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Study Guide and
Intervention Workbook00i_ALG1SGIF
M_890835.indd 100i_ALG1SGIFM_890835.indd 16/26/08 7:46:54 PM6/26/08 7:46:54 PM 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: 978-0-07-890835-4
MHID: 0-07-890835-3 Study Guide and Intervention Workbook, Algebra 1
Printed in the United States of America
1 2 3 4 5 6 7 8 9 10 047 14 13 12 11 10 09 08
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 Algebra 1.
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 Algebra 1. The
answers to these worksheets are available at the end of each Chapter Resource Masters booklet as well
as in your Teacher Wraparound Edition interleaf pages.
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Contents
iii
Lesson/Title Page
1-1 Variables and Expressions .......................1
1-2 Order of Operations ..................................3
1-3 Properties of Numbers ..............................5
1-4 The Distributive Property ..........................7
1-5 Equations ..................................................9
1-6 Relations .................................................11
1-7 Functions ................................................13
1-8 Logical Reasoning and
Counterexamples ....................................15
2-1 Writing Equations ...................................17
2-2 Solving One-Step Equations ..................19
2-3 Solving Multi-Step Equations ..................21
2-4 Solving Equations with the Variable
on Each Side ..........................................23
2-5 Solving Equations Involving
Absolute Value .......................................25
2-6 Ratios and Proportions ...........................27
2-7 Percent of Change ..................................29
2-8 Literal Equations and
Dimensional Analysis .............................31
2-9 Weighted Averages ................................33
3-1 Graphing Linear Relations ......................35
3-2 Solving Linear Equations
by Graphing ............................................37
3-3 Rate of Change and Slope .....................39
3-4 Direct Variation .......................................41
3-5 Arithmetic Sequences as
Linear Functions .....................................43
3-6 Proportional and Nonproportional
Relationships ..........................................45
4-1 Graphing Equations in Slope-Intercept
Form .......................................................47
4-2 Writing Equations in Slope-Intercept
Form .......................................................49
4-3 Writing Equations in Point-Slope
Form .......................................................51 4-4
Parallel and Perpendicular Lines ............53
4-5 Scatter Plots and Lines
of Fit ........................................................55
4-6 Regression and Median-Fit Lines ...........57
4-7 Special Functions ...................................59
5-1 Solving Inequalities by Addition and
Subtraction ..............................................61
5-2 Solving Inequalities by Multiplication
and Division ............................................63
5-3 Solving Multi-Step Inequalities ...............65
5-4 Solving Compound Inequalities ..............67
5-5 Inequalities Involving Absolute
Value .......................................................69
5-6 Graphing Inequalities in Two
Variables .................................................71
Lesson/Title Page
6-1 Graphing Systems of Equations .............73
6-2 Substitution .............................................75
6-3 Elimination Using Addition and
Subtraction ..............................................77
6-4 Elimination Using Multiplication ..............79
6-5 Applying Systems of Linear
Equations ................................................81
6-6 Organizing Dada Using Matrices ............83
6-7 Using Matrices to Solve
Systems of Equations .............................85
6-8 Systems of Inequalities ...........................87
7-1 Multiplying Monomials ............................89
7-2 Dividing Monomials ................................91
7-3 Scientific Notation ...................................93
7-4 Polynomials ............................................95
7-5 Adding and Subtracting
Polynomials ............................................97
7-6 Multiplying a Polynomial by a
Monomial ................................................99
7-7 Multiplying Polynomials ........................100
7-8 Special Products ...................................101
8-1 Monomials and Factoring .....................103
8-2 Using the Distributive Property .............105
8-3 Quadratic Equations:
x 2 + bx + c = 0 ....................................107
8-4 Quadratic Equations:
ax 2 + bx + c = 0 ..................................109
8-5 Quadratic Equations:
Differences of Squares .........................111
8-6 Quadratic Equations: Perfects
Squares ................................................113
9-1 Graphing Quadratic Functions ..............115
9-2 Solving Quadratic Equations
by Graphing ..........................................117
9-3 Transformations of Quadratic
