Study Guide and Intervention Workbook

202 Pages·2008·8.95 MB·English

Study Guide and
Intervention Workbook
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To the Student
This Study Guide and Intervention Workbook gives you additional examples and problems for the
concept exercises in each lesson. The exercises are designed to aid your study of mathematics by
reinforcing important mathematical skills needed to succeed in the everyday world. The materials are
organized by chapter and lesson, with two Study Guide and Intervention worksheets for every lesson
in Glencoe Pre-Algebra.
Always keep your workbook handy. Along with your textbook, daily homework, and class notes, the
completed Study Guide and Intervention Workbook can help you in reviewing for quizzes and tests.
To the Teacher
These worksheets are the same ones found in the Chapter Resource Masters for Glencoe Pre-Algebra.
The answers to these worksheets are available at the end of each Chapter Resource Masters booklet
as well as in your Teacher Edition interleaf pages.
Copyright © 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 written permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, OH 43240
ISBN: 978-0-07-890739-5
MHID: 0-07-890739-X Study Guide and Intervention Workbook, Pre-Algebra
Printed in the United States of America.
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Contents
Lesson/Title Page Lesson/Title Page
1-1 Words and Expressions ............................1 6-7 Similar Figures ........................................73
1-2 Variables and Expressions .......................3 6-8 Dilations ..................................................75
1-3 Properties .................................................5 6-9 Indirect Measurement .............................77
1-4 Ordered Pairs and Relations ....................7
1-5 Words, Equations, Tables, and 7-1 Fractions and Percents ...........................79
Graphs ......................................................9 7-2 Fractions, Decimals, and Percents .........81
1-6 Scatter Plots ...........................................11 7-3 Using the Percent Proportion .................83
7-4 Find Percent of a Number Mentally ........85
2-1 Integers and Absolute Value ..................13 7-5 Using Percent Equations ........................87
2-2 Adding Integers ......................................15 7-6 Percent of Change ..................................89
2-3 Subtracting Integers ...............................17 7-7 Simple and Compound Interest ..............91
2-4 Multiplying Integers .................................19 7-8 Circle Graphs ..........................................93
2-5 Dividing Integers .....................................21
2-6 Graphing in Four Quadrants ..................23 8-1 Functions ................................................95
2-7 T ranslations and Refle ctions on 8-2 Sequences and Equations ......................97
the Coordinate Plane ..............................25 8-3 Representing Linear Functions .............99
8-4 Rate of Change ....................................101
3-1 Fractions and Decimals ..........................27 8-5 Constant Rate of Change and
3-2 Rational Numbers ...................................29 Direct Variation .....................................103
3-3 Multiplying Rational Numbers .................31 8-6 Slope .....................................................105
3-4 Dividing Rational Numbers .....................33 8-7 Slope-Intercept Form ............................107
3-5 Adding and Subtracting Like 8-8 Writing Linear Equations ......................109
Fractions .................................................35 8-9 Prediction Equations .............................111
3-6 Adding and Subtracting Unlike 8-10 Systems of Equations ...........................113
Fractions .................................................37
9-1 Powers and Exponents .........................115
c.
