chapter 1 resource masters - commack schools

Chapter 1 Resource Masters

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Copyright © by The McGraw-Hill Companies, Inc.

All rights reserved. The contents, or parts thereof, may be reproduced in print form for non-profit educational use with Glencoe Algebra 1, provided such reproductions bear copyright notice, but may not be reproduced in any form for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storage or transmission, or broadcast for distance learning.

Send all inquiries to:McGraw-Hill Education8787 Orion PlaceColumbus, OH 43240

ISBN: 978-0-07-660498-2MHID: 0-07-660498-5

Printed in the United States of America.

1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11

CONSUMABLE WORKBOOKS Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish.

MHID ISBNStudy Guide and Intervention Workbook 0-07-660292-3 978-0-07-660292-6Homework Practice Workbook 0-07-660291-5 978-0-07-660291-9

Spanish VersionHomework Practice Workbook 0-07-660294-X 978-0-07-660294-0

Answers For Workbooks The answers for Chapter 1 of these workbooks can be found in the back of this Chapter Resource Masters booklet.

ConnectED All of the materials found in this booklet are included for viewing, printing, and editing at connected.mcgraw-hill.com.

Spanish Assessment Masters (MHID: 0-07-660289-3, ISBN: 978-0-07-660289-6) These masters contain a Spanish version of Chapter 1 Test Form 2A and Form 2C.

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Teacher’s Guide to Using the Chapter 1 Resource Masters .........................................iv

Chapter Resources Chapter 1 Student-Built Glossary ...................... 1Chapter 1 Anticipation Guide (English) ............. 3Chapter 1 Anticipation Guide (Spanish) ............ 4

Lesson 1-1Variables and ExpressionsStudy Guide and Intervention ............................ 5Skills Practice .................................................... 7Practice ............................................................. 8Word Problem Practice ...................................... 9Enrichment ...................................................... 10

Lesson 1-2Order of OperationsStudy Guide and Intervention ...........................11Skills Practice .................................................. 13Practice ........................................................... 14Word Problem Practice .................................... 15Enrichment ...................................................... 16TI-Nspire® Activity ............................................ 17

Lesson 1-3Properties of NumbersStudy Guide and Intervention .......................... 18Skills Practice .................................................. 20Practice ........................................................... 21Word Problem Practice .................................... 22Enrichment ...................................................... 23

Lesson 1-4The Distributive PropertyStudy Guide and Intervention .......................... 24Skills Practice .................................................. 26Practice ........................................................... 27Word Problem Practice .................................... 28Enrichment ...................................................... 29

Lesson 1-5EquationsStudy Guide and Intervention .......................... 30Skills Practice .................................................. 32Practice ........................................................... 33Word Problem Practice .................................... 34Enrichment ...................................................... 35Spreadsheet Activity ........................................ 36

Lesson 1-6RelationsStudy Guide and Intervention .......................... 37Skills Practice .................................................. 39Practice ........................................................... 40Word Problem Practice .................................... 41Enrichment ...................................................... 42

Lesson 1-7FunctionsStudy Guide and Intervention .......................... 43Skills Practice .................................................. 45Practice ........................................................... 46Word Problem Practice .................................... 47Enrichment ...................................................... 48

Lesson 1-8Interpreting Graphs of Functions

Study Guide and Intervention .......................... 49Skills Practice .................................................. 51Practice ........................................................... 52Word Problem Practice .................................... 53Enrichment ...................................................... 54

AssessmentStudent Recording Sheet ................................ 55Rubric for Scoring Extended Response .......... 56Chapter 1 Quizzes 1 and 2 ............................. 57Chapter 1 Quizzes 3 and 4 ............................. 58Chapter 1 Mid-Chapter Test ............................ 59Chapter 1 Vocabulary Test ............................... 60Chapter 1 Test, Form 1 .................................... 61Chapter 1 Test, Form 2A ................................. 63Chapter 1 Test, Form 2B ................................. 65

Chapter 1 Test, Form 2C ................................. 67Chapter 1 Test, Form 2D ................................. 69Chapter 1 Test, Form 3 .................................... 71Chapter 1 Extended Response Test ................ 73Standardized Test Practice ...............................74

Answers ........................................... A1–A36

Contents

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iv

Teacher’s Guide to Using the Chapter 1 Resource Masters

Chapter ResourcesStudent-Built Glossary (pages 1–2) These masters are a student study tool that pres-ents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students high-light or star the terms with which they are not familiar. Give this to students before beginning Lesson 1-1. Encourage them to add these pages to their mathematics study notebooks. Remind them to complete the appropriate words as they study each lesson.

Anticipation Guide (pages 3–4) This mas-ter, presented in both English and Spanish, is a survey used before beginning the chap-ter to pinpoint what students may or may not know about the concepts in the chapter. Students will revisit this survey after they complete the chapter to see if their percep-tions have changed.

Lesson ResourcesStudy Guide and Intervention These masters provide vocabulary, key concepts, additional worked-out examples and Check Your Progress exercises to use as a reteach-ing activity. It can also be used in conjunc-tion with the Student Edition as an instruc-tional tool for students who have been absent.

Skills Practice This master focuses more on the computational nature of the lesson. Use as an additional practice option or as homework for second-day teaching of the lesson.

Practice This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems. Use as an additional prac-tice option or as homework for second-day teaching of the lesson.

Word Problem Practice This master includes additional practice in solving word problems that apply the concepts of the lesson. Use as an additional practice or as homework for second-day teaching of the lesson.

Enrichment These activities may extend the concepts of the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathe-matics they are learning. They are written for use with all levels of students.

Graphing Calculator, TI-Nspire or Spreadsheet Activities These activities present ways in which technology can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of your lesson presentation.

The Chapter 1 Resource Masters includes the core materials needed for Chapter 1. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing, printing, and editing at connectED.mcgraw-hill.com.

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v

Assessment OptionsThe assessment masters in the Chapter 1 Resource Masters offer a wide range of assessment tools for formative (monitoring) assessment and summative (final) assessment.

Student Recording Sheet This master corresponds with the standardized test practice at the end of the chapter.

Extended Response Rubric This master provides information for teachers and stu-dents on how to assess performance on open-ended questions.

Quizzes Four free-response quizzes offer assessment at appropriate intervals in the chapter.

Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and free-response questions.

Vocabulary Test This test is suitable for all students. It includes a list of vocabulary words and 11 questions to assess students’ knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests.

Leveled Chapter Tests• Form 1 contains multiple-choice

questions and is intended for use with below grade level students.

• Forms 2A and 2B contain multiple-choice questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.

