Glencoe Algebra 1 Foldables

348 Pages·2004·24.25 MB·English

Algebra 1
Contributing Author
Dinah Zike
Consultant
Douglas Fisher, PhD
Director of Professional Development
San Diego State University
San Diego, CA
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the
United States of America. Except as permitted under the United States Copyright Act,
no part of this book may be reproduced in any form, electronic or mechanical, includ-
ing photocopy, recording, or any information storage or retrieval system, without prior
written permission of the publisher.
Send all inquiries to:
The McGraw-Hill Companies
8787 Orion Place
Columbus, OH 43240-4027
ISBN: 0-07-872982-3 Algebra 1 (California Student Edition)
Noteables™: Interactive Study Notebook with Foldables™
1 2 3 4 5 6 7 8 9 10 047 09 08 07 06 05 04
Contents
Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . 1 Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 83
Vocabulary Builder . . . . . . . . . . . . . . . . . . 2 Vocabulary Builder . . . . . . . . . . . . . . . . . 84
1-1 Variables and Expressions . . . . . . . . 4 4-1 The Coordinate Plane. . . . . . . . . . . . 86
1-2 Order of Operations . . . . . . . . . . . . 6 4-2 Transformations . . . . . . . . . . . . . . . . 88
1-3 Open Sentences. . . . . . . . . . . . . . . . 9 4-3 Relations. . . . . . . . . . . . . . . . . . . . . . 92
1-4 Identity and Equality Properties . . 11 4-4 Equations as Relations. . . . . . . . . . . 95
1-5 The Distributive Property . . . . . . . 13 4-5 Graphing Linear Equations . . . . . . . 97
1-6 Commutative and Associative 4-6 Functions. . . . . . . . . . . . . . . . . . . . . 100
Properties . . . . . . . . . . . . . . . . . . . 15 4-7 Arithmetic Sequences. . . . . . . . . . . 102
1-7 Logical Reasoning . . . . . . . . . . . . . 17 4-8 Writing Equations from Patterns . 104
1-8 Graphs and Functions . . . . . . . . . . 19 Study Guide . . . . . . . . . . . . . . . . . . . . . 107
1-9 Analyzing Data by Using
Tables and Graphs. . . . . . . . . . . . . 22
Study Guide . . . . . . . . . . . . . . . . . . . . . . 25
Foldables. . . . . . . . . . . . . . . . . . . . . . . . 111
Vocabulary Builder . . . . . . . . . . . . . . . . 112
5-1 Slope . . . . . . . . . . . . . . . . . . . . . . 114
Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 29 5-2 Slope and Direct Variation. . . . . . 116
Vocabulary Builder . . . . . . . . . . . . . . . . . 30 5-3 Slope-Intercept Form. . . . . . . . . . 118
2-1 Rational Numbers on the 5-4 Writing Equations in
Number Line . . . . . . . . . . . . . . . . . 32 Slope-Intercept Form. . . . . . . . . . 121
2-2 Adding and Subtracting 5-5 Point-Slope Form. . . . . . . . . . . . . 123
Rational Numbers . . . . . . . . . . . . . 34 5-6 Parallel and Perpendicular Lines. . 125
2-3 Multiplying Rational Numbers . . . 36 5-7 Scatter Plots and Lines of Fit. . . . 128
2-4 Dividing Rational Numbers . . . . . . 38 Study Guide . . . . . . . . . . . . . . . . . . . . . 131
2-5 Displaying and Analyzing Data. . . 40
2-6 Simple Probability and Odds. . . . . 43
2-7 Square Roots and Real Numbers. . 46
Foldables. . . . . . . . . . . . . . . . . . . . . . . . 135
Study Guide . . . . . . . . . . . . . . . . . . . . . . 49
Vocabulary Builder . . . . . . . . . . . . . . . . 136
6-1 Solving Inequalities by(cid:1)and(cid:2). . 138
6-2 Solving Inequalities by(cid:3)and(cid:4). . 141
Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 53 6-3 Solving Multi-Step Inequalities . . 143
Vocabulary Builder . . . . . . . . . . . . . . . . . 54 6-4 Solving Compound Inequalities. . 145
3-1 Writing Equations . . . . . . . . . . . . . 56 6-5 Solving Open Sentences
3-2 Solving Equations by Involving Absolute Value. . . . . . . 148
