Algebra 2 Common Core Randall I. Charles Basia Hall Dan Kennedy Allan E. Bellman Sadie Chavis Bragg William G. Handlin Stuart J. Murphy Grant Wiggins Boston, Massachusetts • Chandler, Arizona • Glenview, Illinois • Hoboken, New Jersey HSM15SE_A2_NA_FM_Title.indd Page 1 6/19/14 5:06 PM user /131/PE01129_R3/HSM15/FL/SE/2015/0133308073/Layout/Interior_Files/A2/Front_Matter ... Acknowledgments appear on page 1160, which constitutes an extension of this copyright page. Copyright © 2015 Pearson Education, Inc., or its affiliates. All Rights Reserved. Printed in the United States of America. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. 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ISBN-13: 978-0-13-328116-3 ISBN-10: 0-13-328116-7 4 5 6 7 8 9 10 V057 18 17 16 15 14 HSM15SE_A2_NA_FM_CB.indd Page 2 6/19/14 5:02 PM user /131/PE01129_R3/HSM15/FL/SE/2015/0133308073/Layout/Interior_Files/A2/Front_Matter ... E R O C N O M M O C E Contents in Brief R O Welcome to Pearson Algebra 2 Common Core Edition student book. Throughout this textbook, you will find content that has been developed to cover many of the High School Standards for C Mathematical Content and all of the Standards for Mathematical Practice. The End-of-Course Assessment provides students with practice with all of the Standards for Mathematical Content listed on pages xx to xxiii. N O Using Your Book for Success ............................................... viii Contents ................................................................ xxvi M Entry-Level Assessment .................................................... xl CC Content Focus: Seeing Structure in Expressions M Chapter 1 Expressions, Equations, and Inequalities ................................. 1 Chapter 2 Functions, Equations, and Graphs ..................................... 57 O Chapter 3 Linear Systems ...................................................131 CC Content Focus: Interpreting and Building Functions C Chapter 4 Quadratic Functions and Equations ....................................191 Chapter 5 Polynomials and Polynomial Functions................................. 277 E Chapter 6 Radical Functions and Rational Exponents .............................. 357 R Chapter 7 Exponential and Logarithmic Functions ................................ 431 O Chapter 8 Rational Functions................................................ 495 Chapter 9 Sequences and Series ..............................................561 C CC Content Focus: Expressing Geometric Properties with Equations Chapter 10 Quadratic Relations and Conic Sections .................................611 N CC Content Focus: Rules of Probability, Interpreting Data, and Making Inferences O Chapter 11 Probability and Statistics........................................... 671 Chapter 12 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .761 M CC Content Focus: Trigonometric Functions Chapter 13 Periodic Functions and Trigonometry .................................. 825 M Chapter 14 Trigonometric Identities and Equations................................. 901 End-of-Course Assessment ................................................ 964 O Skills Handbook ......................................................... 972 C Reference ............................................................... 985 Visual Glossary.......................................................... 994 E Selected Answers ....................................................... 1047 R Index.................................................................. 1138 Acknowledgments ...................................................... 1160 O C Contents iii N O HSM15SE_A2_NA_FM_CB.indd Page 3 30/09/13 11:07 AM gg_053 /132/PE01129_MIGRATE/HIGH_SCHOOL_MATH_2015/NATIONAL/SE/MATH_2015/G8/XXXXXXXXXX_G/ ... M M O C Series Authors Randall I. Charles, Ph.D., is Professor Emeritus in the Department of Mathematics and Computer Science at San Jose State University, San Jose, California. He began his career as a high school mathematics teacher, and he was a mathematics supervisor for five years. Dr. Charles has been a member of several NCTM committees and is the former Vice President of the National Council of Supervisors of Mathematics. Much of his writing and research has been in the area of problem solving. He has authored more than 90 mathematics textbooks for kindergarten through college. Dan Kennedy, Ph.D., is a classroom