Algebra 1 glencoe mcgraw hill

GLENCOE
MATHEMATICS

interactive student edition

Algebra 1


Contents in Brief
Unit

Unit

Unit

Unit

Unit

Expressions and Equations .................................................2
Chapter 1

The Language of Algebra.........................................4

Chapter 2

Real Numbers ...........................................................66

Chapter 3

Solving Linear Equations .....................................118

Linear Functions .....................................................................188
Chapter 4

Graphing Relations and Functions ....................190

Chapter 5

Analyzing Linear Equations ................................254

Chapter 6

Solving Linear Inequalities ..................................316

Chapter 7

Solving Systems of Linear Equations and
Inequalities ..............................................................366

Polynomials and Nonlinear Functions ....................406
Chapter 8

Polynomials ............................................................408

Chapter 9

Factoring ..................................................................472

Chapter 10

Quadratic and Exponential Functions ..............522

Radical and Rational Functions ...................................582
Chapter 11

Radical Expressions and Triangles .....................584

Chapter 12

Rational Expressions and Equations .................640

Data Analysis ............................................................................704
Chapter 13

Statistics ...................................................................706

Chapter 14

Probability ...............................................................752

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Authors

Berchie Holliday, Ed.D.

Gilbert J. Cuevas, Ph.D.

Former Mathematics
Teacher
Northwest Local School
District
Cincinnati, OH

Professor of Mathematics
Education
University of Miami
Miami, FL

Beatrice Moore-Harris

John A. Carter

Educational Specialist
Bureau of Education
and Research
League City, TX

Director of Mathematics
Adlai E. Stevenson High
School
Lincolnshire, IL

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Authors

Daniel Marks, Ed.D.

Ruth M. Casey

Associate Professor of
Mathematics
Auburn University at
Montgomery
Montgomery, AL

Mathematics Teacher
Department Chair
Anderson County High
School
Lawrenceburg, KY

Roger Day, Ph.D.

Linda M. Hayek

Associate Professor of
Mathematics
Illinois State University
Normal, IL

Mathematics Teacher
Ralston Public Schools

Omaha, NE

Contributing Authors
Dinah Zike

USA TODAY
The USA TODAY Snapshots®, created by
USA TODAY®, help students make the connection
between real life and mathematics.

Educational Consultant
Dinah-Might Activities, Inc.
San Antonio, TX
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Content Consultants
Each of the Content Consultants reviewed every chapter and gave
suggestions for improving the effectiveness of the mathematics
instruction.

Mathematics Consultants
Gunnar E. Carlsson, Ph.D.
Consulting Author
Professor of Mathematics
Stanford University
Stanford, CA

William Collins
Director, The Sisyphus Math Learning
Center
East Side Union High School District
San Jose, CA

Ralph L. Cohen, Ph.D.
Consulting Author
Professor of Mathematics
Stanford University
Stanford, CA

Dora Swart
Mathematics Teacher
W.F. West High School
Chehalis, WA

Alan G. Foster
Former Mathematics Teacher &
Department Chairperson
Addison Trail High School
Addison, IL

David S. Daniels
Former Mathematics Chair
Longmeadow High School
Longmeadow, MA

Les Winters
Instructor

California State University, Northridge
Northridge, CA

Mary C. Enderson, Ph.D.
Associate Professor of Mathematics
Middle Tennessee State University
Murfreesboro, TN

Gerald A. Haber
Consultant, Mathematics
Standards and Professional
Development
New York, NY

Angiline Powell Mikle
Assistant Professor Mathematics
Education
Texas Christian University
Fort Worth, TX

C. Vincent Pané, Ed.D.
Associate Professor of Education/
Coordinator of Secondary
& Special Subjects Education
Molloy College
Rockville Centre, NY

Reading Consultant
Lynn T. Havens
Director of Project CRISS

Kalispell School District
Kalispell, MT

Teacher Reviewers
Each Teacher Reviewer reviewed at least two chapters of the
Student Edition, giving feedback and suggestions for improving
the effectiveness of the mathematics instruction.
Susan J. Barr
Department Chair/Teacher
Dublin Coffman High School
Dublin, OH

Judy Buchholtz
Math Department Chair/Teacher
Dublin Scioto High School
Dublin, OH

Rusty Campbell
Mathematics Instructor/Chairperson
North Marion High School
Farmington, WV

Diana L. Boyle
Mathematics Teacher, 6–8
Judson Middle School
Salem, OR

Holly A. Budzinski
Mathematics Department Chairperson
Green Hope High School

Morrisville, NC

Nancy M. Chilton
Mathematics Teacher
Louis Pizitz Middle School
Birmingham, AL

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Teacher Reviewers
Lisa Cook
Mathematics Teacher
Kaysville Junior High School
Kaysville, UT

