ISBN 10: 1-256-69465-7

ISBN 13: 978-1-256-69465-6

The Center for Mathematics Education Project was developed at Education Development Center, Inc. (EDC) within the Center for Mathematics Education (CME), with partial support from the National Science Foundation.

Education Development Center, Inc.Center for Mathematics EducationNewton, Massachusetts

This material is based upon work supported by the National ScienceFoundation under Grant No. ESI-0242476, Grant No. MDR-9252952, andGrant No. ESI-9617369. Any opinions, findings, and conclusions orrecommendations expressed in this material are those of the author(s)and do not necessarily reflect the views of the National Science Foundation.

Cover Art: Courtesy of Pearson Education, Inc.

Taken from:CME Project: Geometry, Algebra 2, Algebra 1, PrecalculusBy the CME Project Development TeamCopyright © 2009 by Education Development Center, Inc.Published by Pearson Education, Inc.Upper Saddle River, New Jersey 07458

CME Common Core Additional Lessons: Geometry, Precalculus, Algebra 2, Algebra 1By the CME Project Development TeamCopyright © 2012 by Education Development Center, Inc.Published by Pearson Education, Inc.Upper Saddle River, New Jersey 07458

CME Project Development Team

Lead Developers: Al Cuoco and Bowen Kerins

Core Development Team: Anna Baccaglini-Frank, Jean Benson, Nancy Antonellis D’Amato, Daniel Erman, Brian Harvey, Wayne Harvey, Doreen Kilday, Ryota Matsuura, Stephen Maurer, Sarah Sword, Audrey Ting, Kevin Waterman.

1 2 3 4 5 6 7 8 9 10 XXXX 17 16 15 14 13 12

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Copyright © 2013 by Pearson Learning Solutions All rights reserved. Permission in writing must be obtained from the publisher before any part of this work may be reproduced ortransmitted in any form or by any means, electronic or mechanical, including photocopying and recording, orby any information storage or retrieval system. All trademarks, service marks, registered trademarks, and registered service marks are the property of theirrespective owners and are used herein for identification purposes only. Pearson Learning Solutions, 501 Boylston Street, Suite 900, Boston, MA 02116

A Pearson Education Companywww.pearsoned.com

Printed in the United States of America

iii

Contents in BriefIntroduction to the CME Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

CME Project Student Handbook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Chapter 1 Arithmetic to Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Chapter 2 Expressions and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Chapter 3 Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Chapter 4 Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

Chapter 5 Exponents and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360

Chapter 6 Statistics and Fitting Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

Chapter 7 Introduction to Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556

Chapter 8 Congruence and Transformations. . . . . . . . . . . . . . . . . . . . . . . 602

Honors Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684

TI-Nspire™ Technology Handbook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 788

Tables

Math Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 811

Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812

Formulas From Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813

Properties, Postulates, and Theorems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817

Selected Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 858

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

nctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360

ng Lines . . . . . . . . .................... ........... ........ . .. . ... . . . .... ........................... . ... .. ................. ....................... .. ..... ................ . . . ..... . ......... . .... ... ............. . . . . . . . . . . 474

eometry . . . . . . . . ... .. . ... ...... .. .. . .... . .. .. . . .. .. . . ... .. . . . . . . . . . . . . .. . . . .. . ...... .................. . . . . . . . . 556

Transformations. . ........................ . . ............. . . . . ......... . . . . . . . . . . . .. . . . . . .. . . . . . . . . . .... .................... . . . . . . . 602

. . . . . . . . . . . . . . . . . ........... ............ . . . .. . . .. . . .. ................... . . . ... . . . . . . . . . ... ... ............... ... ... .................. ....... .... . .. ....... ... . .. .. . . . . . . . 684

book. . . . . . . . . . . . .... .... . ...... ............ . .......... .. .... ... . . .. .. ..... ......... . ........... . ..... .. .............. .. . . ............ ..... ................... ... ... .... .... . . ... . . .... .......... . . ................... .. . . . . . . . 788

. . . . . . . . . . . . . . . . . . .... ...... .. .. ..... ............ ........ .. . .. ..... ...... . . . . .... . ..... .. . . .... .... .............. . . ............ .... . . ....... ........... . . ........ .... ........ ....................... ....... ................... . . 811

. . . . . . . . . . . . . . . . ............. . .. .. .. .. . ..... . . ... . .. .. ... .. . .... .. . . .. . ............. .............. . .. . . ... ............. ... . . . ... . . ....... ....... . ....... . .. . ...... ..... . ..... . ........ . ............ .. .. .. . .. . . .. .. .. . . .. . . . . 812

