Preparing for Algebra Preparing For Algebras3.amazonaws.com/ecommerce-prod.mheducation.com/unitas/school/explore/... · connectED.mcgraw-hill.comc Your Digital Math Portal Table of

connectED.mcgraw-hill.comccccc Your Digital Math Portal

Table of Contents

i

Preparing For AlgebraPreparing For Algebra

Personal Tutor

p. P18Multilingual

eGlossary

p. P2

Vocabulary

p. P2Foldables

p. P2

Get Started on Chapter 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P2

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

0-1 Plan for Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P5

0-2 Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P7

0-3 Operations with Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P11

0-4 Adding and Subtracting Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . .P13

0-5 Multiplying and Dividing Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . .P17

0-6 The Percent Proportion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P20

0-7 Perimeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P23

0-8 Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P26

0-9 Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P29

0-10 Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P31

0-11 Simple Probability and Odds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P33

0-12 Measures of Center, Variation, and Position . . . . . . . . . . . . . . . . . . . . . . . .P37

0-13 Representing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P41

Posttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P47

Preparing for Algebra

S.ID.1

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ii ii

Your Digital Math PortalconnectED.mcgraw-hill.comccccc

Unit 1 | Relationships between Quantities

Personal Tutor

pp. 6, 99Multilingual

eGlossary

pp. 4, 74

Vocabulary

pp. 4, 139Animation

pp. 18, 90

Expressions, Equations, Expressions, Equations, and Functionsand FunctionsExpressions, Equations, and Functions

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

1-1 Variables and Expressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1-2 Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

1-3 Properties of Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Extend: Algebra Lab Accuracy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1-4 The Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

1-5 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33

1-6 Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40

1-7 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47

Extend: Graphing Technology Lab Representing Functions . . . . . . . . . . . . . . . . . . . . . . 55

1-8 Interpreting Graphs of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56

ASSESSMENT

Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67

Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68

Standardized Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70

A.SSE.1a, A.SSE.2

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

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

N.Q.3

A.SSE.1a, A.SSE.2

A.CED.1, A.REI.3

A.REI.10, F.IF.1

F.IF.1, F.IF.2

A.CED.2

F.IF.4

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iii iii

Unit 1 | Relationships between Quantities

Self-Check

Practice

pp. 3, 100

Foldables

pp. 4, 74Graphing

Calculator

pp. 55, 118

Virtual

Manipulatives

pp. 27, 90

Linear EquationsLinear EquationsLinear Equations

Get Ready for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

2-1 Writing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75

Explore: Algebra Lab Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

2-2 Solving One-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83

Explore: Algebra Lab Solving Multi-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

2-3 Solving Multi-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91

2-4 Solving Equations with the Variable on Each Side . . . . . . . . . . . . . . . . . . . . . .97

2-5 Solving Equations Involving Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . .103

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110

2-6 Ratios and Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111

Extend: Spreadsheet Lab Descriptive Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

2-7 Percent of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119

Extend: Algebra Lab Percentiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

2-8 Literal Equations and Dimensional Analysis. . . . . . . . . . . . . . . . . . . . . . . . . .126

2-9 Weighted Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132

ASSESSMENT

Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .139

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145

Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146

Standardized Test Practice, Chapters 1–2 . . . . . . . . . . . . . . . . . . . . . . . . . .148

A.CED.1

A.REI.3

A.REI.1, A.REI.3

A.REI.3

A.REI.1, A.REI.3

A.REI.1, A.REI.3

A.REI.1, A.REI.3

A.REI.1, A.REI.3

N.Q.2

N.Q.1, A.REI.3

A.CED.4, A.REI.3

A.REI.1, A.REI.3

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iv iv


Unit 2 | Linear Relationships

Personal Tutor


eGlossary

pp. 152, 214

Vocabulary

pp. 152, 272Animation

pp. 150, 248

Linear FunctionsLinear FunctionsLinear Functions

Get Ready for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Explore: Algebra Lab Analyzing Linear Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

3-1 Graphing Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155

3-2 Solving Linear Equations by Graphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163

Extend: Graphing Technology Lab Graphing Linear Functions . . . . . . . . . . . . . . . . . . . 169

Explore: Algebra Lab Rate of Change of a Linear Function . . . . . . . . . . . . . . . . . . . . . 171

3-3 Rate of Change and Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181

3-4 Direct Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182

3-5 Arithmetic Sequences as Linear Functions. . . . . . . . . . . . . . . . . . . . . . . . . . .189