Kimberly A. Hepler
Mathematics Teacher
S. Gordon Stewart Middle School
Fort Defiance, VA

Cindy Plunkett
Math Educator
E.M. Pease Middle School
San Antonio, TX

Bonnie Daigh
Mathematics Teacher

Eudora High School
Eudora, KS

Deborah L. Hewitt
Mathematics Teacher
Chester High School
Chester, NY

Ann C. Raymond
Teacher
Oak Ave. Intermediate School
Temple City, CA

Carol Seay Ferguson
Mathematics Teacher
Forestview High School
Gastonia, NC

Marilyn S. Hughes
Mathematics Department
Chairperson
Belleville West High School
Belleville, IL

Carrie Ferguson
Teacher
West Monroe High School
West Monroe, LA
Melissa R. Fetzer
Teacher/Math Chairperson

Hollidaysburg Area Junior High
School
Hollidaysburg, PA
Diana Flick
Mathematics Teacher
Harrisonburg High School
Harrisonburg, VA
Kathryn Foland
Teacher/Subject Area Leader
Ben Hill Middle School
Tampa, FL
Celia Foster
Assistant Principal Mathematics
Grover Cleveland High School
Ridgewood, NY
Patricia R. Franzer
Secondary Math Instructor
Celina City Schools
Celina, OH
Candace Frewin
Teacher on Special Assignment
Pinellas County Schools
Largo, FL

Larry Hummel
Mathematics Department
Chairperson
Central City High School
Central City, NE
William Leschensky

Former Mathematics Teacher
Glenbard South High School
College of DuPage
Glen Ellyn, IL
Sharon Linamen
Mathematics Teacher
Lake Brantley High School
Altamonte Springs, FL
Patricia Lund
Mathematics Teacher
Divide County High School
Crosby, ND
Marilyn Martau
Mathematics Teacher (Retired)
Lakewood High School
Lakewood, OH
Kathy Massengill
Mathematics Teacher
Midlothian High School
Midlothian, VA

Larry T. Gathers
Mathematics Teacher
Springfield South High School
Springfield, OH

Marie Mastandrea
District Mathematics Coordinator
Amity Regional School District #5
Woodbridge, CT

Maureen M. Grant
Mathematics Teacher/Department
Chair
North Central High School
Indianapolis, IN

Laurie Newton
Teacher
Crossler Middle School
Salem, OR

Marie Green
Mathematics Teacher
Anthony Middle School
Manhattan, KS

James Leo Oliver
Teacher of the Emotionally Impaired
Lakeview Junior High School
Battle Creek, MI

Vicky S. Hamen
High School Math Teacher
Celina High School
Celina, OH

Shannon Collins Pan
Department of Mathematics
Waverly High School

Waverly, NY

Sandy Schoff
Math Curriculum Coordinator K–12
Anchorage School District
Anchorage, AK
Susan E. Sladowski
Assistant Principal–Mathematics
Bayside High School
Bayside, NY
Paul E. Smith
Teacher/Consultant
Plaza Park Middle School
Evansville, IN
Dr. James Henry Snider
Teacher–Math Dept. Chair/Curriculum
& Technology Coordinator
Nashville School of the Arts
Nashville, TN
Diane Stilwell
Mathematics Teacher/Technology
Coordinator
South Middle School
Morgantown, WV
Richard P. Strausz
Math and Technology Coordinator
Farmington Schools
Farmington, MI
Patricia Taepke
Mathematics Teacher and BTSA

Trainer
South Hills High School
West Covina, CA
C. Arthur Torell
Mathematics Teacher and Supervisor
Summit High School
Summit, NJ
Lou Jane Tynan
Mathematics Department Chair
Sacred Heart Model School
Louisville, KY
Julia Dobbins Warren
Mathematics Teacher
Mountain Brook Junior High School
Birmingham, AL
Jo Amy Wynn
Mathematics Teacher
Captain Shreve High School
Shreveport, LA
Rosalyn Zeid
Mathematics Supervisor
Union Township School District
Union, NJ
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Teacher Advisory Board and Field Test Schools

Teacher Advisory Board
Glencoe/McGraw-Hill wishes to thank the following teachers for
their feedback on Glencoe Algebra. They were instrumental in
providing valuable input toward the development of this program.
Mary Jo Ahler
Mathematics Teacher
Davis Drive Middle School
Apex, NC
David Armstrong
Mathematics Facilitator
Huntington Beach Union High School District
Huntington Beach, CA
Berta Guillen
Mathematics Department Chairperson
Barbara Goleman Senior High School
Miami, FL