• Forms 2C and 2D contain free-response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.

• Form 3 is a free-response test for use with above grade level students.

All of the above mentioned tests include a free-response Bonus question.

Extended-Response Test Performance assessment tasks are suitable for all stu-dents. Sample answers and a scoring rubric are included for evaluation.

Standardized Test Practice These three pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and short-answer free-response questions.

Answers• The answers for the Anticipation Guide

and Lesson Resources are provided as reduced pages.

• Full-size answer keys are provided for the assessment masters.

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Chapter 1 1 Glencoe Algebra 1

This is an alphabetical list of the key vocabulary terms you will learn in Chapter 1. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add these pages to your Algebra Study Notebook to review vocabulary at the end of the chapter.

(continued on the next page)

Vocabulary TermFound

on PageDefi nition/Description/Example

coefficient(koh·uh·FIH·shuhnt)

continuous function

coordinate system

dependent variable

domain

end behavior

function

identity

independent variable

intercept

Student-Built Glossary1

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Vocabulary TermFound

on PageDefi nition/Description/Example

like terms

line symmetry

open sentence

order of operations

power

range

relative maximum

relative minimum

replacement set

solution set

variable

Student-Built Glossary (continued)1


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Before you begin Chapter 1

• Read each statement.

• Decide whether you Agree (A) or Disagree (D) with the statement.

• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).

After you complete Chapter 1

• Reread each statement and complete the last column by entering an A or a D.

• Did any of your opinions about the statements change from the first column?

• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.

1 Anticipation GuideExpressions, Equations, and Functions

Step 1

Step 2

STEP 1A, D, or NS

StatementSTEP 2A or D

1. An algebraic expression contains one or more numbers, variables, and arithmetic operations.

2. The expression x4 means x + x + x + x.

3. According to the order of operations, all multiplication and division should be done before anything else.

4. Since 2 makes the equation 3t - 1 = 5 true, {2} is the solution set for the equation.

5. Because of the Reflexive Property of Equality, if a + b = c then c = a + b.

6. The multiplicative inverse of 23 is 1 − 23

.

7. The Distributive Property states that a(b + c) will equal ab + c.

8. The order in which you add or multiply numbers does not change their sum or product.

9. A graph has symmetry in a line if each half of the graph on either side of the line matches exactly.

10. In the coordinate plane, the x-axis is horizontal and the y-axis is vertical.


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Antes de comenzar el Capítulo 1

• Lee cada enunciado.

• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.

• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta, escribe NS (No estoy seguro(a)).

Después de completar el Capítulo 1

• Vuelve a leer cada enunciado y completa la última columna con una A o una D.

• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?

• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los enunciados que marcaste con una D.

1 Ejercicios preparatoriosExpressions, Equations, and Functions

Paso 1

Paso 2

PASO 1A, D o NS

EnunciadoPASO 2A o D

1. Una expresión matemática contiene uno o más números, variables y operaciones aritméticas.

2. La expresión x4 significa x + x + x + x.

3. Según el orden de las operaciones, se debe realizar toda multi-plicación y división antes que cualquier otra operación.

4. Puesto que 2 hace verdadera la ecuación 3t - 1 = 5 , {2} es el conjunto solución para la ecuación.

5. Debido a la propiedad reflexiva de la igualdad, si a + b = c entonces c = a + b.

6. El inverso multiplicativo de 23 es 1 − 23

.

7. La propiedad distributiva dice que a(b + c) es igual a ab + c.

8. El orden en el cual sumas o multiplicas números no altera su suma o su producto.

9. Una gráfica tiene simetría en una línea si cada uno la mitad de la gráfica a cada lado de la línea corresponde exactamente.

10. En el plano de coordenadas, el eje x es horizontal y el eje y es vertical.

Capítulo 1 4 Álgebra 1 de Glencoe


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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. 6n2

the product of 6 and n squaredb. n3 - 12m

the difference of n cubed and twelve times m

ExercisesWrite a verbal expression for each algebraic expression.

1. w - 1 2. 1 − 3 a3

3. 81 + 2x 4. 12d

5. 84 6. 62

7. 2n2 + 4 8. a3 ․ b3

9. 2x3 - 3 10. 6k3 −

5

11. 1 − 4 b2 12. 7n5

13. 3x + 4 14. 2 − 3 k5

15. 3b2 + 2a3 16. 4(n2 + 1)

1-1 Study Guide and InterventionVariables and Expressions

Example


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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 nThe words more than imply addition.four more than a number n4 + nThe algebraic expression is 4 + n.

b. the difference of a number squared and 8The expression difference of implies subtraction.the difference of a number squared and 8n2 - 8The algebraic expression is n2 - 8.

ExercisesWrite 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

1-1 Study Guide and Intervention (continued)

Variables and Expressions

Example


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1. 9a2 2. 52

3. c + 2d 4. 4 - 5h

5. 2b2 6. 7x3 - 1

7. p4 + 6r 8. 3n2 - x


9. the sum of a number and 10

10. 15 less than k

11. the product of 18 and q

12. 6 more than twice m

13. 8 increased by three times a number

14. the difference of 17 and 5 times a number

15. the product of 2 and the second power of y

16. 9 less than g to the fourth power

1-1 Skills PracticeVariables and Expressions


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1. 23f 2. 73

3. 5m2 + 2 4. 4d3 - 10

5. x3 ․ y4 6. b2 - 3c3

7. k5 −

6 8. 4n2

− 7


9. the difference of 10 and u

10. the sum of 18 and a number

11. the product of 33 and j

12. 74 increased by 3 times y

13. 15 decreased by twice a number

14. 91 more than the square of a number

15. three fourths the square of b

16. two fifths the cube of a number

17. BOOKS A used bookstore sells paperback fiction books in excellent condition for $2.50 and in fair condition for $0.50. Write an expression for the cost of buying x excellent-condition paperbacks and f fair-condition paperbacks.

18. GEOMETRY The surface area of the side of a right cylinder can be found by multiplying twice the number π by the radius times the height. If a circular cylinder has radius r and height h, write an expression that represents the surface area of its side.

1-1 PracticeVariables and Expressions


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1. SOLAR SYSTEM It takes Earth about 365 days to orbit the Sun. It takes Uranus about 85 times as long. Write a numerical expression to describe the number of days it takes Uranus to orbit the Sun.

2. TECHNOLOGY There are 1024 bytes in a kilobyte. Write an expression that describes the number of bytes in a computer chip with n kilobytes.

