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Study Guide and Intervention (continued) Dividing Polynomials 5-2 Synthetic Division Use synthetic division to find (23x- 5x2 + 5x - 2) ÷ (x - 1) Thus (2x3 - 5x2 + 5x - 2) ÷ (x - 1) = 2x2 - 3x + 2 Exercises Simplify 1 (3x3 2- 7x + 9x - 14) ÷ (x - 2) 2 (5x3 + 7x2-x - 3) ÷ (x + 1) 2 3 (2x3 + 3x2 - 10x - 3) ÷ (x + 3) 4 (x3 - 8x2 + 19x

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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

iv

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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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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.

1. 5 2 2. 3 3 3. 10 4 4. 12 2 5. 8 3 6. 2 8

7. (8 - 4)

2 8. (12 + 4)

6 9. 10 + 8

1

10. 15 - 12 ÷ 4 11. 12(20 - 17) - 3

6 12. 24 ÷ 3

2 - 3 2 13. 3 2

÷ 3 + 2

2

7 - 20 ÷ 5 14.

4 + 3 2

12 + 1

15. 250 ÷ [5(3

7 + 4)]

16. 2 4 2 - 8 ÷ 2 (5 + 2) 2 17. 4(5 2 ) - 4 3 4(4

5 + 2)

18. 5 2 - 3quotesdbs_dbs8.pdfusesText_14