Norma Molina
Ninth Grade Success Initiative Campus
Coordinator
Holmes High School
San Antonio, TX
Sarah Morrison
Mathematics Department Chairperson
Northwest Cabarrus High School
Concord, NC
Raylene Paustian
Mathematics Curriculum Coordinator
Clovis Unified School District
Clovis, CA

Bonnie Johnston
Academically Gifted Program Coordinator
Valley Springs Middle School
Arden, NC

Tom Reardon
Mathematics Department Chairperson
Austintown Fitch High School
Youngstown, OH

JoAnn Lopykinski
Mathematics Teacher
Lincoln Way East High School
Frankfort, IL

Guy Roy
Mathematics Coordinator
Plymouth Public Schools
Plymouth, MA

David Lorkiewicz
Mathematics Teacher
Lockport High School
Lockport, IL

Jenny Weir
Mathematics Department Chairperson
Felix Verela Sr. High School
Miami, FL

Field Test Schools
Glencoe/McGraw-Hill wishes to thank the following schools that
field-tested pre-publication manuscript during the 2001–2002 school
year. They were instrumental in providing feedback and verifying
the effectiveness of this program.
Northwest Cabarrus High School
Concord, NC

Lincoln Way East High School
Frankfort, IL

Davis Drive Middle School
Apex, NC

Scotia-Glenville High School
Scotia, NY

Barbara Goleman Sr. High School
Miami, FL

Wharton High School
Tampa, FL

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Table of Contents

Expressions and Equations

2

Chapter

4

The Language of Algebra
1-1

Variables and Expressions................................................6

1-2

Order of Operations........................................................11

1-3

Open Sentences................................................................16
Practice Quiz 1: Lessons 1-1 through 1-3 ....................20

• Introduction 3
• Follow-Ups 55, 100, 159

1-4

Identity and Equality Properties...................................21

• Culmination 177

1-5

The Distributive Property...............................................26

1-6

Commutative and Associative Properties....................32
Practice Quiz 2: Lessons 1-4 through 1-6.....................36

1-7

Logical Reasoning.............................................................37

1-8

Graphs and Functions.....................................................43
Algebra Activity: Investigating Real-World
Functions ........................................................................49

1-9

Statistics: Analyzing Data by Using Tables
and Graphs.....................................................................50
Spreadsheet Investigation: Statistical Graphs..........56
Study Guide and Review ..............................................57
Practice Test .....................................................................63
Standardized Test Practice...........................................64

Lesson 1-7, p. 41

Prerequisite Skills

Standardized Test Practice

• Getting Started 5

• Multiple Choice 9, 15, 20, 25, 31, 36, 39, 40, 42, 48, 55,
63, 64

• Getting Ready for the Next Lesson 9, 15, 20, 25, 31,
36, 48

• Short Response/Grid In 42, 65
• Quantitative Comparison 65
• Open Ended 65

Study Organizer 5
Reading and Writing Mathematics

Snapshots 27, 50, 53

• Translating from English to Algebra 10
• Reading Math Tips 18, 37
• Writing in Math 9, 15, 20, 25, 31, 35, 42, 48, 55

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Unit 1
Chapter

Real Numbers

66

2-1

Rational Numbers on the Number Line......................68

2-2

Adding and Subtracting Rational Numbers ...............73

2-3

Multiplying Rational Numbers.....................................79
Practice Quiz 1: Lessons 2-1 through 2-3 ....................83

2-4

Dividing Rational Numbers...........................................84

2-5

Statistics: Displaying and Analyzing Data..................88

2-6

Probability: Simple Probability and Odds...................96
Practice Quiz 2: Lessons 2-4 through 2-6..................101
Algebra Activity: Investigating Probability
and Pascal’s Triangle.................................................102

2-7

Square Roots and Real Numbers................................103
Study Guide and Review............................................110
Practice Test...................................................................115
Standardized Test Practice........................................116

Lesson 2-4, p. 87

Prerequisite Skills

Standardized Test Practice

• Getting Started 67

• Multiple Choice 72, 78, 83, 87, 94, 101, 106, 107,
109, 115, 116

• Getting Ready for the Next Lesson 72, 78, 83, 87, 94, 101

• Short Response/Grid In 117
• Quantitative Comparison 117

Study Organizer 67

• Open Ended 117

Reading and Writing Mathematics
• Interpreting Statistics 95

Snapshots 78, 80

• Reading Math Tips 97, 103
• Writing in Math 72, 78, 82, 87, 94, 100, 109

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Unit 1
Chapter

Solving Linear Equations
3-1

Writing Equations ..........................................................120
Algebra Activity: Solving Addition and
Subtraction Equations...............................................127