teacher and the Lupton Distinguished Professor of Mathematics at the Baylor School in Chattanooga, Tennessee. A frequent speaker at professional meetings on the subject of mathematics education reform, Dr. Kennedy has conducted more than 50 workshops and institutes for high school teachers. He is coauthor of textbooks in calculus and precalculus, and from 1990 to 1994, he chaired the College Board’s AP Calculus Development Committee. He is a 1992 Tandy Technology Scholar and a 1995 Presidential Award winner. Basia Hall currently serves as Manager of Instructional Programs for the Houston Independent School District. With 33 years of teaching experience, Ms. Hall has served as a department chair, instructional supervisor, school improvement facilitator, and professional development trainer. She has developed curricula for Algebra 1, Geometry, and Algebra 2 and co-developed the Texas state mathematics standards. A 1992 Presidential Awardee, Ms. Hall is past president of the Texas Association of Supervisors of Mathematics and is a state representative for the National Council of Supervisors of Mathematics (NCSM). Consulting Authors Stuart J. Murphy is a visual learning author and consultant. He is a champion of helping students develop learning skills so they become more successful students. He is the author of MathStart, a series of children’s books that presents mathematical concepts in the context of stories and I See I Learn, a Pre-Kindergarten and Kindergarten learning initiative that focuses on social and emotional skills. A graduate of the Rhode Island School of Design, he has worked extensively in educational publishing and has been on the authorship teams of a number of elementary and high school mathematics programs. He is a frequent presenter at meetings of the National Council of Teachers of Mathematics, the International Reading Association, and other professional organizations. Grant Wiggins, Ed.D., is the President of Authentic Education in Hopewell, New Jersey. He earned his B.A. from St. John’s College in Annapolis and his Ed.D. from Harvard University. Dr. Wiggins consults with schools, districts, and state education departments on a variety of reform matters; organizes conferences and workshops; and develops print materials and Web resources on curricular change. He is perhaps best known for being the coauthor, with Jay McTighe, of Understanding by Design and The Understanding by Design Handbook1, the award-winning and highly successful materials on curriculum published by ASCD. His work has been supported by the Pew Charitable Trusts, the Geraldine R. Dodge Foundation, and the National Science Foundation. 1 ASCD, publisher of “The Understanding by Design Handbook” coauthored by Grant Wiggins and registered owner of the trademark “Understanding by Design,” has not authorized or sponsored this work and is in no way affiliated with Pearson or its products. iv HSM15SE_A2_NA_FM_CB.indd Page 4 30/09/13 11:07 AM gg_053 /132/PE01129_MIGRATE/HIGH_SCHOOL_MATH_2015/NATIONAL/SE/MATH_2015/G8/XXXXXXXXXX_G/ ... E R O C N O M M O C E Program Authors R O Algebra 1 and Algebra 2 C Allan E. Bellman, Ph.D., is an Associate Professor of Mathematics Education at the University of Mississippi. He previously taught at the University of California, Davis for 12 years and in public school in Montgomery County, Maryland for 31. He has been an instructor for both the Woodrow N Wilson National Fellowship Foundation and the Texas Instruments’ T3 program. Dr. Bellman has a expertise in the use of technology in education and assessment-driven instruction, and speaks O frequently on these topics. He was a 1992 Tandy Technology Scholar and has twice been listed in Who’s Who Among America’s Teachers. M Sadie Chavis Bragg, Ed.D., is Senior Vice President of Academic Affairs and professor of mathematics at the Borough of Manhattan Community College of the City University of New York. M She is a past president of the American Mathematical Association of Two-Year Colleges (AMATYC). In recognition of her service to the field of mathematics locally, statewide, nationally, and O internationally, she was awarded AMATYC’s most prestigious award, the Mathematics Excellence Award for 2010. Dr. Bragg has coauthored more than 50 mathematics textbooks for kindergarten C through college. William G. Handlin, Sr., is a classroom teacher and Department Chair of Mathematics and