Functions ..............................................119
9-4 Solving Quadratic Equations by
Completing the Square .........................121
9-5 Solving Quadratic Equations by Using
the Quadratic Formula ..........................123
9-6 Exponential Functions ..........................125
9-7 Growth and Decay ................................127
9-8 Geometric Sequences as
Exponential Functions ..........................129
9-9 Analyzing Functions with Successive
Differences and Ratios .........................131
10-1 Square Root Functions .........................133
10-2 Simplifying Radical Expressions ..........135
10-3 Operations with Radical
Expressions ..........................................137
10-4 Radical Equations.................................139
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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Lesson/Title Page
10-5 The Pythagorean Theorem .................141
10-6 The Distance and Midpoint
Formulas .............................................143
10-7 Similar Triangles .................................145
10-8 Trigonometric Ratios ..........................147
11-1 Inverse Variation .................................149
11-2 Rational Functions ..............................151
11-3 Simplifying Rational Expressions .......153
11-4 Multiplying and Dividing
Rational Expressions ..........................155
11-5 Dividing Polynomials ..........................157
11-6 Adding and Subtracting Rational
Expressions ........................................159
Lesson/Title Page
11-7 Mixed Expressions and
Complex Fractions ..............................161
11-8 Rational Equations and Functions ......163
12-1 Designing a Survey ............................165
12-2 Analyzing Survey Results ...................167
12-3 Statistics and Parameters ...................169
12-4 Permutations and Combinations ........171
12-5 Probability of Compound Events ........173
12-6 Probability Distributions ......................175
12-7 Probability Simulations .......................177
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NAME DATE PERIOD
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Chapter 1 1 Glencoe Algebra 1
Write Verbal Expressions An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. In algebra, variables are symbols used to represent unspecified numbers or values. Any letter may be used as a variable. Write a verbal expression for each algebraic expression. a. 6n 2 the product of 6 and n squared b. n 3 - 12m the difference of n cubed and twelve times m
Exercises
Write a verbal expression for each algebraic expression.
1. w - 1 2.
1 3 a 3
3. 81 + 2x 4. 12d
5. 8 4 6. 6 2 7. 2n 2 + 4 8. a 3 b 3 9. 2x 3 - 3 10. 6k 3 5 11. 1 4 b 2
12. 7n
5
13. 3x + 4 14.
2 3 k 5
15. 3b
2 + 2a 3
16. 4(n
2 + 1)
1-1Study Guide and Intervention
Variables and Expressions
Example
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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Chapter 1 2 Glencoe Algebra 1
Write Algrebraic Expressions Translating verbal expressions into algebraic expressions is an important algebraic skill. Write an algebraic expression for each verbal expression. a. four more than a number n
The words more than imply addition.
four more than a number n 4 + n
The algebraic expression is 4 + n.
b. the difference of a number squared and 8
The expression difference of implies subtraction.
the difference of a number squared and 8 n 2 - 8
The algebraic expression is n
2 - 8.
Exercises
Write an algebraic expression for each verbal expression.
1. a number decreased by 8
2. a number divided by 8
3. a number squared
4. four times a number
5. a number divided by 6
6. a number multiplied by 37
7. the sum of 9 and a number
8. 3 less than 5 times a number
9. twice the sum of 15 and a number
10. one-half the square of b
11. 7 more than the product of 6 and a number
12. 30 increased by 3 times the square of a number
1-1Study Guide and Intervention (continued)
Variables and Expressions
Example
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NAME DATE PERIOD
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Chapter 1 3 Glencoe Algebra 1
Evaluate Numerical Expressions Numerical expressions often contain more than one operation. To evaluate them, use the rules for order of operations shown below.
Order of
Operations
Step 1 Evaluate expressions inside grouping symbols.
Step 2 Evaluate all powers.
Step 3 Do all multiplication and/or division from left to right. Step 4 Do all addition and/or subtraction from left to right.
Evaluate each expression.
a. 3 4 3 4 = 3 3 3
3 Use 3 as a factor 4 times.
= 81 Multiply. b. 6 3 6 3 = 6 6
6 Use 6 as a factor 3 times.
= 216 Multiply.
Evaluate each expression.
a. 3[2 + (12 ÷ 3) 2
3[2 + (12 ÷ 3)
2 ] = 3(2 + 4 2 ) Divide 12 by 3. = 3(2 + 16) Find 4 squared. = 3(18) Add 2 and 16. = 54 Multiply 3 and 18. b. 3 + 2 3 4 2 3 3 + 8 4 2 3
Evaluate power in numerator.
11 4 2 3
Add 3 and 8 in the numerator.
11 16 3
Evaluate power in denominator.
11 48
Multiply.
3 + 2 3 4 2 ? 3 3 + 2 3 4 2 ? 3
Exercises
Evaluate each expression.
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