3. THEATER H. Howard Hughes, Professor Emeritus of Texas Wesleyan College and his wife Erin Connor Hughes attended a record 6136 theatrical shows. Write an expression for the average number of shows they attended per year if they accumulated the record over y years.

4. TIDES The difference between high and low tides along the Maine coast in November is 19 feet on Monday and x feet on Tuesday. Write an expression to show the average rise and fall of the tide for Monday and Tuesday.

5. BLOCKS A toy manufacturer produces a set of blocks that can be used by children to build play structures. The product packaging team is analyzing different arrangements for packaging their blocks. One idea they have is to arrange the blocks in the shape of a cube, with b blocks along one edge.

a. Write an expression representing the total number of blocks packaged in a cube measuring b blocks on one edge.

b. The packaging team decides to take one layer of blocks off the top of this package. Write an expression representing the number of blocks in the top layer of the package.

c. The team finally decides that their favorite package arrangement is to take 2 layers of blocks off the top of a cube measuring b blocks along one edge. Write an expression representing the number of blocks left behind after the top two layers are removed.

b

b

b

1-1 Word Problem Practice Variables and Expressions


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Toothpick TrianglesVariable expressions can be used to represent patterns and help solve problems. Consider the problem of creating triangles out of toothpicks shown below.

Figure 3Figure 2Figure 1

1. How many toothpicks does it take to create each figure?

2. How many toothpicks does it take to make up the perimeter of each image?

3. Sketch the next three figures in the pattern.

4. Continue the pattern to complete the table.

5. Let the variable n represent the figure number. Write an expression that can be used to find the number of toothpicks needed to create figure n.

6. Let the variable n represent the figure number. Write an expression that can be used to find the number of toothpicks in the perimeter of figure n.

1-1 Enrichment

Image Number 1 2 3 4 5 6 7 8 9 10

Number of toothpicks 3 5 7

Number of toothpicks in

Perimeter3 4 5


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Evaluate Numerical Expressions Numerical expressions often contain more than one operation. To evaluate them, use the rules for order of operations shown below.

Order ofOperations

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. 34

34 = 3 ․ 3 ․ 3 ․ 3 Use 3 as a factor 4 times.

= 81 Multiply.

b. 63

63 = 6 ․ 6 ․ 6 Use 6 as a factor 3 times.

= 216 Multiply.


a. 3[2 + (12 ÷ 3)2]3[2 + (12 ÷ 3)2] = 3(2 + 42) Divide 12 by 3.

= 3(2 + 16) Find 4 squared.

= 3(18) Add 2 and 16.

= 54 Multiply 3 and 18.

b. 3 + 23

−

42 · 3

3 + 23

− 42

· 3 =

3 + 8 − 42

· 3 Evaluate power in numerator.

= 11 − 42

· 3 Add 3 and 8 in the numerator.

= 11 − 16 · 3

Evaluate power in denominator.

= 11 − 48

Multiply.

ExercisesEvaluate each expression.

1. 52 2. 33 3. 104

4. 122 5. 83 6. 28

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 - 32

13. 32 ÷ 3 + 22 ․ 7 - 20 ÷ 5 14. 4 + 32

− 12 + 1

15. 250 ÷ [5(3 ․ 7 + 4)]

16. 2 · 42 - 8 ÷ 2 − (5 + 2) · 2

17. 4(52) - 4 · 3 −

4(4 · 5 + 2) 18. 52

- 3 − 20(3) + 2(3)

1-2 Study Guide and InterventionOrder of Operations

Example 1 Example 2


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Evaluate Algebraic Expressions Algebraic expressions may contain more than one operation. Algebraic expressions can be evaluated if the values of the variables are known. First, replace the variables with their values. Then use the order of operations to calculate the value of the resulting numerical expression.

Evaluate x3 + 5(y - 3) if x = 2 and y = 12.x3 + 5(y - 3) = 23 + 5(12 - 3) Replace x with 2 and y with 12.

= 8 + 5(12 - 3) Evaluate 23.

= 8 + 5(9) Subtract 3 from 12.

= 8 + 45 Multiply 5 and 9.

= 53 Add 8 and 45.

The solution is 53.

ExercisesEvaluate each expression if x = 2, y = 3, z = 4, a = 4 −

5 , and b = 3 −

5 .

1. x + 7 2. 3x - 5 3. x + y2

4. x3 + y + z2 5. 6a + 8b 6. 23 - (a + b)

7. y2

− x2

8. 2xyz + 5 9. x(2y + 3z)

10. (10x)2 + 100a 11. 3xy - 4

− 7x

12. a2 + 2b

13. z2

- y2

− x2

14. 6xz + 5xy 15. (z - y) 2

− x

16. 25ab + y

− xz 17. 5 a 2 b − y 18. (z ÷ x)2 + ax

19. ( x − z ) 2 + (

y − z )

2 20. x + z

− y + 2z

21. ( z ÷ x − y ) + (

y ÷ x − z )


Order of Operations

Example


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1. 82 2. 34

3. 53 4. 33

5. (5 + 4) � 7 6. (9 - 2) � 3

7. 4 + 6 � 3 8. 12 + 2 � 2

9. (3 + 5) � 5 + 1 10. 9 + 4(3 + 1)

11. 30 - 5 � 4 + 2 12. 10 + 2 � 6 + 4

13. 14 ÷ 7 � 5 - 32 14. 4[30 - (10 - 2) � 3]

15. 5 + [30 - (6 - 1)2] 16. 2[12 + (5 - 2)2]

Evaluate each expression if x = 6, y = 8, and z = 3.

17. xy + z 18. yz - x

19. 2x + 3y - z 20. 2(x + z) - y

21. 5z + ( y - x) 22. 5x - ( y + 2z)

23. x2 + y2 - 10z 24. z3 + ( y2 - 4x)

25. y + xz

− 2 26.

3y + x2

− z

1-2 Skills PracticeOrder of Operations


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1. 112 2. 83 3. 54

4. (15 - 5) ․ 2 5. 9 ․ (3 + 4) 6. 5 + 7 ․ 4

7. 4(3 + 5) - 5 ․ 4 8. 22 ÷ 11 ․ 9 - 32 9. 62 + 3 ․ 7 - 9

10. 3[10 - (27 ÷ 9)] 11. 2[52 + (36 ÷ 6)] 12. 162 ÷ [6(7 - 4)2]

13. 52 ․ 4 - 5 ․ 42

− 5(4)

14. (2 ․ 5)2 + 4 −

32 - 5

15. 7 + 32

− 42

· 2

Evaluate each expression if a = 12, b = 9, and c = 4.