Extend: Algebra Lab Inductive and Deductive Reasoning . . . . . . . . . . . . . . . . . . . . . . 196

3-6 Proportional and Nonproportional Relationships . . . . . . . . . . . . . . . . . . . . . .197

ASSESSMENT


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .207



F.IF.4

F.IF.4, F.IF.7a

A.REI.10, F.IF.7a

N.Q.1, F.IF.7a

F.IF.6, F.LE.1a

F.IF.6, F.LE.1a

A.REI.10, F.IF.7a

F.BF.2, F.LE.2

F.LE.1b, F.LE.2

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v v


Self-Check

Practice

pp. 207, 213

Foldables

pp. 152, 214Graphing

Calculator

pp. 169, 215

Virtual

Manipulatives

pp. 158, 248

Equations ofEquations ofLinear FunctionsLinear FunctionsEquations of Linear Functions


Explore: Graphing Technology Lab Investigating Slope-Intercept Form . . . . . . . . . . . . 215

4-1 Graphing Equations in Slope-Intercept Form . . . . . . . . . . . . . . . . . . . . . . . . .216

Extend: Graphing Technology Lab The Family of Linear Graphs. . . . . . . . . . . . . . . . . . 224

4-2 Writing Equations in Slope-Intercept Form. . . . . . . . . . . . . . . . . . . . . . . . . . .226

4-3 Writing Equations in Point-Slope Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .233

4-4 Parallel and Perpendicular Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .239

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .246

4-5 Scatter Plots and Lines of Fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .247

Extend: Algebra Lab Correlation and Causation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

4-6 Regression and Median-Fit Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255

4-7 Inverse Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .263

Extend: Algebra Lab Drawing Inverses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

ASSESSMENT


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .277



F.IF.7a, S.ID.7

F.BF.3, S.ID.7

F.BF.1, F.LE.2

F.IF.2, F.LE.2

F.LE.2, S.ID.7

S.ID.6a, S.ID.6c

S.ID.9

S.ID.6, S.ID.8

A.CED.2, F.BF.4a

F.BF.4a

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vi vi



Personal Tutor


eGlossary

pp. 284 334

Vocabulary


pp. 291, 332

Linear InequalitiesLinear InequalitiesLinear Inequalities


5-1 Solving Inequalities by Addition and Subtraction. . . . . . . . . . . . . . . . . . . . . .285

Explore: Algebra Lab Solving Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

5-2 Solving Inequalities by Multiplication and Division . . . . . . . . . . . . . . . . . . . .292

5-3 Solving Multi-Step Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .298

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .304

Explore: Algebra Lab Reading Compound Statements . . . . . . . . . . . . . . . . . . . . . . . . 305

5-4 Solving Compound Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .306

5-5 Inequalities Involving Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .312

5-6 Graphing Inequalities in Two Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .317

Extend: Graphing Technology Lab Graphing Inequalities . . . . . . . . . . . . . . . . . . . . . . . 323

ASSESSMENT


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .327



A.CED.1, A.REI.3

A.REI.3

A.CED.1, A.REI.3

A.CED.1, A.REI.3

A.CED.1, A.REI.3

A.CED.1, A.REI.3

A.CED.3, A.REI.12

A.REI.12

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vii vii


Self-Check

Practice

pp. 300, 383

Foldables


Calculator

pp. 323, 342

Virtual

Manipulatives

pp. 291, 336

Systems of LinearSystems of LinearEquations and InequalitiesEquations and InequalitiesSystems of LinearEquations and Inequalities


6-1 Graphing Systems of Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .335

Extend: Graphing Technology Lab Systems of Equations. . . . . . . . . . . . . . . . . . . . . . . 342

6-2 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .344

6-3 Elimination Using Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . .350

6-4 Elimination Using Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .357

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .363

6-5 Applying Systems of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .364

Extend: Algebra Lab Using Matrices to Solve Systems of Equations . . . . . . . . . . . . . . 370

6-6 Systems of Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .372

Extend: Graphing Technology Lab Systems of Inequalities . . . . . . . . . . . . . . . . . . . . . 377