Prerequisite Skills
• Getting Started 119
• Getting Ready for the Next Lesson

126, 134, 140, 148, 154, 159,
164, 170

118

3-2

Solving Equations by Using Addition and
Subtraction ..................................................................128

3-3

Solving Equations by Using Multiplication and
Division .......................................................................135
Practice Quiz 1: Lessons 3-1 through 3-3..................140

Study Organizer 119

Algebra Activity: Solving Multi-Step Equations......141
3-4

Solving Multi-Step Equations......................................142

Reading and Writing
Mathematics

3-5

Solving Equations with the Variable on
Each Side.....................................................................149

• Sentence Method and Proportion
Method 165

3-6

Ratios and Proportions .................................................155

3-7

Percent of Change..........................................................160

• Reading Math Tips 121, 129, 155
• Writing in Math 126, 134, 140,
147, 154, 159, 164, 170, 177

Standardized Test Practice
• Multiple Choice 126, 134, 140,
147, 151, 152, 154, 159, 164,
170, 177, 185, 186
• Short Response/Grid In 187
• Quantitative Comparison 187

Practice Quiz 2: Lessons 3-4 through 3-7 ..................164
3-8

Solving Equations and Formulas................................166

3-9

Weighted Averages........................................................171
Spreadsheet Investigation: Finding a
Weighted Average...........................................................178
Study Guide and Review............................................179
Practice Test...................................................................185
Standardized Test Practice.........................................186

• Open Ended 187

Lesson 3-4, p. 142

Snapshots 158

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Linear Functions
Chapter

Graphing Relations and
Functions

• Culmination 398

190

4-1

The Coordinate Plane....................................................192

4-2

Transformations on the Coordinate Plane.................197
Graphing Calculator Investigation:
Graphs of Relations...................................................204

• Introduction 189
• Follow-Ups 230, 304, 357, 373

188

4-3

Relations..........................................................................205
Practice Quiz 1: Lessons 4-1 through 4-3..................211

4-4

Equations as Relations ..................................................212

4-5

Graphing Linear Equations..........................................218
Graphing Calculator Investigation: Graphing
Linear Equations........................................................224

4-6

Functions.........................................................................226
Practice Quiz 2: Lessons 4-4 through 4-6 ..................231
Spreadsheet Investigation: Number Sequences....232

4-7

Arithmetic Sequences...................................................233

4-8

Writing Equations from Patterns.................................240
Study Guide and Review............................................246
Practice Test ..................................................................251
Standardized Test Practice.........................................252

Lesson 4-5, p. 222

Prerequisite Skills

Standardized Test Practice

• Getting Started 191

• Multiple Choice 196, 203, 210, 216, 223, 228, 229,
231, 238, 245, 251, 252

• Getting Ready for the Next Lesson 196, 203, 211, 217,
223, 231, 238

• Short Response/Grid In 210, 253

• Quantitative Comparison 253
• Open Ended 253

Study Organizer 191
Reading and Writing Mathematics

Snapshots 210

• Reasoning Skills 239
• Reading Math Tips 192, 198, 233, 234
• Writing in Math 196, 203, 210, 216, 222, 231, 238, 245

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Unit 2
Chapter
Prerequisite Skills

Analyzing Linear Equations

254

5-1

Slope................................................................................256

5-2

Slope and Direct Variation...........................................264

• Getting Started 255

Practice Quiz 1: Lessons 5-1 and 5-2..........................270

• Getting Ready for the Next Lesson
262, 270, 277, 285, 291, 297

Algebra Activity: Investigating Slope-Intercept
Form ............................................................................271
5-3

Study Organizer 255
Reading and Writing
Mathematics
• Mathematical Words and Everyday
Words 263
• Reading Math Tips 256
• Writing in Math 262, 269, 277,
285, 291, 297, 304

Slope-Intercept Form.....................................................272
Graphing Calculator Investigation: Families of
Linear Graphs............................................................278

5-4

Writing Equations in Slope-Intercept Form...............280

5-5

Writing Equations in Point-Slope Form.....................286

5-6

Geometry: Parallel and Perpendicular Lines............292
Practice Quiz 2: Lessons 5-3 through 5-6..................297

5-7

Statistics: Scatter Plots and Lines of Fit......................298
Graphing Calculator Investigation: Regression
and Median-Fit Lines................................................306
Study Guide and Review ............................................308