s, In 4-1 The Distributive Property ........................39 9-2 Prime Factorization ...............................117
e 4-2 Simplifying Algebraic Expressions ..........41 9-3 Multiplying and Dividing
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Mc 4-5 Solving Two-Step Equations .................47 9-7 Linear and Nonlinear Functions ...........127
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of 9-9 Cubic and Exponential Functions .........131
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w- 5-3 Inequalities ..............................................55 10-3 Triangles .............................................137
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Measurements ........................................65 11-4 Quadrilaterals .....................................151
6-4 Proportional and Nonproportional 11-5 Polygons .............................................153
Relationships ..........................................67 11-6 Area of Parallelograms, Triangles,
6-5 Solving Proportions ................................69 and Trapezoids ...................................155
6-6 Scale Drawings and Models ...................71 11-7 Circles and Circumference .................157
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Lesson/Title Page Lesson/Title Page
11-8 Area of Circles ....................................159 13-1 Measures of Central Tendency ..........179
11-9 Area of Composite Figures .................161 13-2 Stem-and-Leaf Plots ...........................181
13-3 Measures of Variation .........................183
12-1 Three-Dimensional Figures ................163 13-4 Box-and-Whisker Plots .......................185
12-2 Volume of Prisms ...............................165 13-5 Histograms ..........................................187
12-3 Volume of Cylinders ...........................167 13-6 Theoretical and Experimental
12-4 V olume of Pyramids, Cones and Probability ...........................................189
Spheres ..............................................169 13-7 Using Sampling to Predict ..................191
12-5 Surface Area of Prisms ......................171 13-8 Counting Outcomes ............................193
12-6 Surface Area of Cylinders ..................173 13-9 Permutations and Combinations ........195
12-7 S urface Area of Pyramids and 13-10 Probability of Compound Events ........197
Cones .................................................175
12-8 Similar Solids ......................................177
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1-1 Study Guide and Intervention
Words and Expressions
Translate Verbal Phrases into Expressions A numerical expression contains a
combination of numbers and operations such as addition, subtraction, multiplication, and
division. Verbal phrases can be translated into numerical expressions by replacing words
with operations and numbers.
+ - × ÷
plus minus times divide
the sum of the difference the product the quotient
of of of
increased decreased by of divided by
by
more than less than among
Example Write a numerical expression for each verbal phrase.
a. the product of seventeen and three
Phrase the product of seventeen and three
Expression 17 × 3
b. t he total number of pencils given to each student if 18 pencils
are shared among 6 students
Phrase 18 shared among 6
Expression 18 ÷ 6
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Chapter 1 1 Glencoe Pre-Algebra
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1-1 Study Guide and Intervention
(continued)
Words and Expressions
Order of Operations Evaluate, or find the numerical value of, expressions with more
than one operation by following the order of operations.
Step 1 Evaluate the expressions inside grouping symbols.
Step 2 Multiply and/or divide from left to right.
Step 3 Add and/or subtract from left to right.
Example Evaluate each expression.
a. 6 (cid:2) 5 - 10 ÷ 2
6 (cid:2) 5 - 10 ÷ 2 = 30 - 10 ÷ 2 Multiply 6 and 5.
= 30 - 5 Divide 10 by 2.
= 25 Subtract 5 from 30.
b. 4(3 + 6) + 2 (cid:2) 11
4(3 + 6) + 2 (cid:2) 11 = 4(9) + 2 (cid:2) 11 Evaluate (3 + 6).
= 36 + 22 Multiply 4 and 9, and 2 and 11.
= 58 Add 36 and 22.
c. 3[(7 + 5) ÷ 4 - 1]
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10. 4[(10 - 6) + 6(2)] 11. − 12. 6(4 - 2) + 8 nie
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13. 3[(2 + 7) ÷ 9] - 3 14. (8 (cid:2) 7) ÷ 14 - 1 15. − .
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16. (9 (cid:2) 8) - (100 ÷ 5)
Chapter 1 2 Glencoe Pre-Algebra
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1-2 Study Guide and Intervention
Variables and Expressions
Translate Verbal Phrases An algebraic expression is a combination of variables,
numbers, and at least one operation. A variable is a letter or symbol used to represent an
unknown value. To translate verbal phrases with an unknown quantity into algebraic
expressions, first define the variable.
Algebraic Expressions
The letter x is most often 7d means 7 × d. b
− means b ÷ 5.
used as a variable. mn means m × n. 5
b
x + 3 7d - 2 mn − 5
Example Translate each phrase into an algebraic expression.
a. five inches longer than the length of a book
Words five inches longer than the length of a book
Variable Let b represent the length of the book.