Using (cid:1)and(cid:2) . . . . . . . . . . . . . . . . 59 6-6 Graphing Inequalities in
3-3 Solving Equations by Two Variables. . . . . . . . . . . . . . . . 150
Using(cid:3)and(cid:4) . . . . . . . . . . . . . . . . 61 Study Guide . . . . . . . . . . . . . . . . . . . . . 153
3-4 Solving Multi-Step Equations . . . . 64
3-5 Solving Equations with the
Variable on Each Side . . . . . . . . . . 67
Foldables. . . . . . . . . . . . . . . . . . . . . . . . 157
3-6 Ratios and Proportion. . . . . . . . . . 69
Vocabulary Builder . . . . . . . . . . . . . . . . 158
3-7 Percent of Change. . . . . . . . . . . . . 72
7-1 Graphing Systems of Equations. . 159
3-8 Solving Equations and Formulas . . 74
7-2 Substitution. . . . . . . . . . . . . . . . . 161
3-9 Weighted Averages. . . . . . . . . . . . 77
7-3 Elimination Using (cid:1)and(cid:2) . . . . . 164
Study Guide . . . . . . . . . . . . . . . . . . . . . . 79
Glencoe Algebra 1 iii
7-4 Elimination Using Multiplication. 166 Vocabulary Builder . . . . . . . . . . . . . . . . 252
7-5 Graphing Systems of Inequalities 168 11-1 Simplifying Radical Expressions. . 254
Study Guide . . . . . . . . . . . . . . . . . . . . . 171 11-2 Operations with Radical
Expressions. . . . . . . . . . . . . . . . . . 257
11-3 Radical Equations . . . . . . . . . . . . 259
11-4 The Pythagorean Theorem . . . . . 261
Foldables. . . . . . . . . . . . . . . . . . . . . . . . 175
11-5 The Distance Formula . . . . . . . . . 264
Vocabulary Builder . . . . . . . . . . . . . . . . 176
11-6 Similar Triangles. . . . . . . . . . . . . . 266
8-1 Multiplying Monomials . . . . . . . . 178
11-7 Trigonometric Ratios . . . . . . . . . . 269
8-2 Dividing Monomials. . . . . . . . . . . 181
Study Guide . . . . . . . . . . . . . . . . . . . . . 273
8-3 Scientific Notation. . . . . . . . . . . . 183
8-4 Polynomials . . . . . . . . . . . . . . . . . 185
8-5 Add and Subtract Polynomials . . 188
8-6 Multiplying a Polynomial by Foldables. . . . . . . . . . . . . . . . . . . . . . . . 277
a Monomial. . . . . . . . . . . . . . . . . 190 Vocabulary Builder . . . . . . . . . . . . . . . . 278
8-7 Multiplying Polynomials . . . . . . . 192 12-1 Inverse Variation . . . . . . . . . . . . . 279
8-8 Special Products. . . . . . . . . . . . . . 195 12-2 Rational Expressions . . . . . . . . . . 281
Study Guide . . . . . . . . . . . . . . . . . . . . . 197 12-3 Multiplying Rational Expressions. . 283
12-4 Dividing Rational Expressions . . . 285
12-5 Dividing Polynomials. . . . . . . . . . 288
12-6 Rational Expressions with
Foldables. . . . . . . . . . . . . . . . . . . . . . . . 201
Like Denominators. . . . . . . . . . . . 290
Vocabulary Builder . . . . . . . . . . . . . . . . 202
12-7 Rational Expressions with
9-1 Factors and GCF. . . . . . . . . . . . . . 203
Unlike Denominators. . . . . . . . . . 292
9-2 Factoring Using the
12-8 Mixed Expressions and
Distributive Property . . . . . . . . . . 206
Complex Fractions . . . . . . . . . . . . 295
9-3 Factoring Trinomials: x2 (cid:1) bx(cid:1)c. . 208
12-9 Solving Rational Equations
9-4 Factoring Trinomials: ax2(cid:1)bx(cid:1)c. 210
and Inequalities. . . . . . . . . . . . . . 297
9-5 Factoring Differences of Squares. . 213
Study Guide . . . . . . . . . . . . . . . . . . . . . 301
9-6 Perfect Squares and Factoring. . . 215
Study Guide . . . . . . . . . . . . . . . . . . . . . 219
Foldables. . . . . . . . . . . . . . . . . . . . . . . . 305
Vocabulary Builder . . . . . . . . . . . . . . . . 306
Foldables. . . . . . . . . . . . . . . . . . . . . . . . 223
13-1 Sampling and Bias. . . . . . . . . . . . 308
Vocabulary Builder . . . . . . . . . . . . . . . . 224
13-2 Introduction to Matrices . . . . . . . 310