Standardized Test Practice

Practice Test...................................................................313

• Multiple Choice 262, 269, 277,
281, 283, 285, 291, 297, 304,
305, 313, 314

Standardized Test Practice.........................................314

• Short Response/Grid In 315
• Quantitative Comparison 315
• Open Ended 291, 315

Lesson 5-2, p. 266

Snapshots 258, 284

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Unit 2
Chapter

Solving Linear Inequalities
6-1

Prerequisite Skills

Solving Inequalities by Addition and
Subtraction..................................................................318
Algebra Activity: Solving Inequalities.......................324

• Getting Started 317
• Getting Ready for the Next Lesson
323, 331, 337, 344, 351

316

6-2

Solving Inequalities by Multiplication and
Division.......................................................................325
Practice Quiz 1: Lessons 6-1 and 6-2..........................331

Study Organizer 317

6-3

Solving Multi-Step Inequalities...................................332

6-4

Solving Compound Inequalities .................................339
Practice Quiz 2: Lessons 6-3 and 6-4..........................344

Reading and Writing
Mathematics

6-5

Solving Open Sentences Involving Absolute
Value............................................................................345

• Compound Statements 338

6-6

Graphing Inequalities in Two Variables ....................352

• Reading Math Tips 319, 339, 340

• Writing in Math 323, 331, 337,
343, 351, 357

Graphing Calculator Investigation: Graphing
Inequalities.................................................................358
Study Guide and Review............................................359
Practice Test...................................................................363

Standardized Test Practice

Standardized Test Practice.........................................364

• Multiple Choice 323, 328, 329,
331, 337, 343, 351, 357, 363, 364
• Short Response/Grid In 365
• Quantitative Comparison 365
• Open Ended 365
Lesson 6-1, p. 322

Snapshots 318, 350

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Unit 2
Chapter

Solving Systems of Linear

Equations and Inequalities

366

Spreadsheet Investigation: Systems
of Equations ................................................................368
7-1

Graphing Systems of Equations..................................369
Graphing Calculator Investigation: Systems
of Equations ................................................................375

7-2

Substitution ....................................................................376
Practice Quiz 1: Lessons 7-1 and 7-2..........................381

7-3

Elimination Using Addition and Subtraction ...........382

7-4

Elimination Using Multiplication ...............................387
Practice Quiz 2: Lessons 7-3 and 7-4 ..........................392

7-5

Graphing Systems of Inequalities ...............................394
Study Guide and Review ............................................399

Practice Test ..................................................................403
Standardized Test Practice.........................................404

Lesson 7-2, p. 380

Prerequisite Skills

Standardized Test Practice

• Getting Started 367

• Multiple Choice 374, 381, 384, 385, 386, 392, 398,
403, 404

• Getting Ready for the Next Lesson 374, 381, 386, 392

• Short Response/Grid In 405
• Quantitative Comparison 405

Study Organizer 367

• Open Ended 405

Reading and Writing Mathematics
Snapshots 386

• Making Concept Maps 393
• Writing in Math 374, 381, 386, 392, 398

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Polynomials and Nonlinear
Functions
Chapter

Polynomials
8-1

406

408

Multiplying Monomials ...............................................410
Algebra Activity: Investigating Surface
Area and Volume .......................................................416

• Introduction 407

8-2

Dividing Monomials.....................................................417

• Follow-Ups 429, 479, 537

8-3

Scientific Notation.........................................................425

• Culmination 572

Practice Quiz 1: Lessons 8-1 through 8-3..................430
Algebra Activity: Polynomials ....................................431
8-4

Polynomials....................................................................432
Algebra Activity: Adding and Subtracting
Polynomials................................................................437

8-5

Adding and Subtracting Polynomials........................439

8-6

Multiplying a Polynomial by a Monomial ................444
Practice Quiz 2: Lessons 8-4 through 8-6 ..................449
Algebra Activity: Multiplying Polynomials .............450

8-7

Multiplying Polynomials ..............................................452

8-8

Special Products............................................................458
Study Guide and Review ............................................464
Practice Test...................................................................469

Standardized Test Practice.........................................470

Lesson 8-2, p. 422

Prerequisite Skills

Standardized Test Practice

• Getting Started 409

• Multiple Choice 415, 420, 421, 423, 430, 436, 443,
448, 457, 463, 469, 470

• Getting Ready for the Next Lesson 415, 423, 430, 436,
443, 449, 457

• Short Response/Grid In 471
• Quantitative Comparison 436, 471
• Open Ended 471

Study Organizer 409
Reading and Writing Mathematics

Snapshots 427

• Mathematical Prefixes and Everyday Prefixes 424
• Reading Tips 410, 425
• Writing in Math 415, 423, 430, 436, 443, 448, 457, 463