. . . . . . . . . . . . . . . . ... . ...... .. . ............ ... ...... .. . . .. .... . ... .. .. ... ..... .... ......... ........ ..... ..... .... ... .. . . . ... .......... ...... ..... .. .. . . .... ... . . ...... . . . . . . 813

heorems. . . . . . . . .. . .. ...... . . .. . ... . .................. ........ .. .. ...................... .. . .. .. .. . . . .. ......... .... . . . ...... .. .......... .... .. ......... . ...... ............ . . . . . . . 814

. . . . . . . . . . . . . . . . .................. ....... ............. ...... . .. ... .... . ......... . .... . . ... . . ..... ............. . . . ...... ..... ....... . . . . ...... ....... ................ . . . . . 817

. . . . . . . . . . . . . . ....... ...... ........ .............. . . . .. . . .. ..... ... ........ ...... .. .. ..... ... . . .... . ...... ........ ..... ........ .. ....... .. . . .... ... ...... ........................ ..... . ...... ...... ......... ........... . .. ... . .. ... .. ..... . . . . . 823

. . . . . . . . . . . . . .. ........ .. ... ...... .... .. ....... ........... .......... ... ............ .. .. . . .. . . . . . . . . .. . . . . . . .. . ... . .. .............. .... . . ......... ....... .... .. . ............ . ........... . .... ............ . . . . 858

. . . . . . . . . . . . . . ........ .............. . ...... .... ... . .. ... .. ......... ... ... ..... .......... .......... ... .. . ...... .... .. . . . . . .. . . . . . .. . .. .. . . . ... . .. .. . ... ... ..... .... ..... ..... . .. . . . . . . . . ... . . . . . .... .............. . . . 865

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iv

Introduction to the CME Project

The CME Project, developed by EDC’s Center for Mathematics Education, is a new NSF-funded high school program, organized around the familiar courses of algebra 1, geometry, algebra 2, and precalculus. The CME Project provides teachers and schools with a third alter native to the choice between traditional texts driven by basic skill development and more pro gressive texts that have unfamiliar organizations. This program gives teachers the option of a problem-based, student-centered program, organized around the mathematical themes with which teachers and parents are familiar. Furthermore, the tremendous success of NSF-funded middle school programs has left a need for a high school program with similar rigor and pedagogy. The CME Project fills this need.

The goal of the CME Project is to help students acquire a deep understanding of mathematics. Therefore, the mathematics here is rigorous. We took great care to create lesson plans that, while challenging, will capture and engage students of all abilities and improve their mathematical achievement.

The Program’s Approach The organization of the CME Project provides students the time and focus they need to develop fundamental mathematical ways of thinking. Its primary goal is to develop in students robust mathematical proficiency.

• The program employs innovative instructional methods, developed over decades of classroom experience and informed by research, that help students master mathematical topics.

• One of the core tenets of the CME Project is to focus on developing students’ Habits of Mind, or ways in which students approach and solve mathematical challenges.

• The program builds on lessons learned from high-performing countries: develop an idea thoroughly and then revisit it only to deepen it; organize ideas in a way that is faithful to how they are organized in mathematics; and reduce clutter and extraneous topics.

• It also employs the best American models that call for grappling with ideas and problems as preparation for instruction, moving from concrete problems to abstractions and general theories, and situating mathematics in engaging contexts.

• The CME Project is a comprehensive curriculum that meets the dual goals of mathematical rigor and accessibility for a broad range of students.

About CMEEDC’s Center for Mathematics Education, led by mathematician and teacher Al Cuoco, brings together an eclectic staff of mathematicians, teachers, cognitive scientists, education researchers, curriculum developers, specialists in educational technology, and teacher educators, internationally known for leadership across the entire range of K–16 mathematics education. We aim to help students and teachers in this country experience the thrill of solving problems and building theories, understand the history of ideas behind the evolution of mathematical disciplines, and appreciate the standards of rigor that are central to mathematical culture.

CME PROJECT

iv CME Project

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Mathematics I

National Advisory Board The National Advisory Board met early in the project, providing critical feedback on the instructional design and the overall organization. Members include

Richard Askey, University of Wisconsin Edward Barbeau, University of Toronto Hyman Bass, University of MichiganCarol Findell, Boston University Arthur Heinricher, Worcester Polytechnic InstituteRoger Howe, Yale UniversityBarbara Janson, Janson AssociatesKenneth Levasseur, University of Massachusetts, LowellJames Madden, Louisiana State University, Baton RougeJacqueline Miller, Education Development CenterJames Newton, University of MarylandRobert Segall, Greater Hartford Academy of Mathematics and ScienceGlenn Stevens, Boston UniversityHerbert Wilf, University of PennsylvaniaHung-Hsi Wu, University of California, Berkeley

Core Mathematical Consultants Dick Askey, Ed Barbeau, and Roger Howe have been involved in an even more substantial way, reviewing chapters and providing detailed and critical advice on every aspect of the program. Dick and Roger spent many hours reading and criticizing drafts, brainstorming with the writing team, and offering advice on everything from the logical organization to the actual numbers used in problems. We can’t thank them enough.