ASSESSMENT


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .383



A.CED.3, A.REI.6

A.REI.6, A.REI.11

A.CED.3, A.REI.6

A.CED.2, A.REI.6

A.REI.5, A.REI.6

A.REI.6

A.REI.6

A.REI.12

A.REI.12

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viii viii


Unit 3 | Exponential and Quadratic Relationships

Personal Tutor

pp. 406,473Multilingual

eGlossary

pp. 390, 462

Vocabulary


pp. 398, 481

Exponents and Exponents and Exponential FunctionsExponential FunctionsExponents and Exponential Functions


7-1 Multiplication Properties of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .391

7-2 Division Properties of Exponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .398

7-3 Rational Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .406

7-4 Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .414

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .421

Explore: Graphing Technology Lab Family of Exponential Functions . . . . . . . . . . . . . . 422

7-5 Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .424

Extend: Graphing Technology Lab Solving Exponential Equations and Inequalities . . . 430

7-6 Growth and Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .432

Extend: Algebra Lab Transforming Exponential Expressions . . . . . . . . . . . . . . . . . . . . 437

7-7 Geometric Sequences as Exponential Functions . . . . . . . . . . . . . . . . . . . . . .438

Extend: Algebra Lab Average Rate of Change of Exponential Functions . . . . . . . . . . . 444

7-8 Recursive Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .445

ASSESSMENT


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .455



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

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

N.RN.1, N.RN.2

A.SSE.2

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

F.IF.7e, F.LE.2

A.REI.11

F.IF.8b, F.LE.2

A.SSE.3c, F.IF.8b

F.BF.2, F.LE.1

F.IF.6

F.IF.3, F.BF.2

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ix ix


Self-Check

Practice

pp. 389, 518

Foldables

pp. 390, 462Virtual

Manipulatives

pp. 424, 480

Quadratic Expressions Quadratic Expressions and Equationsand EquationsQuadratic Expressions and Equations


Explore: Algebra Lab Adding and Subtracting Polynomials . . . . . . . . . . . . . . . . . . . . . 463

8-1 Adding and Subtracting Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .465

8-2 Multiplying a Polynomial by a Monomial . . . . . . . . . . . . . . . . . . . . . . . . . . . .472

Explore: Algebra Lab Multiplying Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

8-3 Multiplying Polynomials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .480

8-4 Special Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .486

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .492

Explore: Algebra Lab Factoring Using the Distributive Property . . . . . . . . . . . . . . . . . . 493

8-5 Using the Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .494

Explore: Algebra Lab Factoring Trinomials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

8-6 Solving x2 + bx + c = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .503

8-7 Solving ax2 + bx + c = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .510

8-8 Differences of Squares. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .516

8-9 Perfect Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .522

ASSESSMENT


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .535



A.APR.1

A.SSE.1a, A.APR.1

A.APR.1

A.APR.1

A.APR.1

A.APR.1

A.SSE.2

A.SSE.2, A.SSE.3a

A.SSE.2

A.SSE.3a, A.REI.4b

A.SSE.3a, A.REI.4b

A.SSE.3a, A.REI.4b

A.SSE.3a, A.REI.1

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Personal Tutor

pp. 572, 627 Multilingual

eGlossary

pp. 524, 618

Vocabulary


pp. 574, 655

Quadratic Functions and Quadratic Functions and EquationsEquationsQuadratic Functions and Equations


9-1 Graphing Quadratic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .543

Extend: Algebra Lab Rate of Change of a Quadratic Function . . . . . . . . . . . . . . . . . . . 554

9-2 Solving Quadratic Equations by Graphing. . . . . . . . . . . . . . . . . . . . . . . . . . . .555

Extend: Graphing Technology Lab Quadratic Inequalities . . . . . . . . . . . . . . . . . . . . . . 561

Explore: Graphing Technology Lab Family of Quadratic Functions . . . . . . . . . . . . . . . . 562

9-3 Transformations of Quadratic Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . .564

Extend: Graphing Technology Lab Systems of Linear and Quadratic Equations . . . . . . 572

9-4 Solving Quadratic Equations by Completing the Square . . . . . . . . . . . . . . . .574

Extend: Algebra Lab Finding the Maximum or Minimum Value . . . . . . . . . . . . . . . . . . 580

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .582

9-5 Solving Quadratic Equations by Using the Quadratic Formula. . . . . . . . . . . .583

9-6 Analyzing Functions with Successive Differences . . . . . . . . . . . . . . . . . . . . .590

Extend: Graphing Technology Lab Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596

9-7 Special Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .598

Extend: Graphing Technology Lab Piecewise-Linear Functions . . . . . . . . . . . . . . . . . . 606