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Unit 3
Chapter

Factoring
9-1

Factors and Greatest Common Factors......................474
Algebra Activity: Factoring Using the
Distributive Property................................................480

Prerequisite Skills
• Getting Started 473
• Getting Ready for the Next Lesson
479, 486, 494, 500, 506

472

9-2

Factoring Using the Distributive Property................481
Practice Quiz 1: Lessons 9-1 and 9-2 .........................486
Algebra Activity: Factoring Trinomials .....................487

Study Organizer 473

9-3

Factoring Trinomials: x2 ϩ bx ϩ c...............................489

9-4

Factoring Trinomials: ax2 ϩ bx ϩ c .............................495
Practice Quiz 2: Lessons 9-3 and 9-4 .........................500

Reading and Writing
Mathematics
• The Language of Mathematics 507
• Reading Tips 489, 511
• Writing in Math 479, 485, 494,
500, 506, 514

9-5

Factoring Differences of Squares ................................501

9-6

Perfect Squares and Factoring.....................................508
Study Guide and Review............................................515
Practice Test ..................................................................519
Standardized Test Practice ........................................520

Standardized Test Practice
• Multiple Choice 479, 486, 494,
500, 503, 505, 506, 514, 519, 520

Lesson 9-5, p. 505

• Short Response/Grid In 494, 506,
521
• Quantitative Comparison 486, 521
• Open Ended 521

Snapshots 494

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Unit 3
Chapter

Quadratic and Exponential
Functions
10-1

522

Graphing Quadratic Functions ...................................524
Graphing Calculator Investigation: Families
of Quadratic Graphs .................................................531

10-2

Solving Quadratic Equations by Graphing...............533

10-3

Solving Quadratic Equations by Completing
the Square ...................................................................539
Practice Quiz 1: Lessons 10-1 through 10-3 ..............544
Graphing Calculator Investigation:
Graphing Quadratic Functions in Vertex
Form ...........................................................................545

10-4

Solving Quadratic Equations by Using the
Quadratic Formula....................................................546
Graphing Calculator Investigation:
Solving Quadratic-Linear Systems .........................553

10-5

Exponential Functions ..................................................554
Practice Quiz 2: Lessons 10-4 and 10-5 .....................560

10-6

Growth and Decay ........................................................561

10-7

Geometric Sequences ....................................................567
Algebra Activity: Investigating Rates of Change.....573

Study Guide and Review............................................574
Practice Test ..................................................................579
Standardized Test Practice ........................................580

Lesson 10-4, p. 551

Prerequisite Skills

Standardized Test Practice

• Getting Started 523

• Multiple Choice 527, 528, 530, 538, 543, 552, 560,
565, 572, 579, 580

• Getting Ready for the Next Lesson 530, 538, 544, 552,
560, 565

• Short Response/Grid In 572, 581
• Quantitative Comparison 581

Study Organizer 523
Reading and Writing Mathematics

• Open Ended 581

Snapshots 561, 563, 564

• Growth and Decay Formulas 566
• Reading Tips 525

• Writing in Math 530, 537, 543, 552, 560, 565, 572

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Radical and Rational
Functions
Chapter

Radical Expressions and
Triangles

584

11-1

Simplifying Radical Expressions ................................586

11-2

Operations with Radical Expressions ........................593

11-3

Radical Equations..........................................................598

• Introduction 583

Practice Quiz 1: Lessons 11-1 through 11-3 ..............603

• Follow-Ups 590, 652

Graphing Calculator Investigation: Graphs of
Radical Equations......................................................604

• Culmination 695

Prerequisite Skills

582

11-4

The Pythagorean Theorem...........................................605

11-5

The Distance Formula...................................................611

11-6

Similar Triangles............................................................616

• Getting Started 585

Practice Quiz 2: Lessons 11-4 through 11-6 ..............621

• Getting Ready for the Next Lesson

592, 597, 603, 610, 615, 621

Algebra Activity: Investigating Trigonometric
Ratios...........................................................................622
11-7

Trigonometric Ratios.....................................................623
Study Guide and Review............................................632

Study Organizer 585
Reading and Writing
Mathematics

Practice Test ..................................................................637
Standardized Test Practice ........................................638

• The Language of Mathematics 631

Lesson 11-2, p. 596

• Reading Tips 586, 611, 616, 623
• Writing in Math 591, 597, 602,
610, 614, 620, 630

