . .807

12-4 Law of Sines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .814

Extend: Geometry Lab Regular Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822

12-5 Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .823

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .829

12-6 Circular and Periodic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .830

12-7 Graphing Trigonometric Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .837

Explore: Graphing Technology Lab Trigonometric Graphs . . . . . . . . . . . . . . . . . . . . 844

12-8 Translations of Trigonometric Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .845

12-9 Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .853

Assessment


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .865



F.TF.1

F.TF.1, F.TF.2

F.IF.7.e, F.TF.5

F.BF.3

F.IF.7.e, F.BF.3

A.CED.2

MathematicalContent

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xiv xiv



Animation

p. 870

vvvvvvvvvv

Vocabulary

p. 873Multilingual

eGlossary

p. 872

Personal Tutor

p. 875

Unit 5 | Trigonometry

Trigonometric Identities Trigonometric Identities and Equationsand Equations

Self-Check

Practice

p. 897

Foldables

p. 872Graphing

Calculator

p. 900

Maria Teijeiro/Photodisc/Getty Im

ages

Trigonometric Identities and Equations


13-1 Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .873

13-2 Verifying Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .880

13-3 Sum and Difference of Angles Identities . . . . . . . . . . . . . . . . . . . . . . . . . . .886

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .892

13-4 Double-Angle and Half-Angle Identities . . . . . . . . . . . . . . . . . . . . . . . . . . .893

Explore: Graphing Technology Lab Solving Trigonometric Equations . . . . . . . . . . . . 900

13-5 Solving Trigonometric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .901

Assessment


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .911



F.TF.8

F.TF.8

F.TF.8

F.TF.8

F.TF.8

MathematicalContent

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Student HandbookStudent Handbook

Contents

How to Use the Student Handbook

Extra Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R1

Selected Answers and Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R14

Glossary/Glosario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R124

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R149

Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover

Symbols and Parent Functions . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover

xv

Rubb

erba

ll/Ge

tty Im

ages

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