10-1 Graphing Quadratic Functions. . . 226
13-3 Histograms. . . . . . . . . . . . . . . . . . 313
10-2 Solving Quadratic Equations
13-4 Measures of Variation . . . . . . . . . 315
by Graphing. . . . . . . . . . . . . . . . . 229
13-5 Box-and-Whisker Plots. . . . . . . . . 317
10-3 Solving Quadratic Equations
Study Guide . . . . . . . . . . . . . . . . . . . . . 320
by Completing the Square. . . . . . 232
10-4 Solving Quadratic Equations by
Using the Quadratic Formula . . . 235
10-5 Exponential Functions. . . . . . . . . 238 Foldables. . . . . . . . . . . . . . . . . . . . . . . . 323
10-6 Growth and Decay. . . . . . . . . . . . 241 Vocabulary Builder . . . . . . . . . . . . . . . . 324
10-7 Geometric Sequences. . . . . . . . . . 244 14-1 Counting Outcomes. . . . . . . . . . . 326
Study Guide . . . . . . . . . . . . . . . . . . . . . 247 14-2 Permutations and Combinations. 328
14-3 Probabilities of Compound Events. 330
14-4 Probability Distributions . . . . . . . 333
14-5 Probability Simulations . . . . . . . . 335
Foldables. . . . . . . . . . . . . . . . . . . . . . . . 251
Study Guide . . . . . . . . . . . . . . . . . . . . . 338
iv Glencoe Algebra 1
Organizing Your Foldables
Make this Foldable to help you organize and
store your chapter Foldables. Begin with one
sheet of 11”(cid:3)17” paper.
Fold
Fold the paper in half lengthwise. Then unfold.
Fold and Glue
Fold the paper in half widthwise and glue all of the edges.
Glue and Label
Glue the left, right, and bottom edges of the Foldable
to the inside back cover of your Noteables notebook.
Foldables Organizer
Reading and Taking Notes As you read and study each chapter, record
notes in your chapter Foldable. Then store your chapter Foldables inside
this Foldable organizer.
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Glencoe Algebra 1 v
This note-taking guide is designed to help you succeed in Algebra 1. Each
chapter includes:
The Chapter Opener
contains instructions and
illustrations on how to make
a Foldable that will help you
to organize your notes.
A Note-Taking Tip
provides a helpful
hint you can use
when taking notes.
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Within each chapter,
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The Build Your Vocabulary Build Your Vocabulary le
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table allows you to write boxes will remind you to co
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definitions and examples fill in this table. FCAT /M
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vi Glencoe Algebra 1
Lessons cover the content of
1–3 Open Sentences the lessons in your textbook.
Standard 25.2 Students judge the validity of an argument according to whether the As your teacher discusses each
properties of the real number system and the order of operations have been applied
correctly at each step.
Each lessWoHATnY OiUs’LLLEARN BUILD YOUR VOCABULARY (pages 2–3) example, follow along and
•Seoqluvaet ioopnesn. sentence The process of finding a value for a variable that results complete the fill-in boxes.
correlated to the
•Sinoelvqeu aolpiteiens .sentence in a sentence is called solvingthe open sentence. Take notes as appropriate.
California Content
A sentence that contains an sign is called an
Standards. equation.
A set of numbers from which replacements for a
may be chosen is called a replacement set.
Examples parallel the
EXAMPLE Use a Replacement Set to Solve an Equation examples in your textbook.
Find the solution set for 4a(cid:1)7(cid:2)23 if the replacement
set is {2, 3, 4, 5, 6}.
Replace ain 4a(cid:1)7(cid:5)23 with each value in the replacement set.
a 4a(cid:1)7(cid:2)23 True or False?