Standardized Test Practice
• Multiple Choice 591, 597, 606,
608, 610, 615, 620, 630, 637, 638
• Short Response/Grid In 639
• Quantitative Comparison 602, 639
• Open Ended 639

Snapshots 615

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Unit 4
Chapter

Prerequisite Skills

Rational Expressions and
Equations
12-1

Inverse Variation ...........................................................642

12-2

Rational Expressions.....................................................648
Graphing Calculator Investigation:
Rational Expressions.................................................654

• Getting Started 641
• Getting Ready for the Next Lesson
647, 653, 659, 664, 671, 677,
683, 689

Study Organizer 641

640

12-3

Multiplying Rational Expressions ..............................655
Practice Quiz 1: Lessons 12-1 through 12-3 ..............659

12-4

Dividing Rational Expressions....................................660

12-5

Dividing Polynomials...................................................666

12-6

Rational Expressions with Like Denominators ........672
Practice Quiz 2: Lessons 12-4 through 12-6 ..............677

Reading and Writing
Mathematics
• Rational Expressions 665
• Writing in Math 646, 653, 658,
664, 671, 676, 683, 688, 695

12-7

Rational Expressions with Unlike Denominators ....678

12-8

Mixed Expressions and Complex Fractions..............684

12-9

Solving Rational Equations..........................................690
Study Guide and Review............................................696
Practice Test ..................................................................701

Standardized Test Practice

Standardized Test Practice ........................................702

• Multiple Choice 646, 647, 653,
659, 664, 671, 676, 680, 681,
683, 688, 695, 701, 702

Lesson 12-5, p. 670

• Short Response/Grid In 703
• Quantitative Comparison 703
• Open Ended 703

Snapshots 672, 689

xx

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Data Analysis

704

Chapter

706

Statistics
13-1

Sampling and Bias.........................................................708

13-2

Introduction to Matrices...............................................715
Practice Quiz 1: Lessons 13-1 and 13-2 .....................721

13-3

• Introduction 705

Histograms .....................................................................722
Graphing Calculator Investigation:
Curve Fitting ..............................................................729

• Follow-Ups 742, 766

• Culmination 788

13-4

Measures of Variation...................................................731
Practice Quiz 2: Lessons 13-3 and 13-4 .....................736

13-5

Box-and-Whisker Plots.................................................737
Algebra Activity: Investigating Percentiles ..............743
Study Guide and Review............................................745
Practice Test ..................................................................749
Standardized Test Practice ........................................750

Lesson 13-5, p. 738

Prerequisite Skills

Standardized Test Practice

• Getting Started 707

• Multiple Choice 713, 720, 723, 724, 726, 728, 736,
742, 749, 750

• Getting Ready for the Next Lesson 713, 721, 728, 736

• Short Response/Grid In 751
• Quantitative Comparison 751

Study Organizer 705

• Open Ended 751

Reading and Writing Mathematics
Snapshots 730

• Survey Questions 714
• Reading Tips 732, 737
• Writing in Math 713, 720, 728, 736, 742

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Unit 5
Chapter

Probability
14-1

Prerequisite Skills
• Getting Started 753
• Getting Ready for the Next Lesson
758, 767, 776, 781

752

Counting Outcomes ......................................................754
Algebra Activity: Finite Graphs..................................759

14-2

Permutations and Combinations ................................760
Practice Quiz 1: Lessons 14-1 and 14-2 .....................767

14-3

Probability of Compound Events ...............................769

14-4

Probability Distributions..............................................777
Practice Quiz 2: Lessons 14-3 and 14-4 .....................781

Study Organizer 753

14-5

Probability Simulations ................................................782
Study Guide and Review............................................789
Practice Test ..................................................................793

Reading and Writing
Mathematics

Standardized Test Practice ........................................794

• Mathematical Words and Related
Words 768
• Reading Tips 771, 777
• Writing in Math 758, 766, 776,
780, 787

Standardized Test Practice
• Multiple Choice 758, 762, 764,
766, 776, 780, 787, 793, 794
• Short Response/Grid In 795
• Quantitative Comparison 795
• Open Ended 795

Student Handbook
Skills
Prerequisite Skills..................................................................................798
Extra Practice .........................................................................................820
Mixed Problem Solving........................................................................853

Reference
English-Spanish Glossary ......................................................................R1
Selected Answers ..................................................................................R17
Photo Credits.........................................................................................R61
Index .......................................................................................................R62
Symbols and Formulas ..............................................Inside Back Cover

Snapshots 780

Lesson 14-1, p. 756

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Expressions
and Equations
Equations
You can use algebraic
expressions and
equations to model
and analyze real-world
situations. In this unit,
you will learn about
expressions, equations,
and graphs.