former E Department Chair of Technology Applications at Spring Woods High School in Houston, Texas. R Awarded Life Membership in the Texas Congress of Parents and Teachers for his contributions to the well-being of children, Mr. Handlin is also a frequent workshop and seminar leader in professional O meetings. Geometry C Laurie E. Bass is a classroom teacher at the 9–12 division of the Ethical Culture Fieldston School in N Riverdale, New York. A classroom teacher for more than 30 years, Ms. Bass has a wide base of teaching experience, ranging from Grade 6 through Advanced Placement Calculus. She was the O recipient of a 2000 Honorable Mention for the Radio Shack National Teacher Awards. She has been a contributing writer for a number of publications, including software-based activities for the M Algebra 1 classroom. Among her areas of special interest are cooperative learning for high school students and geometry exploration on the computer. Ms. Bass is a frequent presenter at local, regional, and national conferences. M Art Johnson, Ed.D., is a professor of mathematics education at Boston University. He is a O mathematics educator with 32 years of public school teaching experience, a frequent speaker and workshop leader, and the recipient of a number of awards: the Tandy Prize for Teaching Excellence, the Presidential Award for Excellence in Mathematics Teaching, and New Hampshire Teacher of the C Year. He was also profiled by the Disney Corporation in the American Teacher of the Year Program. Dr. Johnson has contributed 18 articles to NCTM journals and has authored over 50 books on E various aspects of mathematics. R O C v N O HSM15SE_A2_NA_FM_CB.indd Page 5 30/09/13 11:07 AM gg_053 /132/PE01129_MIGRATE/HIGH_SCHOOL_MATH_2015/NATIONAL/SE/MATH_2015/G8/XXXXXXXXXX_G/ ... M M O C Reviewers National Tammy Baumann Sharon Liston Robert Thomas, Ph.D. K-12 Mathematics Coordinator Mathematics Department Chair Mathematics Teacher School District of the City Moore Public Schools Yuma Union High School of Erie Oklahoma City, Oklahoma District #70 Erie, Pennsylvania Yuma, Arizona Ann Marie Palmeri Monahan Sandy Cowgill Mathematics Supervisor Linda Ussery Mathematics Department Chair Bayonne Public Schools Mathematics Consultant Muncie Central High School Bayonne, New Jersey Alabama Department of Muncie, Indiana Education Indika Morris Tuscumbia, Alabama Sheryl Ezze Mathematics Department Chair Mathematics Chairperson Queen Creek School District Denise Vizzini DeWitt High School Queen Creek, Arizona Mathematics Teacher Lansing, Michigan Clarksburg High School Jennifer Petersen Montgomery County, Dennis Griebel K-12 Mathematics Curriculum Maryland Mathematics Coordinator Facilitator Cherry Creek School District Springfield Public Schools Marcia White Aurora, Colorado Springfield, Missouri Mathematics Specialist Academic Operations, Bill Harrington Tammy Popp Technology and Innovations Secondary Mathematics Mathematics Teacher Memphis City Schools Coordinator Mehlville School District Memphis, Tennessee State College School District St. Louis, Missouri State College, Pennsylvania Merrie Wolf Mickey Porter Mathematics Department Chair Michael Herzog Mathematics Teacher Tulsa Public Schools Mathematics Teacher Dayton Public Schools Tulsa, Oklahoma Tucson Small School Project Dayton, Ohio Tucson, Arizona Steven Sachs Camilla Horton Mathematics Department Chair Secondary Instruction Support Lawrence North High School Memphis School District Indianapolis, Indiana Memphis, Tennessee John Staley Gary Kubina Secondary Mathematics Mathematics Consultant Coordinator Mobile County School System Office of Mathematics, PK-12 Mobile, Alabama Baltimore, Maryland vi HSM15SE_A2_NA_FM_CB.indd Page 6 30/09/13 11:07 AM gg_053 /132/PE01129_MIGRATE/HIGH_SCHOOL_MATH_2015/NATIONAL/SE/MATH_2015/G8/XXXXXXXXXX_G/ ... E R O C N O M M O C E From the Authors R O Welcome C Math is a powerful tool with far-reaching applications throughout your life. We have designed a unique and engaging program that will enable you to tap into the power of mathematics N and mathematical reasoning. This award-winning program has been developed to align fully to the Common Core State Standards. O Developing mathematical skills and problem-solving strategies is an ongoing process—a journey both inside and outside the classroom. This course is designed to help make sense M of the mathematics you encounter in and