16. a2 + b - c2 17. b2 + 2a - c2

18. 2c(a + b) 19. 4a + 2b - c2

20. (a2 ÷ 4b) + c 21. c2 · (2b - a)

22. bc2 + a − c 23. 2c3 - ab − 4

24. 2(a - b)2 - 5c 25. b

2 - 2c2 −

a + c - b

26. CAR RENTAL Ann Carlyle is planning a business trip for which she needs to rent a car. The car rental company charges $36 per day plus $0.50 per mile over 100 miles. Suppose Ms. Carlyle rents the car for 5 days and drives 180 miles.

a. Write an expression for how much it will cost Ms. Carlyle to rent the car.

b. Evaluate the expression to determine how much Ms. Carlyle must pay the car rental company.

27. GEOMETRY The length of a rectangle is 3n + 2 and its width is n - 1. The perimeter of the rectangle is twice the sum of its length and its width.

a. Write an expression that represents the perimeter of the rectangle.

b. Find the perimeter of the rectangle when n = 4 inches.

1-2 Practice Order of Operations


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1. SCHOOLS Jefferson High School has 100 less than 5 times as many students as Taft High School. Write and evaluate an expression to find the number of students at Jefferson High School if Taft High School has 300 students.

2. GEOGRAPHY Guadalupe Peak in Texas has an altitude that is 671 feet more than double the altitude of Mount Sunflower in Kansas. Write and evaluate an expression for the altitude of Guadalupe Peak if Mount Sunflower has an altitude of 4039 feet.

3. TRANSPORTATION The Plaid Taxi Cab Company charges $1.75 per passenger plus $3.45 per mile for trips less than 10 miles. Write and evaluate an expression to find the cost for Max to take a Plaid taxi 8 miles to the airport.

4. GEOMETRY The area of a circle is related to the radius of the circle such that the product of the square of the radius and a number π gives the area. Write and evaluate an expression for the area of a circular pizza below. Approximate π as 3.14.

7 in.

5. BIOLOGY Lavania is studying the growth of a population of fruit flies in her laboratory. She notices that the number of fruit flies in her experiment is five times as large after any six-day period. She observes 20 fruit flies on October 1. Write and evaluate an expression to predict the population of fruit flies Lavania will observe on October 31.

6. CONSUMER SPENDING During a long weekend, Devon paid a total of x dollars for a rental car so he could visit his family. He rented the car for 4 days at a rate of $36 per day. There was an additional charge of $0.20 per mile after the first 200 miles driven.

a. Write an algebraic expression to represent the amount Devon paid for additional mileage only.

b. Write an algebraic expression to represent the number of miles over 200 miles that Devon drove the rented car.

c. How many miles did Devon drive overall if he paid a total of $174 for the car rental?

1-2 Word Problem PracticeOrder of Operations


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The Four Digits ProblemOne well-known mathematics problem is to write expressions for consecutive numbers beginning with 1. On this page, you will use the digits 1, 2, 3, and 4. Each digit is used only once. You may use addition, subtraction, multiplication (not division), exponents, and parentheses in any way you wish. Also, you can use two digits to make one number, such as 12 or 34.

Express each number as a combination of the digits 1, 2, 3, and 4.

1 = (3 × 1) - (4 - 2) 18 = 35 = 2(4+1) + 3

2 = 19 = 3(2 + 4) + 1 36 =

3 = 20 = 37 =

4 = 21 = 38 =

5 = 22 = 39 =

6 = 23 = 31 - (4 × 2) 40 =

7 = 24 = 41 =

8 = 25 = 42 =

9 = 26 = 43 = 42 + 13

10 = 27 = 44 =

11 = 28 = 45 =

12 = 29 = 46 =

13 = 30 = 47 =

14 = 31 = 48 =

15 = 32 = 49 =

16 = 33 = 50 =

17 = 34 =

Does a calculator help in solving these types of puzzles? Give reasons for your opinion.

1-2 Enrichment


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When evaluating algebraic expressions, it is sometimes helpful to use the store keyon the calculator, especially to check solutions, evaluate several expressions for the same values of variables, or evaluate the same expression for multiple values of the variables.

Evaluate a2 - 4a + 6 if a = 8.

First, open a new Calculator page on the TI-Nspire.

Then, delete any instances of stored variables by entering CLEARAZ.

Store 8 as the value for a.

Finally enter the expression, including the variables, to evaluate.

The answer is 38.

Exercises

Evaluate each expression if a = 4, b = 6, x = 8, and y = 12. Express answers as integers or fractions.

1. bx - ay ÷ b 2. a[ x + (y ÷ a)2] 3. a3 - (y - b)2 + x2

4. b + a2

− x2

- b2 5. 2a(x - b)

− xy - 9b 6. b3 - [3(a + b2

) + 5b] −−

y ÷ a(x - 1)

Evaluate xy - 4y

− 5x

if x = 4 and y = 12.

Enter 4 as the value for x and 12 as the value for y.

Evaluate the expression. The TI-Nspire will display the answer as a fraction.

The answer is 228 − 5 .

1-2 TI-Nspire® ActivityUsing the Store Key

Example 1

Example 2


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Evaluate 24 � 1 - 8 + 5(9 ÷ 3 - 3). Name the property used in each step.24 ․ 1 - 8 + 5(9 ÷ 3 - 3) = 24 ․ 1 - 8 + 5(3 - 3) Substitution; 9 ÷ 3 = 3

= 24 ․ 1 - 8 + 5(0) Substitution; 3 - 3 = 0

= 24 - 8 + 5(0) Multiplicative Identity; 24 ․ 1 = 24

= 24 - 8 + 0 Multiplicative Property of Zero; 5(0) = 0

= 16 + 0 Substitution; 24 - 8 = 16

= 16 Additive Identity; 16 + 0 = 16

ExercisesEvaluate each expression. Name the property used in each step.

1. 2 [ 1 − 4 + ( 1 −

2 )

2 ] 2. 15 ․ 1 - 9 + 2(15 ÷ 3 - 5)

3. 2(3 ․ 5 ․ 1 - 14) - 4 ․ 1 − 4 4. 18 ․ 1 - 3 ․ 2 + 2(6 ÷ 3 - 2)

1-3 Study Guide and InterventionProperties of Numbers

Identity and Equality Properties The identity and equality properties in the chart below can help you solve algebraic equations and evaluate mathematical expressions.

Additive Identity For any number a, a + 0 = a.

Additive Inverse For any number a, a + (-a) = 0.

Multiplicative Identity For any number a, a . 1 = a.

Multiplicative Property of 0 For any number a, a . 0 = 0.