Chapter 1
The Language of Algebra

Chapter 2
Real Numbers

Chapter 3
Solving Linear Equations

2 Unit 1 Expressions and Equations

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Can You Fit 100 Candles
on a Cake?
Source: USA TODAY, January, 2001

“The mystique of living to be 100 will be lost by
the year 2020 as 100th birthdays become commonplace,
predicts Mike Parker, assistant professor of social
work, University of Alabama, Tuscaloosa, and a
gerontologist specializing in successful aging. He says
that, in the 21st century, the fastest growing age
group in the country will be centenarians—those
who live 100 years or longer.” In this project, you
will explore how equations, functions, and graphs
can help represent aging and population growth.
Log on to www.algebra1.com/webquest.
Begin your WebQuest by reading the Task.

USA TODAY Snapshots®
Longer lives ahead
Projected life expectancy for American men and women
born in these years:
Men
Women

74
years

1999

80
years

78
years

1999

2025

84
years

81
years

2025

2050

87
years

2050

Source: U.S. Census Bureau

Then continue working
on your WebQuest as
you study Unit 1.

Lesson
Page

1-9
55

2-6
100

3-6
159

By James Abundis and Quin Tian, USA TODAY

Unit 1 Expressions and Equations

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3


The Language of
Algebra
• Lesson 1-1 Write algebraic expressions.
• Lessons 1-2 and 1-3 Evaluate expressions and
solve open sentences.
• Lessons 1-4 through 1-6 Use algebraic
properties of identity and equality.
• Lesson 1-7 Use conditional statements and

counterexamples.
• Lessons 1-8 and 1-9 Interpret graphs of
functions and analyze data in statistical graphs.

In every state and in every country, you find unique
and inspiring architecture. Architects can use algebraic
expressions to describe the volume of the structures
they design. A few of the shapes these buildings can
resemble are a rectangle, a pentagon, or even a
pyramid. You will find the amount of space occupied by a
pyramid in Lesson 1-2.

4 Chapter 1 The Language of Algebra

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Key Vocabulary
•
•
•
•
•

variable (p. 6)
order of operations (p. 11)
identity (p. 21)
like terms (p. 28)
counterexample (p. 38)

Prerequisite Skills To be successful in this chapter, you’ll need to master
these skills and be able to apply them in problem-solving situations. Review
these skills before beginning Chapter 1.
For Lessons 1-1, 1-2, and 1-3

Multiply and Divide Whole Numbers

Find each product or quotient.
1. 8 и 8
2. 4 и 16
5. 57 Ϭ 3

6. 68 Ϭ 4

3. 18 и 9

4. 23 и 6

72
7. ᎏᎏ
3

90
8. ᎏᎏ
6

For Lessons 1-1, 1-2, 1-5, and 1-6

Find Perimeter

Find the perimeter of each figure. (For review, see pages 820 and 821.)
9.
10.
5.6 m
6.5 cm
2.7 m

3.05 cm

11.

12.
3

5

42 8 ft

1 8 ft

1

25 4 ft

For Lessons 1-5 and 1-6

Multiply and Divide Decimals and Fractions

Find each product or quotient. (For review, see page 821.)
13. 6 и 1.2

14. 0.5 и 3.9
15. 3.24 Ϭ 1.8
3
17. ᎏᎏ и 12
4

16. 10.64 Ϭ 1.4

5
9
19. ᎏᎏ Ϭ ᎏᎏ
16
12

2 3
18. 1ᎏᎏ и ᎏᎏ
3 4

5
2
20. ᎏᎏ Ϭ ᎏᎏ
6

3

Make this Foldable to help you organize information about
algebraic properties. Begin with a sheet of notebook paper.
Fold

Cut

Cut along the
top line and
then cut 9 tabs.

Fold lengthwise
to the holes.

Label
Label
the tabs using
the lesson numbers
and concepts.

1-1
1-1
1-2
1-3
1-4
1-5
1-6
1-6
1-7
1-8

s
ssionns
Expreua
tio
and Eq

Factors

and Prod

ucts

Powers

Order

of Ope

rations

es
entenc
Open S and

IdentitPryoperties
Equality
ty

ive
Distribut

Proper

ty
Proper
utative

Comm

Associ

ative Pr

operty

s
Function

Store the Foldable in a 3-ring binder. As you read and study
the chapter, write notes and examples under the tabs.

Reading and Writing

Chapter 1 The Language of Algebra 5

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