Expression b + 5
b. two less than the product of a number and eight
Words two less than the product of a number and eight
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7. a number of books less than twenty-three
8. five more than six times a number
9. seven more boys than girls
10. twenty dollars divided among a number of friends minus three
Chapter 1 3 Glencoe Pre-Algebra
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1-2 Study Guide and Intervention
(continued)
Variables and Expressions
Evaluate Expressions To evaluate an algebraic expression, replace the variable(s)
with known values and follow the order of operations.
Substitution Property of Equality
Words If two quantities are equal, then one quantity can be replaced by the other.
Symbols For all numbers a and b, if a = b, then a may be replaced by b.
Example ALGEBRA Evaluate each expression if r = 6 and s = 2.
a. 8s - 2r
8s - 2r = 8(2) - 2(6) Replace r with 6 and s with 2.
= 16 - 12 or 4 Multiply. Then subtract.
b. 3(r + s)
3(r + s) = 3(2 + 6) Replace r with 6 and s with 2.
= 3 (cid:3) 8 or 24 Evaluate the parentheses. Then multiply.
5 rs
c. −
4
5rs
− = 5rs ÷ 4 Rewrite as a division expression.
4
= 5(6) (2) ÷ 4 Replace r with 6 and s with 2.
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= 60 ÷ 4 or 15 Multiply. Then divide. op
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ALGEBRA Evaluate each expression if x = 10, y = 5, and z = 1. ra
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Chapter 1 4 Glencoe Pre-Algebra
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1-3 Study Guide and Intervention
Properties
Properties of Addition and Multiplication In algebra, there are certain
statements called properties that are true for any numbers.
Property Explanations Example
Commutative Property 6 + 3 = 3 + 6
a + b = b + a
of Addition 9 = 9
Commutative Property 4 (cid:2) 5 = 5 (cid:2) 4
a (cid:2) b = b (cid:2) a
of Multiplication 20 = 20
Associative Property (a + b) + c = (3 + 4) + 7 = 3 + (4 + 7)
of Addition a + (b + c) 14 = 14
Associative Property (a (cid:2) b) (cid:2) c = (2 (cid:2) 5) (cid:2) 8 = 2 (cid:2) (5 . 8)
of Multiplication a (cid:2) (b (cid:2) c) 80 = 80
Additive Identity a + 0 = 0 + a = a 10 + 0 = 0 + 10 = 10
Multiplicative Identity a (cid:2) 1 = 1 (cid:2) a = a 5 (cid:2) 1 = 1 (cid:2) 5 = 5
Multiplicative Property
a (cid:2) 0 = 0 (cid:2) a = 0 15 (cid:2) 0 = 0 (cid:2) 15 = 0
of Zero
Example 1 Is subtraction of whole numbers associative? If not, give a
counterexample.
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2. 75 + 25 = 25 + 75 3. 2 (cid:2) (3 (cid:2) 4) = (2 (cid:2) 3) (cid:2) 4
4. 14 (cid:2) 1 = 14 5. p (cid:2) 0 = 0
Chapter 1 5 Glencoe Pre-Algebra
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1-3 Study Guide and Intervention
(continued)
Properties
Simplify Algebraic Expressions To simplify an algebraic expression, perform all
possible operations. Properties can be used to help simplify an expression that contains
variables.
Example Simplify each expression.
a. (9 + r) + 7
(9 + r) + 7 = (r + 9) + 7 Commutative Property of Addition
= r + (9 + 7) Associative Property of Addition
= r + 16 Add 9 and 7.
b. 3 (cid:2) (x (cid:2) 5)
3 (cid:2) (x (cid:2) 5) = 3 (cid:2) (5 (cid:2) x) Commutative Property of Multiplication
= (3 (cid:2) 5) (cid:2) x Associative Property of Multiplication
= 15 x Multiply 3 and 5.
Exercises
Simplify each expression.
1. 24 + (x + 6) 2. 3 (cid:2) (4a)
3. 9 + (12 + c) 4. 13d (cid:2) 0
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Chapter 1 6 Glencoe Pre-Algebra
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