Multiplicative Inverse

Property

For every number a − b , where a, b ≠ 0, there is exactly one number b − a such that

a − b . b −

a = 1.

Refl exive Property For any number a, a = a.

Symmetric Property For any numbers a and b, if a = b, then b = a.

Transitive Property For any numbers a, b, and c, if a = b and b = c, then a = c.

Substitution Property If a = b, then a may be replaced by b in any expression.

Example


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Study Guide and Intervention (continued)

Properties of Numbers

1-3

Commutative and Associative Properties The Commutative and Associative Properties can be used to simplify expressions. The Commutative Properties state that the order in which you add or multiply numbers does not change their sum or product. The Associative Properties state that the way you group three or more numbers when adding or multiplying does not change their sum or product.

Evaluate 6 � 2 � 3 � 5 using properties of numbers. Name the property used in each step.6 ․ 2 ․ 3 ․ 5 = 6 ․ 3 ․ 2 ․ 5 Commutative Property

= (6 ․ 3)(2 ․ 5) Associative Property

= 18 ․ 10 Multiply.

= 180 Multiply.

The product is 180.

Evaluate 8.2 + 2.5 + 2.5 + 1.8 using properties of numbers. Name the property used in each step.8.2 + 2.5 + 2.5 + 1.8

= 8.2 + 1.8 + 2.5 + 2.5 Commutative Prop.

= (8.2 + 1.8) + (2.5 + 2.5) Associative Prop.

= 10 + 5 Add.

= 15 Add.

The sum is 15.

ExercisesEvaluate each expression using properties of numbers. Name the property used in each step.

1. 12 + 10 + 8 + 5 2. 16 + 8 + 22 + 12 3. 10 ․ 7 ․ 2.5

4. 4 ․ 8 ․ 5 ․ 3 5. 12 + 20 + 10 + 5 6. 26 + 8 + 4 + 22

7. 3 1 − 2 + 4 + 2 1 −

2 + 3 8. 3 −

4 ․ 12 ․ 4 ․ 2 9. 3.5 + 2.4 + 3.6 + 4.2

10. 4 1 − 2 + 5 + 1 −

2 + 3 11. 0.5 ․ 2.8 ․ 4 12. 2.5 + 2.4 + 2.5 + 3.6

13. 4 − 5 ․ 18 ․ 25 ․

2 − 9 14. 32 ․ 1 −

5 ․ 1 −

2 ․ 10 15. 1 −

4 ․ 7 ․ 16 ․ 1 −

7

16. 3.5 + 8 + 2.5 + 2 17. 18 ․ 8 ․ 1 − 2 ․ 1 −

9 18. 3 −

4 ․ 10 ․ 16 ․ 1 −

2

Example 1 Example 2

Commutative Properties For any numbers a and b, a + b = b + a and a � b = b � a.

Associative Properties For any numbers a, b, and c, (a + b) + c = a + (b + c ) and (ab)c = a(bc).


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Evaluate each expression. Name the property used in each step.

1. 7(16 ÷ 42) 2. 2[5 - (15 ÷ 3)]

3. 4 - 3[7 - (2 ․ 3)] 4. 4[8 - (4 ․ 2)] + 1

5. 6 + 9[10 - 2(2 + 3)] 6. 2(6 ÷ 3 - 1) ․ 1 − 2

7. 16 + 8 + 14 + 12 8. 36 + 23 + 14 + 7

9. 5 ․ 3 ․ 4 ․ 3 10. 2 ․ 4 ․ 5 ․ 3

1-3 Skills PracticeProperties of Numbers


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Evaluate each expression. Name the property used in each step.

1. 2 + 6(9 - 32) - 2 2. 5(14 - 39 ÷ 3) + 4 ․ 1 − 4

Evaluate each expression using properties of numbers. Name the property used in each step.

3. 13 + 23 + 12 + 7 4. 6 ․ 0.7 ․ 5

5. SALES Althea paid $5.00 each for two bracelets and later sold each for $15.00. She paid $8.00 each for three bracelets and sold each of them for $9.00.

a. Write an expression that represents the profit Althea made.

b. Evaluate the expression. Name the property used in each step.

6. SCHOOL SUPPLIES Kristen purchased two binders that cost $1.25 each, two binders that cost $4.75 each, two packages of paper that cost $1.50 per package, four blue pens that cost $1.15 each, and four pencils that cost $0.35 each.

a. Write an expression to represent the total cost of supplies before tax.

b. What was the total cost of supplies before tax?

1-3 PracticeProperties of Numbers


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1. EXERCISE Annika goes on a walk every day in order to get the exercise her doctor recommends. If she walks at a

rate of 3 miles per hour for 1−3

of an hour, then she will have walked 3 × 1

−3

miles. Evaluate the expression and name the

property used.

2. SCHOOL SUPPLIES At a local school supply store, a highlighter costs $1.25, a ballpoint pen costs $0.80, and a spiral notebook costs $2.75. Use mental math and the Associative Property of Addition to find the total cost if one of each item is purchased.

3. MENTAL MATH The triangular banner has a base of 9 centimeters and a height of 6 centimeters. Using the formula for area of a triangle, the banner’s area can

be expressed as 1 − 2 × 9 × 6. Gabrielle

finds it easier to write and evaluate

( 1 − 2 × 6) × 9 to find the area. Is

Gabrielle’s expression equivalent to the area formula? Explain.

b

h

4. ANATOMY The human body has 60 bones in the arms and hands, 84 bones in the upper body and head, and 62 bones in the legs and feet. Use the Associative Property to write and evaluate an expression that represents the total number of bones in the human body.

5. TOLL ROADS Some toll highways assess tolls based on where a car entered and exited. The table below shows the highway tolls for a car entering and exiting at a variety of exits. Assume that the toll for the reverse direction is the same.

Entered Exited Toll

Exit 5 Exit 8 $0.50

Exit 8 Exit 10 $0.25

Exit 10 Exit 15 $1.00

Exit 15 Exit 18 $0.50

Exit 18 Exit 22 $0.75

a. Running an errand, Julio travels from Exit 8 to Exit 5. What property would you use to determine the toll?

b. Gordon travels from home to work and back each day. He lives at Exit 15 on the toll road and works at Exit 22. Write and evaluate an expression to find his daily toll cost. What property or properties did you use?

Word Problem PracticeProperties of Numbers

1-3



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Properties of Operations

Let’s make up a new operation and denote it by �, so that a � b means ba.

2 � 3 = 32 = 9(1 � 2) � 3 = 21 � 3 = 32 = 9

1. What number is represented by 2 � 3?

2. What number is represented by 3 � 2?

3. Does the operation � appear to be commutative?

4. What number is represented by (2 � 1) � 3?

5. What number is represented by 2 � (1 � 3)?

6. Does the operation � appear to be associative?

Let’s make up another operation and denote it by ⊕, so that

a ⊕ b = (a + 1)(b + 1).

3 ⊕ 2 = (3 + 1)(2 + 1) = 4 ․ 3 = 12(1 ⊕ 2) ⊕ 3 = (2 ․ 3) ⊕ 3 = 6 ⊕ 3 = 7 ․ 4 = 28

7. What number is represented by 2 ⊕ 3?

8. What number is represented by 3 ⊕ 2?

9. Does the operation ⊕ appear to be commutative?

10. What number is represented by (2 ⊕ 3) ⊕ 4?

11. What number is represented by 2 ⊕ (3 ⊕ 4)?

12. Does the operation ⊕ appear to be associative?

13. What number is represented by 1 � (3 ⊕ 2)?

14. What number is represented by (1 � 3) ⊕ (1 � 2)?

15. Does the operation � appear to be distributive over the operation ⊕?

16. Let’s explore these operations a little further. What number is represented by 3 � (4 ⊕ 2)?

17. What number is represented by (3 � 4) ⊕ (3 � 2)?

18. Is the operation � actually distributive over the operation ⊕?

1-3 Enrichment


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Evaluate Expressions The Distributive Property can be used to help evaluate expressions.

Distributive PropertyFor any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + ca and

a(b - c) = ab - ac and (b - c)a = ba - ca.

Use the Distributive Property to rewrite 6(8 + 10). Then evaluate.

6(8 + 10) = 6 ․ 8 + 6 ․ 10 Distributive Property

= 48 + 60 Multiply.

= 108 Add.

Use the Distributive Property to rewrite -2(3x2 + 5x + 1). Then simplify.

-2(3x2 + 5x + 1) = -2(3x2) + (-2)(5x) + (-2)(1) Distributive Property

= -6x2 + (-10x) + (-2) Multiply.

= -6x2 - 10x - 2 Simplify.

ExercisesUse the Distributive Property to rewrite each expression. Then evaluate.

1. 20(31) 2. 12 � 4 1 − 2 3. 5(311)

4. 5(4x - 9) 5. 3(8 - 2x) 6. 12 (6 - 1 − 2 x)

7. 12 (2 + 1 − 2 x) 8. 1 −

4 (12 - 4t) 9. 3(2x - y)

10. 2(3x + 2y - z) 11. (x - 2)y 12. 2(3a - 2b + c)

13. 1 − 4 (16x - 12y + 4z) 14. (2 - 3x + x2)3 15. -2(2x2 + 3x + 1)

1-4 Study Guide and InterventionThe Distributive Property

Example 1

Example 2


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Simplify Expressions A term is a number, a variable, or a product or quotient of numbers and variables. Like terms are terms that contain the same variables, with corresponding variables having the same powers. The Distributive Property and properties of equalities can be used to simplify expressions. An expression is in simplest form if it is replaced by an equivalent expression with no like terms or parentheses.

Simplify 4(a2 + 3ab) - ab.

4(a2 + 3ab) - ab = 4(a2 + 3ab) - 1ab Multiplicative Identity

= 4a2 + 12ab - 1ab Distributive Property

= 4a2 + (12 - 1)ab Distributive Property

= 4a2 + 11ab Substitution

ExercisesSimplify each expression. If not possible, write simplified.

1. 12a - a 2. 3x + 6x 3. 3x - 1

4. 20a + 12a - 8 5. 3x2 + 2x2 6. -6x + 3x2 + 10x2

7. 2p + 1 − 2 q 8. 10xy - 4(xy + xy) 9. 21a + 18a + 31b - 3b

10. 4x + 1 − 4 (16x - 20y) 11. 2 - 1 - 6x + x2 12. 4x2 + 3x2 + 2x

Write an algebraic expression for each verbal expression. Then simplify, indicating the properties used.

13. six times the difference of 2a and b, increased by 4b

14. two times the sum of x squared and y squared, increased by three times the sum of x squared and y squared


The Distributive Property

Example


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Use the Distributive Property to rewrite each expression. Then evaluate.

1. 4(3 + 5) 2. 2(6 + 10)

3. 5(7 - 4) 4. (6 - 2)8

5. 5 ․ 89 6. 9 ․ 99

7. 15 ․ 104 8. 15 (2 1 − 3 )


9. (a + 7)2 10. 7(h - 10)

11. 3(m + n) 12. 2(x - y + 1)

Simplify each expression. If not possible, write simplified.

13. 2x + 8x 14. 17g + g

15. 2x2 + 6x2 16. 7a2 - 2a2

17. 3y2 - 2y 18. 2(n + 2n)

19. 4(2b - b) 20. 3q2 + q - q2


21. The product of 9 and t squared, increased by the sum of the square of t and 2

22. 3 times the sum of r and d squared minus 2 times the sum of r and d squared

Skills PracticeThe Distributive Property

1-4


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1. 9(7 + 8) 2. 7(6 - 4) 3. (4 + 6)11

4. 9 ․ 499 5. 7 ․ 110 6. 16 (4 1 − 4 )

Use the Distributive property to rewrite each expression. Then simplify.

7. (9 - p)3 8. (5y - 3)7 9. 15 ( f + 1 − 3 )

10. 16(3b - 0.25) 11. m(n + 4) 12. (c - 4)d


13. w + 14w - 6w 14. 3(5 + 6h) 15. 12b2 + 9b2

16. 25t3 - 17t3 17. 3a2 + 6a + 2b2 18. 4(6p + 2q - 2p)


19. 4 times the difference of f squared and g, increased by the sum of f squared and 2g

20. 3 times the sum of x and y squared plus 5 times the difference of 2x and y

21. DINING OUT The Ross family recently dined at an Italian restaurant. Each of the four family members ordered a pasta dish that cost $11.50, a drink that cost $1.50, and dessert that cost $2.75.

a. Write an expression that could be used to calculate the cost of the Ross’ dinner before adding tax and a tip.

b. What was the cost of dining out for the Ross family?

1-4 Practice The Distributive Property


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1. OPERA Mr. Delong’s drama class is planning a field trip to see Mozart’s famous opera Don Giovanni. Tickets cost $39 each, and there are 23 students and 2 teachers going on the field trip. Write and evaluate an expression to find the group’s total ticket cost.

2. SALARY In a recent year, the median salary for an engineer in the United States was $55,000 and the median salary for a computer programmer was $52,000. Write and evaluate an expression to estimate the total cost for a business to employ an engineer and a programmer for 5 years.