ASSESSMENT


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .611



F.IF.4, F.IF.7a

F.IF.6

A.REI.4b, F.IF.7a

F.IF.7a, F.BF.3

A.SSE.3b, F.IF.7a

A.REI.7, F.IF.7a

A.REI.4, F.IF.8a

A.SSE.3b, F.IF.8a

A.REI.4

F.IF.6, F.LE.1

F.LE.2, S.ID.6a

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

F.IF.7b

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Unit 4 | Advanced Functions and Equations

Self-Check

Practice

pp. 611, 617

Foldables


Calculator

pp. 572, 627

Virtual

Manipulatives

pp. 548, 649

Radical Functions Radical Functions and Geometryand GeometryRadical Functions and Geometry

Get Ready for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617

Explore: Algebra Lab Inverse Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619

10-1 Square Root Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .621

Extend: Graphing Technology Lab Graphing Square Root Functions . . . . . . . . . . . . 627

10-2 Simplifying Radical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .628

Extend: Algebra Lab Rational and Irrational Numbers . . . . . . . . . . . . . . . . . . . . . . . 634

10-3 Operations with Radical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .635

Extend: Algebra Lab Simplifying nth Root Expressions . . . . . . . . . . . . . . . . . . . . . . 640

10-4 Radical Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .642

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .647

10-5 The Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .648

Extend: Algebra Lab Distance on the Coordinate Plane. . . . . . . . . . . . . . . . . . . . . . 654

Explore: Algebra Lab Investigating Trigonometric Ratios . . . . . . . . . . . . . . . . . . . . . 655

10-6 Trigonometric Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .656

ASSESSMENT

Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .663

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .667

Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .668

Standardized Test Practice, Chapters 1–10 . . . . . . . . . . . . . . . . . . . . . . .670

F.BF.4a

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

F.IF.7b

A.REI.4a

N.RN.3

N.RN.2

N.RN.2

N.RN.2, A.CED.2

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Unit 4 | Advanced Functions and Equations

Personal Tutor


eGlossary

pp. 674, 746

Vocabulary


pp. 672, 793

Rational Functions Rational Functions and Equationsand EquationsRational Functions and Equations


Explore: Graphing Technology Lab Inverse Variation . . . . . . . . . . . . . . . . . . . . . . . . 675

11-1 Inverse Variation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .676

Explore: Graphing Technology Lab Family of Rational Functions . . . . . . . . . . . . . . 683

11-2 Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .684

11-3 Simplifying Rational Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .690

Extend: Graphing Technology Lab Simplifying Rational Expressions . . . . . . . . . . . . 697

11-4 Multiplying and Dividing Rational Expressions . . . . . . . . . . . . . . . . . . . . . .698

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .705

11-5 Dividing Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .706

11-6 Adding and Subtracting Rational Expressions . . . . . . . . . . . . . . . . . . . . . .712

11-7 Mixed Expressions and Complex Fractions. . . . . . . . . . . . . . . . . . . . . . . . .720

11-8 Rational Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .726

Extend: Graphing Technology Lab Solving Rational Equations . . . . . . . . . . . . . . . . . 733

ASSESSMENT


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .739



A.CED.2

A.CED.2

A.REI.11

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xiii xiii

Unit 5 | Data Analysis

Self-Check

Practice

pp. 679, 751

Foldables


Calculator

pp. 697, 810

Virtual

Manipulatives

pp. 686, 764

Statistics and Statistics and ProbabilityProbabilityStatistics and Probability


12-1 Samples and Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .747

Extend: Algebra Lab Evaluating Published Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 755

12-2 Statistics and Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .757

12-3 Distributions of Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .764

12-4 Comparing Sets of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .771

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .779

12-5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .780

12-6 Permutations and Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .786

12-7 Probability of Compound Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .793

Extend: Algebra Lab Two-Way Frequency Tables . . . . . . . . . . . . . . . . . . . . . . . . . 801

12-8 Probability Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .803

Extend: Graphing Technology Lab The Normal Curve . . . . . . . . . . . . . . . . . . . . . . . 810

ASSESSMENT


Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .817



S.ID.2

S.ID.2, S.ID.3

S.ID.2, S.ID.3

S.ID.5

S.ID.2

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Student HandbookStudent Handbook

Built-In Workbooks

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

Reference

Selected Answers and Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R13

Glossary/Glosario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R97

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R118

Formulas and Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover

Symbols and Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover

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