2 4(2)(cid:1)7(cid:5)23Æ (cid:5)23
ORGANIZEIT
Under the tab for 3 4(3)(cid:1)7(cid:5)23Æ (cid:5)23
Lheoswso tno 1s-o3l,v eex opplaeinn 4 4(4)(cid:1)7(cid:5)23Æ (cid:5)23
sentence equations
and inequalities. Include 5 4(5)(cid:1)7(cid:5)23Æ (cid:5)23
examples.
©Glencoe/McGraw-Hill 1111111111----------6635842711FOCADOaorsicEmdssptqtoeoemaurFcIrrindanEbsu iuPdlaxeou i t tpnanSoatfEytritin qetcwvivePOitusdeevtyrnesae io p iatoPPPtorp einPoensenrrrrndsroroonasst opdpictepeeiuseeorrctrnsttytyssy TifY htoeh ues orrl 6euTptuiloarncn4e (sm6e)tFe (cid:1)niisnt 7d s (cid:5)etht 2ei.s 3s {oÆ0lu, t1i,o n2, s(cid:5)3e,t 2 4f3o}.r the equation 6c(cid:2)5(cid:5)7
Foldables feature
Glencoe Algebra 1 9
reminds you to take
notes in your Foldable.
Your Turn Exercises allow
you to solve similar
exercises on your own.
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w Study Guide reviews the
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concepts from each lesson.
Glencoe Algebra 1 vii
NOTE-TAKING TIPS
Your notes are a reminder of what you learned in class. Taking good notes
can help you succeed in mathematics. The following tips will help you take
better classroom notes.
• Before class, ask what your teacher will be discussing in class. Review
mentally what you already know about the concept.
• Be an active listener. Focus on what your teacher is saying. Listen for
important concepts. Pay attention to words, examples, and/or diagrams
your teacher emphasizes.
• Write your notes as clear and concise as possible. The following symbols
and abbreviations may be helpful in your note-taking.
Symbol or Symbol or
Word or Phrase Word or Phrase
Abbreviation Abbreviation
for example e.g. not equal (cid:6)
such as i.e. approximately (cid:1)
with w/ therefore (cid:1)
without w/o versus vs
and + angle (cid:2)
• Use a symbol such as a star (★) or an asterisk (*) to emphasis important
concepts. Place a question mark (?) next to anything that you do not
understand.
• Ask questions and participate in class discussion.
• Draw and label pictures or diagrams to help clarify a concept.
• When working out an example, write what you are doing to solve the
problem next to each step. Be sure to use your own words.
• Review your notes as soon as possible after class. During this time, organize
and summarize new concepts and clarify misunderstandings. C
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Note-Taking Don’ts ht ©
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• Don’t write every word. Concentrate on the main ideas and concepts. le
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• Don’t use someone else’s notes as they may not make sense. o
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• Don’t doodle. It distracts you from listening actively. c
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• Don’t lose focus or you will become lost in your note-taking. w
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viii Glencoe Algebra 1
H A PTE
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1
The Language of Algebra

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Use the instructions below to make a Foldable to help you
organize your notes as you study the chapter. You will see
Foldable reminders in the margin of this Interactive Study
Notebook to help you in taking notes.
Begin with a sheet of notebook paper.
Fold
Fold lengthwise
to the holes.
Cut
Cut along the
top line and
then cut 9 tabs.
Label
©Glencoe/M Luncoasuinbmncegebl petthhtrssee. a ltneasdbs so n 1111111111----------6635842711 FOCADOaorsicEmdssptqtoeoemaurFcIrrindanEbsu iuPdlaxeou i t tpnanSotafEytritin qetcwvievPOitusdeevtyrnesae io p iaotPPPtorp einPoensenrrrrdnsrooronasst opdpictepeeiuseeorrctrnsttytyssy
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w
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concise definitions in your own words. Add
examples that illustrate the concepts.
Glencoe Algebra 1 1
H A PTE
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BUILD YOUR VOCABULARY
This is an alphabetical list of new vocabulary terms you will learn in Chapter 1.
As you complete the study notes for the chapter, you will see Build Your
Vocabulary reminders to complete each term’s definition or description on
these pages. Remember to add the textbook page number in the second
column for reference when you study.
Found Description or
Vocabulary Term Definition
on Page Example
coefficient
[KOH·uh·FIH·shuhnt]
conclusion
conditional statement
coordinate system
counterexample
deductive reasoning
[dih·DUHK·tihv]
dependent variable
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equation ra
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function
2 Glencoe Algebra 1