out of class each day and to help you develop mathematical proficiency. M You will learn important mathematical principles. You will also learn how the principles are connected to one another and to what you already know. You will learn to solve problems and O learn the reasoning that lies behind your solutions. You will also develop the key mathematical practices of the Common Core State Standards. C Each chapter begins with the “big ideas” of the chapter and some essential questions that you will learn to answer. Through this question-and-answer process you will develop your ability to analyze problems independently and solve them in different applications. E Your skills and confidence will increase through practice and review. Work through the problems R so you understand the concepts and methods presented and the thinking behind them. Then do O the exercises. Ask yourself how new concepts relate to old ones. Make the connections! Everyone needs help sometimes. You will find that this program has built-in opportunities, both C in this text and online, to get help whenever you need it. This course will also help you succeed on the tests you take in class and on other tests like N the SAT, ACT, and state exams. The practice exercises in each lesson will prepare you for the format and content of such tests. No surprises! O The problem-solving and reasoning habits and skills you develop in this program will serve you in all your studies and in your daily life. They will prepare you for future success not only as a M student, but also as a member of a changing technological society. Best wishes, M O C E R O C vii N O HSM15SE_A2_NA_FM_CB.indd Page 7 30/09/13 11:07 AM gg_053 /132/PE01129_MIGRATE/HIGH_SCHOOL_MATH_2015/NATIONAL/SE/MATH_2015/G8/XXXXXXXXXX_G/ ... M M O C PowerAlgebra.com Welcome to Algebra 2. Pearson Algebra 2 Common Core Edition is part of a blended digital and print environment for the study of high school mathematics. Take some time to look through the features of our mathematics program, starting with PowerAlgebra.com, the site of the digital features of the program. Hi, I’m Darius. My friends and I will be showing you the great features of Pearson Algebra 2 Common Core Edition program. On each Chapter Opener, you will find a listing of the online features of the program. Look for these buttons throughout the lessons. viii HSM15SE_A2_NA_FM_mkt.indd Page 8 09/10/13 2:03 AM gg-40 /132/PE01129_MIGRATE/HIGH_SCHOOL_MATH_2015/NATIONAL/SE/MATH_2015/G8/XXXXXXXXXX_G/ ... E R O C N O M M O The Common Core State Standards have C a similar organizing structure. They begin with Conceptual Categories, E Big Ideas such as Algebra or Functions. R Within each category are We start with Big Ideas. Each chapter is C domains and clusters. ds O o r a organized around Big Ideas that convey the m d m n o a C key mathematics concepts you will be studying n Core Stat e S t in the program. Take a look at the Big Ideas on N pages xxiv and xxv. O M M O C E R O C N O The Big Ideas are organizing ideas for all In the Chapter Review at the end of the M of the lessons in the program. At the beginning of chapter, you’ll find an answer to the Essential each chapter, we’ll tell you which Big Ideas you’ll Question for each Big Idea. We’ll also remind M be studying. We’ll also present an Essential you of the lesson(s) where you studied the Question for each Big Idea. concepts that support the Big Ideas. O C E R O C Using Your Book for Success ix N O HSM15SE_A2_NA_FM_mkt.indd Page 9 09/10/13 2:03 AM gg-40 /132/PE01129_MIGRATE/HIGH_SCHOOL_MATH_2015/NATIONAL/SE/MATH_2015/G8/XXXXXXXXXX_G/ ... M M O C Exploring Concepts The lessons offer many opportunities to explore concepts in different contexts and through different media. Hi, I’m Serena. I never have to power down when I am in math class now. For each chapter, there is a Common Here’s another cool feature. Each lesson opens Core Performance Task that you with a Solve It, a problem that helps will work on throughout the chapter. See you connect what you know to an important pages xii and xiii for more information. concept in the lesson. Do you notice how the Solve It frame looks like it comes from a computer? That’s because all of the Solve Its can be found at PowerAlgebra.com. x HSM15SE_A2_NA_FM_mkt.indd Page 10 09/10/13 2:03 AM gg-40 /132/PE01129_MIGRATE/HIGH_SCHOOL_MATH_2015/NATIONAL/SE/MATH_2015/G8/XXXXXXXXXX_G/ ...