Algebra 1.pdf - GLENCOE MATHEMATICS interactive student edition Algebra 1 Contents in Brief Unit Unit Unit Unit Unit Expressions and Equations.2 Chapter

Algebra 1.pdf - GLENCOE MATHEMATICS interactive student...

This preview shows page 1 out of 949 pages.

You've reached the end of your free preview.

Want to read all 949 pages?

Unformatted text preview: 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 iii Authors iv 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 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 USA TODAY The USA TODAY Snapshots®, created by USA TODAY®, help students make the connection between real life and mathematics. Dinah Zike Educational Consultant Dinah-Might Activities, Inc. San Antonio, TX v 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. vi 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 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 vii 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. viii 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 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 Study Organizer 5 Reading and Writing Mathematics • Open Ended 65 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 ix 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 • Reading Math Tips 97, 103 • Writing in Math 72, 78, 82, 87, 94, 100, 109 x Snapshots 78, 80 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 • Open Ended 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 Lesson 3-4, p. 142 Snapshots 158 xi 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 Study Organizer 191 Reading and Writing Mathematics • Reasoning Skills 239 • Reading Math Tips 192, 198, 233, 234 • Writing in Math 196, 203, 210, 216, 222, 231, 238, 245 xii • Open Ended 253 Snapshots 210 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 Snapshots 258, 284 Lesson 5-2, p. 266 xiii 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 • R...
View Full Document

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture