California algebra 1: concepts, skills, and problem solving

897 Pages·2007·45.64 MB·English

by  McGraw Hill

i s e
nteractive tudent dition
About the Cover
The cable car railway system was invented specifically to operate
on San Francisco’s famous hills. Every cable car is pulled along its
track by an underground cable. The cable is gripped with a vise-
like mechanism that is operated by the driver using a grip lever in
the front of the car. In Chapter 4, you will learn about slopes like
the slope of a hill.
About the Graphics
Twisted torus. Created with Mathematica.
A torus with rose-shaped cross section is constructed. Then
the cross section is rotated around its center as it moves
along a circle to form a twisted torus. For more information,
and for programs to construct such graphics,
see: www.wolfram.com/r/textbook.
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Except as
permitted under the United States Copyright Act, no part of this publication may be
reproduced or distributed in any form or by any means, or stored in a database or
retrieval system, without prior permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, OH 43240-4027
ISBN: 978-0-07-877852-0
MHID: 0-07-877852-2
Printed in the United States of America.
4 5 6 7 8 9 10 043/079 16 15 14 13 12 11 10 09 08
Contents
in Brief

Unit 1 Foundations for Functions
1 The Language and Tools of Algebra
2 Solving Linear Equations
Unit 2 Linear Functions
3 Functions and Patterns
4 Analyzing Linear Equations
5 Solving Systems of Linear Equations
6 Solving Linear Inequalities
Unit 3 Polynomials and Nonlinear Functions
7 Polynomials
8 Factoring
9 Quadratic and Exponential Functions
Unit 4 Advanced Expressions and Data Analysis
10 Radical Expressions and Triangles
11 Rational Expressions and Equations
12 Statistics and Probability
Standards Review
iii
ii--iixx FFMM__IInnddeexx__CCAA--887777885522..iinndddd iiiiii 1111//1155//0066 77::0000::5500 PPMM
Authors
Berchie Holliday, Ed.D. Gilbert J. Cuevas, Ph.D. Beatrice Luchin
National Mathematics Professor of Mathematics Mathematics Consultant
Consultant Education League City, TX
Silver Spring, MD University of Miami
Miami, FL
John A. Carter, Ph.D. Daniel Marks, Ed.D. Roger Day, Ph.D.
Director of Mathematics Professor Emeritus of Mathematics Department
Adlai E. Stevenson High Mathematics Chairperson
School Auburn University at Pontiac Township High
Lincolnshire, IL Montgomery School
Montgomery, AL Pontiac, IL
iv Meet the Authors at ca.algebra1.com
Ruth M. Casey Linda M. Hayek
Mathematics Teacher Mathematics Teacher
Department Chair Ralston Public Schools
Anderson County High Omaha, NE
School
Lawrenceburg, KY
Contributing Authors
Carol E. Malloy, Ph.D. Viken Hovsepian Dinah Zike
Associate Professor Professor of Mathematics Educational Consultant,
University of North Carolina Rio Hondo College Dinah-Might Activities, Inc.
at Chapel Hill Whittier, CA San Antonio, TX
Chapel Hill, NC
v
ii--iixx FFMM__IInnddeexx__CCAA--887777885522..iinndddd vv 1111//22//0066 44::4444::0066 PPMM
California Mathematics Advisory Board
G lencoe wishes to thank the following professionals for their invaluable
feedback during the development of the program. They reviewed the
table of contents, the prototype of the Teacher Wraparound Edition, and
the Get Ready for the California Test chapter.
Cheryl L. Avalos William M. Bokesch Patty Brown David J. Chamberlain
Mathematics Consultant Rancho Bernardo Teacher Secondary Mathematics
Retired Teacher High School John Muir Elementary Resource Teacher
Hacienda Heights, California San Diego, California Fresno, California Capistrano Unified School
District
San Juan Capistrano, California
Eppie Chung Lisa Marie Cirrincione Carol Cronk Ilene Foster
K-6 Teacher Middle School Teacher Mathematics Program Specialist Teacher Specialist – Mathematics
Modesto City Schools Lincoln Middle School San Bernardino City Unified Pomona Unified School District
Modesto, California Oceanside, California School District Pomona, California
San Bernardino, California
Grant A. Fraser, Ph.D. Suzanne Bocskai Freire Beth Holguin Donna M. Kopenski, Ed.D.
Professor of Mathematics Teacher Teacher Mathematics Coordinator K-5
California State University, Kingswood Elementary Graystone Elementary City Heights Educational
Los Angeles Citrus Heights, California San Jose, California Collaborative
Los Angeles, California San Diego, California
vi
ii--iixx FFMM__IInnddeexx__CCAA--887777885522..iinndddd vvii 1111//11//0066 99::5588::2266 AAMM
Kelly Mack Juvenal Martinez John McGuire Dr. Donald R. Price
6th Grade Teacher Dual Immersion/ESL Instructor Associate Principal Teacher, Adjunct Professor,
Captain Jason Dahl Elementary Aeolian Elementary Pacific Union School Motivational Speaker
San Jose, California Whittier, California Arcata, California Rowland Unified School
District
Rowland Heights, California
Kasey St. James Arthur K. Wayman, Ph.D. Beverly Wells Frances Basich Whitney
Mathematics Teacher Professor of Mathematics First Grade Teacher Project Director,
Sunny Hills High School Emeritus Mineral King Elementary Mathematics K-12
Fullerton, California California State University, School Santa Cruz County Office
Long Beach Visalia, California of Education
Long Beach, California Capitola, California
vii
CCoonnssuullttaannttss
G lencoe/McGraw-Hill wishes to thank the following professionals for
their feedback. They were instrumental in providing valuable input
toward the development of this program in these specific areas.
Mathematical Content Graphing Calculator
Viken Hovsepian Ruth M. Casey
Professor of Mathematics Mathematics Teacher
Rio Hondo College Department Chair
Whittier, California Anderson County High School
Lawrenceburg, Kentucky
Grant A. Fraser, Ph.D.
Professor of Mathematics Jerry Cummins
California State University, Los Angeles Past President
Los Angeles, California National Council of Supervisors of Mathematics
Western Springs, Illinois
Bob McCollum
Associate Principal
Learning Disabilities
Curriculum and Instruction
Glenbrook South High School Kate Garnett, Ph.D.
Glenview, Illinois Chairperson, Coordinator Learning Disabilities
School of Education
Arthur K. Wayman, Ph.D.
Department of Special Education
Professor of Mathematics Emeritus
Hunter College, CUNY
California State University, Long Beach
New York, New York
Long Beach, California
Mathematical Fluency
Differentiated Instruction
Jason Mutford
Nancy Frey, Ph.D.
Mathematics Instructor
Associate Professor of Literacy
Coxsackie-Athens Central School District
San Diego State University
Coxsackie, New York
San Diego, California
Pre-AP
English Language Learners
Dixie Ross
Mary Avalos, Ph.D.
AP Calculus Teacher
Assistant Chair, Teaching and Learning
Pflugerville High School
Assistant Research Professor
Pflugerville, Texas
University of Miami, School of Education
Coral Gables, Florida
Reading and Vocabulary
Jana Echevarria, Ph.D.
Douglas Fisher, Ph.D.
Professor, College of Education
Director of Professional Development and Professor
California State University, Long Beach
City Heights Educational Collaborative
Long Beach, California
San Diego State University
Josefina V. Tinajero, Ph.D. San Diego, California
Dean, College of Educatifon
Lynn T. Havens
The University of Texas at El Paso
Director of Project CRISS
El Paso, Texas
Kalispell School District
Gifted and Talented Kalispell, Montana
Ed Zaccaro
Author
Mathematics and science books for gifted children
Bellevue, Iowa
vviiiiii Meet the Authors at ca.algebra1.com
CCaalliiffoorrnniiaa RReevviieewweerrss
Each California Reviewer reviewed at least two chapters of
the Student Edition, giving feedback and suggestions for
improving the effectiveness of the mathematics instruction.
Tammera Boehme Susan A. Holtzapple David Robathan
Mathematics Chairperson Mathematics Teacher Teacher
Las Plumas High School Cupertino Middle School Shasta High School
Oroville, California Sunnyvale, California Redding, California
Don Castle Alice M. Keeler Brian Shay
Geometry Teacher Mathematics Teacher Mathematics Chairperson and Teacher
Carter High School Clovis High School Canyon Crest Academy
Rialto, California Clovis, California San Diego, California
Karen D. Cliffe Eric Kimmel Kathryn E. Sinclear
Mathematics Department Chair Department Chair of Mathematics Mathematics Department Chair
Bonita Vista High School Frontier High School Los Banos High School
Chula Vista, California Bakersfield, California Los Banos, California
Barbara R. Donner Jennifer Marple Douglas S. Taylor
Teacher Mathematics Teacher Mathematics Teacher
Chadwick School Monroe High School Taft Union High School
Palos Verdes Peninsula, California North Hills, California Taft, California
Michael R. Erickson Jeff Matthew Martha Tikalsky
Teacher Mathematics & Science Department Chairman Mathematics Teacher
Niguel Hills Hughson High School Sam Lawson Middle School
Laguna Niguel, California Hughson, California Cupertino, California
Shayne B. Fleming Jennifer Moening Beatrice Tyk
Mathematics Teacher Mathematics Teacher Mathematics Teacher
Alameda Unified School District Santiago High School Sylvan Middle School
Alameda, California Garden Grove, California Citrus Heights, California
Kris Fondaw Terry Murray Joanne Wainscott
Mathematics Dept. Chair/Teacher Teacher Mathematics Department Chairperson
Christian High School Crystal Middle School La Jolla High School
El Cajon, California Suisun City, California La Jolla, California
Anna L. Garfinkel Glenn Quan Greg Wood
Mathematics Teacher Mathematics Teacher Mathematics Teacher
Diegueño Middle School Richard Henry Dana Middle School Los Banos Junior High School
Encinitas, California San Pedro, California Los Banos, California
Marlene Greco Ryan Rienstra David Zylstra
Mathematics Teacher Mathematics Teacher Mathematics Teacher
Rancho Santa Margarita Intermediate School Northview High School Hughson High School
Rancho Santa Margarita, California Covina, California Hughson, California
John T. Guseman Laurie Riggs
Mathematics Teacher Associate Professor
Mission Hills High School California State Polytechnic University
San Marcos, California Pomona, California
State Flower:
California poppy
ix
ii--iixx FFMM__IInnddeexx__CCAA--887777885522..iinndddd iixx 1111//22//0066 44::4444::1144 PPMM
Unit 1
C H APTER The Language and Tools
1
of Algebra
1-1 Variables and Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
1-2 Order of Operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1-3 Open Sentences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1-4 Identity and Equality Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1-5 The Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
Mid-Chapter Quiz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
1-6 Commutative and Associative Properties . . . . . . . . . . . . . . . . . . .33
Reading Math: Arguments with Properties
of Real Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
1-7 Logical Reasoning and Counterexamples. . . . . . . . . . . . . . . . . . .39
Extend 1-7 Algebra Lab: Logic and Properties of Numbers. . . . .45
1-8 Number Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46
Prerequisite Skills
(cid:129) Get Ready for Chapter 1 5 1-9 Functions and Graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
(cid:129) Get Ready for the Next Lesson
Extend 1-9 Algebra Lab: Investigating Real-World Functions. . . .59
9, 14, 20, 25, 31, 37, 44, 52
ASSESSMENT
Reading and Writing Mathematics
Study Guide and Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
(cid:129) Reading Math 38
Practice Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
(cid:129) Vocabulary Link 26, 33
(cid:129) Writing in Math 9, 14, 19, 25, 31, California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . .66
37, 44, 52, 58
California Standards Practice
(cid:129) Multiple Choice 9, 14, 20, 25, 31,
37, 42, 44, 52, 58
(cid:129) Worked Out Example 41
H.O.T. Problems
Higher Order Thinking
(cid:129) Challenge 9, 14, 19, 24, 31, 37,
44, 52, 58
(cid:129) Find the Error 13, 30
(cid:129) Open Ended 9, 14, 19, 25, 30, 37,
44, 52, 58
(cid:129) Reasoning 9, 19, 25, 30, 44, 58
(cid:129) Which One Doesn’t Belong? 37
x
xx--xxxxii FFMM__TTOOCC__CCAA--887777885522..iinndddd xx 1100//2277//0066 22::2266::5544 PPMM