Teacher Advisory Board The Teacher Advisory Board for the CME Project was essential in help ing us create an effective format for our lessons that embodies the philosophy and goals of the program. Their debates about pedagogi cal issues and how to develop mathematical top ics helped to shape the distinguishing features of the curriculum so that our lessons work effective ly in the classroom. The advisory board includes

Jayne Abbas, Richard Coffey, Charles Garabedian, Dennis Geller, Eileen Herlihy, Doreen Kilday, Gayle Masse, Hugh McLaughlin, Nancy McLaughlin, Allen Olsen, Kimberly Osborne, Brian Shoemaker, and Benjamin Sinwell

Field-Test Teachers Our field-test teachers gave us the benefit of their classroom experi ence by teaching from our draft lessons and giv ing us extensive, critical feedback that shaped the drafts into realistic, teachable lessons. They shared their concerns, questions, challenges, and successes and kept us focused on the real world. Some of them even welcomed us into their classrooms as co-teachers to give us the direct experience with students that we needed to hone our lessons. Working with these expert professionals has been one of the most gratifying parts of the development—they are “highly qualified” in the most profound sense.

California Barney Martinez, Jefferson High School, Daly City; Calvin Baylon and Jaime Lao, Bell Junior High School, San Diego; Colorado Rocky Cundiff, Ignacio High School, Ignacio; Illinois Jeremy Kahan, Tammy Nguyen, and Stephanie Pederson, Ida Crown Jewish Academy, Chicago; Massachusetts Carol Martignette, Chris Martino and Kent Werst, Arlington High School, Arlington, Larry Davidson, Boston University Academy, Boston; Joe Bishop and Carol Rosen, Lawrence High School, Lawrence; Maureen Mulryan, Lowell High School, Lowell; Felisa Honeyman, Newton South High School, Newton Centre; Jim Barnes and Carol Haney, Revere High School, Revere; New Hampshire Jayne Abbas and Terin Voisine, Cawley Middle School, Hooksett; New Mexico Mary Andrews, Las Cruces High School, Las Cruces; Ohio James Stallworth, Hughes Center, Cincinnati; Texas Arnell Crayton, Bellaire High School, Bellaire; Utah Troy Jones, Waterford School, Sandy; Washington Dale Erz, Kathy Greer, Karena Hanscom, and John Henry, Port Angeles High School, Port Angeles; Wisconsin Annette Roskam, Rice Lake High School, Rice Lake.

Special thanks go to our colleagues at Pearson, most notably Elizabeth Lehnertz, Joe Will, and Stewart Wood. The program benefits from their expertise in every way, from the actual mathematics to the design of the printed page.

Contributors to the CME Project

CME Project v

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1Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.0 Habits of Mind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

The Tables of Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.02 Thinking About Negative Numbers . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.03 Extending the Addition Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.04 Extending the Multiplication Table . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.05 The Basic Rules of Arithmetic—Properties of Operations. . . . . . . . 28 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

The Number Line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.06 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1.07 Numbers Besides the Integers—Fractions . . . . . . . . . . . . . . . . . . . . 37 1.08 Decimals—Addresses on the Number Line. . . . . . . . . . . . . . . . . . . . 41 1.09 Number Line Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.10 Number Line Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

The Algorithms of Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 1.11 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.12 Addition and Subtraction Algorithms . . . . . . . . . . . . . . . . . . . . . . . 61 1.13 Adding and Subtracting Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . 67 1.14 Multiplication Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 1.15 Multiplying and Dividing Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . 77 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Project: Using Mathematical Habits Lo . . . ong Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

1A

1B

1C

vi Algebra 1

Arithmetic to Algebra

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2A

2B

2D

2C

Contents vii

2 Expressions and EquationsChapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 2.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 2.02 Modeling General Situations—Writing Expressions . . . . . . . . . . . . 93 2.03 Evaluating Expressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2.04 Simplifying Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 2.05 Rephrasing the Basic Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 2.06 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 2.07 Reversing Operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 2.08 Solving Equations by Backtracking . . . . . . . . . . . . . . . . . . . . . . . . . 126 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Solving Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 2.09 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 2.10 When Backtracking Does Not Work . . . . . . . . . . . . . . . . . . . . . . . . 138 2.11 The Basic Moves for Solving Equations. . . . . . . . . . . . . . . . . . . . . . 143 2.12 Solutions of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 2.13 Focus on the Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . 153 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Word Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 2.14 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 2.15 Building Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 2.16 Solving Word Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 2.17 More Than One Variable— Solving in Terms of Each Other . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Project: Using Mathematical Habits Good Questions About Perfect Squares . . . . . . . . . . . . . . . . . . . . . . . . . 179

Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182. . . . . . . . . . . . . . . . . . . . . . 18

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3

viii

Graphs

3C

3B

3A

Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Equations and Their Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 186 3.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 3.02 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 3.03 Equations as Point-Testers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 3.04 Graphing by Plotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 3.05 Graphin g Related Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 3.06 Intersections of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Basic Graphs and Translations . . . . . . . . . . . . . . . . . . . . . . . . 220 3.07 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 3.08 Two Basic Graphs: Direct and Inverse. . . . . . . . . . . . . . . . . . . . . . . . . 225 3.09 Four More Basic Graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

All About Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 3.10 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 3.11 Pitch and Slope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 3.12 Rates of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 3.13 Collinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

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Mathematics I

Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

Linear Equations and Graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 4.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 4.02 Equations of Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 4.03 Jiffy Graphs: Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 4.04 Overtaking—Slope in Distance-Time Graphs . . . . . . . . . . . . . . . . . . 289 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 4.05 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 4.06 Solving Systems: Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 4.07 Slope and Parallel Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 4.08 Solving Systems: Elimination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

Applications of Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 4.09 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 4.10 Solving by Graphing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 4.11 Inequalities with One Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 4.12 Inequalities with Two Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 4.13 Graphing Linear Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358

4 Lines

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Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360

Functions—The Basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 5.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 5.02 Building Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 5.03 Is It a Function? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 5.04 Naming Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 5.05 Function Inputs and Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 5.06 Graphing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Mathematical Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396

Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 5.07 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 5.08 Squares, Cubes, and Beyond—Some Basic Rules of Exponents . . . 402 5.09 More Basic Rules of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 5.10 Zero and Negative Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 5.11 Scientifi c Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

Functions, Graphs, and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 5.12 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 5.13 Constant Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 5.14 Recursive Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 5.15 Constant Ratios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 5.16 Compound Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 5.17 Graphs of Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . 462 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

Project: Using Mathematical Habits Managing Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468

Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472

5

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Exponents and Functions

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5B

5C

. . . and out comes 5 . . .

. . . or is it 6?

You put in 3 . . .

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Mathematics I

Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

Statistical Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 6.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 6.02 Mean, Median, and Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 6.03 Data Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 6.04 Paired Comparisons—Box-and-Whisker Plots . . . . . . . . . . . . . . . . . 495 6.05 Categorical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 6.06 Two-Variable Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

Fitting and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 6.07 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 6.08 Linear Trends in Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528 6.09 Fitting Lines to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536 6.10 The Line of Best Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550

Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554

Statistics and Fitting Lines

6

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6B

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Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556

Picturing and Drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 7.01 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 7.02 Drawing 3-D Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 7.03 Drawing and Describing Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . 566 7.04 Drawing from a Recipe—Reading and Writing Directions

for Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573

Constructing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 7.05 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 7.06 Compasses, Angles, and Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584

Geometry Software. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 7.07 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 7.08 Drawings vs. Constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 7.09 Drawing UnMessUpable Figures—Building Constructions . . . . . . 592 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597

Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600

7 Introduction to Geometry

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7B

7C

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Mathematiacs I

Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602

The Congruence Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604 8.01 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605 8.02 Length, Measure, and Congruence . . . . . . . . . . . . . . . . . . . . . . . . . 607 8.03 Corresponding Parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 8.04 Triangle Congruence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619

Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 8.05 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621 8.06 Refl ections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 8.07 Translations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631 8.08 Rotations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639 8.09 Congruence and Isometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656

Geometry in the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . 658 8.10 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659 8.11 Midpoint and Distance Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . 662 8.12 Parallel Lines and Collinear Points . . . . . . . . . . . . . . . . . . . . . . . . . . 669 8.13 Perpendicular Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679

Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682

8

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8B

8C

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Congruence and Transformations

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Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684

Exploring Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686 H.01 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687 H.02 Introduction to Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692 H.03 The Vector Equation of a Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700 H.04 Using the Vector Equation of a Line . . . . . . . . . . . . . . . . . . . . . . . . 705 H.05 Vector Equations of Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717

Matrix Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 718 H.06 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 H.07 Basic Matrix Operations—Addition, Subtraction,

and Scalar Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724 H.08 Dot Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 H.09 Matrix Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753

Applications of Matrix Multiplication. . . . . . . . . . . . . . . . . . . . . 754 H.10 Matrix Inverses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755 H.11 Matrix Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 761 H.12 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 770 H.13 Geometric Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775 Mathematical Refl ections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787

H Honors Appendix

Honors Appendix

A

xiv

Honors Appendix

B

Honors Appendix

C

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Mathematics I