3. COSTUMES Isabella’s ballet class is performing a spring recital for which they need butterfly costumes. Each

butterfly costume is made from 3 3 − 5 yards

of fabric. Use the Distributive Property to find the number of yards of fabric needed for 5 costumes. (Hint: A mixed number can be written as the sum of an integer and a fraction.)

4. FENCES Demonstrate the Distributive Property by writing two equivalent expressions to represent the perimeter of the fenced dog pen below.

5. MENTAL MATH During a math facts speed contest, Jamal calculated the following expression faster than anyone else in his class.

197 × 4 When classmates asked him how he was

able to answer so quickly, he told them he used the Distributive Property to think of the problem differently. Write and evaluate an expression using the Distributive Property that would help Jamal perform the calculation quickly.

6. INVESTMENTS Letisha and Noel each opened a checking account, a savings account, and a college fund. The chart below shows the amounts that they deposited into each account.

Checking Savings College

Letisha $125 $75 $50

Noel $250 $50 $50

a. If Noel used only $50 bills when he deposited the money to open his accounts, how many $50 bills did he deposit?

b. If all accounts earn 1.5% interest per year and no further deposits are made, how much interest will Letisha have earned one year after her accounts were opened?

m

nDog Pen

Word Problem Practice The Distributive Property

1-4


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The Maya The Maya were a Native American people who lived from about 1500 B.C. to about 1500 A.D. in the region that today encompasses much of Central America and southern Mexico. Their many accomplishments include exceptional architecture, pottery, painting, and sculpture, as well as significant advances in the fields of astronomy and mathematics. The Maya developed a system of numeration that was based on the number twenty. The basic symbols of this system are shown in the table at the right. The places in a Mayan numeral are written vertically—the bottom place represents ones, the place above represents twenties, the place above that represents 20 × 20, or four hundreds, and so on. For instance, this is how to write the number 997 in Mayan numerals.

← 2 × 400 = 800

← 9 × 20 = 180

← 17 × 1 = 17 997

Evaluate each expression when v = •_____, w = • • • _______________, x = • • • • , y = � , and z = • •__________. Then write the answer in Mayan numerals. Exercise 5 is done for you.

1. z − w 2. v + w + z − x 3. xv

4. vxy 5. wx - z 6. vz + xy

7. w(v + x + z) 8. vwz 9. z(wx - x)

Tell whether each statement is true or false.

10. • • •__________ + •_____ = •_____ + • • •__________ 11. • • •__________

•_____ =

•_____

• • •__________ 12.

• • •_______________ =

• • •____________________

13. (• • • + _____) + __________ = • • • + (_____ + __________)

14. How are Exercises 10 and 11 alike? How are they different?

• •_______________

• • • •_____

• •

0 10

1 11

2 12

3 13

4 14

5 15

6 16

7 17

8 18

9 19

�

•

• •

• • •

• • • •

_____

•_____

• •_____

• • •_____

• • • •_____

__________

•__________

• •__________

• • •__________

• • • •_______________

• • • •__________

_______________

•_______________

• •_______________

• • • _______________

Enrichment1-4

• • •

�


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Solve Equations A mathematical sentence with one or more variables is called an open sentence. Open sentences are solved by finding replacements for the variables that result in true sentences. The set of numbers from which replacements for a variable may be chosen is called the replacement set. The set of all replacements for the variable that result in true statements is called the solution set for the variable. A sentence that contains an equal sign, =, is called an equation.

Find the solution set of 3a + 12 = 39 if the replacement set is {6, 7, 8, 9, 10}.

Replace a in 3a + 12 = 39 with each value in the replacement set.3(6) + 12 � 39 → 30 ≠ 39 false

3(7) + 12 � 39 → 33 ≠ 39 false

3(8) + 12 � 39 → 36 ≠ 39 false

3(9) + 12 � 39 → 39 = 39 true

3(10) + 12 � 39 → 42 ≠ 39 false

Since a = 9 makes the equation 3a + 12 = 39 true, the solution is 9.The solution set is {9}.

Solve 2(3 + 1) −

3(7 - 4) = b.

2(3 + 1)

− 3(7 - 4)

= b Original equation

2(4) −

3(3) = b Add in the numerator; subtract in the denominator.

8 − 9 = b Simplify.

The solution is 8 − 9 .

ExercisesFind the solution of each equation if the replacement sets are x =

{

1 −

4 , 1 −

2 , 1, 2, 3

}

and y = {2, 4, 6, 8}.

1. x + 1 − 2 = 5 −

2 2. x + 8 = 11 3. y - 2 = 6

4. x2 - 1 = 8 5. y2 - 2 = 34 6. x2 + 5 = 5 1 − 16

7. 2(x + 3) = 7 8. ( y + 1)2 = 9 9. y2 + y = 20

Solve each equation.

10. a = 23 - 1 11. n = 62 - 42 12. w = 62 ․ 32

13. 1 − 4 + 5 −

8 = k 14. 18 - 3 −

2 + 3 = p 15. t = 15 - 6 −

27 - 24

16. 18.4 - 3.2 = m 17. k = 9.8 + 5.7 18. c = 3 1 − 2 + 2 1 −

4

Study Guide and InterventionEquations

1-5

Example 1 Example 2


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Equations

1-5

Solve Equations with Two Variables Some equations contain two variables. It is often useful to make a table of values in which you can use substitution to find the corresponding values of the second variable.

MUSIC DOWNLOADS Emily belongs to an Internet music service that charges $5.99 per month and $0.89 per song. Write and solve an equation to find the total amount Emily spends if she downloads 10 songs this month.

The cost of the music service is a flat rate. The variable is the number of songs she downloads. The total cost is the price of the service plus $0.89 times the number of songs.

C = 0.89n + 5.99

To find the total cost for the month, substitute 10 for n in the equation.C = 0.89n + 5.99 Original equation

= 0.89(10) + 5.99 Substitute 10 for n.

= 8.90 + 5.99 Multiply.

= 14.89 Add.

Emily spent $14.89 on music downloads in one month.

Exercises 1. AUTO REPAIR A mechanic repairs Mr. Estes’ car. The amount for parts is $48.00 and

the rate for the mechanic is $40.00 per hour. Write and solve an equation to find the total cost of repairs to Mr. Estes’ car if the mechanic works for 1.5 hours.

2. SHIPPING FEES Mr. Moore purchases an inflatable kayak weighing 30 pounds from an online company. The standard rate to ship his purchase is $2.99 plus $0.85 per pound. Write and solve an equation to find the total amount Mr. Moore will pay to have the kayak shipped to his home.

3. SOUND The speed of sound is 1088 feet per second at sea level at 32° F. Write and solve an equation to find the distance sound travels in 8 seconds under these conditions.

4. VOLLEYBALL Your town decides to build a volleyball court. If the court is approximately 40 by 70 feet and its surface is of sand, one foot deep, the court will require about 166 tons of sand. A local sand pit sells sand for $11.00 per ton with a delivery charge of $3.00 per ton. Write and solve an equation to find the total cost of the sand for this court.

Example


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Find the solution of each equation if the replacement sets are A = {4, 5, 6, 7, 8} and B = {9, 10, 11, 12, 13}.

1. 5a - 9 = 26 2. 4a - 8 = 16

3. 7a + 21 = 56 4. 3b + 15 = 48

5. 4b - 12 = 28 6. 36 − b - 3 = 0

Find the solution of each equation using the given replacement set.

7. 1 − 2 + x = 5 −

4 ; { 1 −

2 , 3 −

4 , 1, 5 −

4 } 8. x + 2 −

3 = 13 −

9 ; { 5 −

9 , 2 −

3 , 7 −

9 }

9. 1 − 4 (x + 2) = 5 −

6 ; { 2 −

3 , 3 −

4 , 5 −

4 , 4 −

3 } 10. 0.8(x + 5) = 5.2; {1.2, 1.3, 1.4, 1.5}


11. 10.4 - 6.8 = x 12. y = 20.1 - 11.9

13. 46 - 15 − 3 + 28

= a 14. c = 6 + 18 − 31 - 25

15. 2(4) + 4 −

3(3 - 1) = b 16. 6(7 - 2)

− 3(8) + 6

= n

17. SHOPPING ONLINE Jennifer is purchasing CDs and a new CD player from an online store. She pays $10 for each CD, as well as $50 for the CD player. Write and solve an equation to find the total amount Jennifer spent if she buys 4 CDs and a CD player from the store.

18. TRAVEL An airplane can travel at a speed of 550 miles per hour. Write and solve an equation to find the time it will take to fly from London to Montreal, a distance of approximately 3300 miles.

Skills PracticeEquations

1-5


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Find the solution of each equation if the replacement sets are a = {0, 1 − 2 , 1, 3 −

2 , 2}

and b = {3, 3.5, 4, 4.5, 5}.

1. a + 1 − 2 = 1 2. 4b - 8 = 6 3. 6a + 18 = 27

4. 7b - 8 = 16.5 5. 120 - 28a = 78 6. 28 − b + 9 = 16


7. x = 18.3 - 4.8 8. w = 20.2 - 8.95 9. 37 - 9 − 18 - 11

= d

10. 97 - 25 − 41 - 23

= k 11. y = 4(22 - 4)

− 3(6) + 6

12. 5( 2 2 ) + 4(3)

− 4( 2 3 - 4)

= p

13. TEACHING A teacher has 15 weeks in which to teach six chapters. Write and then solve an equation that represents the number of lessons the teacher must teach per week if there is an average of 8.5 lessons per chapter.

14. CELL PHONES Gabriel pays $40 a month for basic cell phone service. In addition, Gabriel can send text messages for $0.20 each. Write and solve an equation to find the total amount Gabriel spent this month if he sends 40 text messages.

1-5 Practice Equations


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1. TIME There are 6 time zones in the United States. The eastern part of the U.S., including New York City, is in the Eastern Time Zone. The central part of the U.S., including Dallas, is in the Central Time Zone, which is one hour behind Eastern Time. San Diego is in the Pacific Time Zone, which is 3 hours behind Eastern Time. Write and solve an equation to determine what time it is in California if it is noon in New York.

2. FOOD Part of the Nutrition Facts label from a box of macaroni and cheese is shown below.

Nutrition FactsServing Size 1 cup (228g)Servings Per Container 2

Amount Per Serving

Calories 250 Calories from Fat 110

Total Fat 12g

Saturated Fat 3g

Trans Fat 3g

Cholesterol 30mg

% Daily Value *

18 %

15 %

10 %

Write and solve an equation to determine how many servings of this item Alisa can eat each day if she wants to consume exactly 45 grams of cholesterol.

3. CRAFTS You need 30 yards of yarn to crochet a small scarf. Cheryl bought a 100-yard ball of yarn and has already used 10 yards. Write and solve an equation to find how many scarves she can crochet if she plans on using up the entire ball.

4. POOLS There are approximately 202 gallons per cubic yard of water. Write and solve an equation for the number of gallons of water that fill a pool with a volume of 1161 cubic feet. (Hint: There are 27 cubic feet per cubic yard.)

5. VEHICLES Recently developed hybrid cars contain both an electric and a gasoline engine. Hybrid car batteries store extra energy, such as the energy produced by braking. Since the car can use this stored energy to power the car, the hybrid uses less gasoline per mile than cars powered only by gasoline. Suppose a new hybrid car is rated to drive 45 miles per gallon of gasoline.

a. It costs $40 to fill the gasoline tank with gas that costs $3.00 per gallon. Write and solve an equation to find the distance the hybrid car can go using one tank of gas.

b. Write and solve an equation to find the cost of gasoline per mile for this hybrid car. Round to the nearest cent.

1-5 Word Problem PracticeEquations


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Solution Sets

Consider the following open sentence.

It is the name of a month between March and July.

You know that a replacement for the variable It must be found in order to determine if the sentence is true or false. If It is replaced by either April, May, or June, the sentence is true.The set {April, May, June} is called the solution set of the open sentence given above. This set includes all replacements for the variable that make the sentence true.

Write the solution set for each open sentence.

1. It is the name of a state beginning with the letter A.

2. It is a primary color.

3. Its capital is Harrisburg.

4. It is a New England state.

5. x + 4 = 10

6. It is the name of a month that contains the letter r.

7. She was the wife of a U.S. President who served in the years 2000-2010.

8. It is an even number between 1 and 13.

9. 31 = 72 - k

10. It is the square of 2, 3, or 4.

Write an open sentence for each solution set.

11. {A, E, I, O, U}

12. {1, 3, 5, 7, 9}

13. {June, July, August}

14. {Atlantic, Pacific, Indian, Arctic}

Enrichment1-5


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A spreadsheet is a tool for working with and analyzing numerical data. The data is entered into a table in which each row is numbered and each column is labeled by a letter. You can use a spreadsheet to find solutions of open sentences.

Exercises

Use a spreadsheet to find the solution of each equation using the given replacement set.

1. x + 7.5 = 18.3; {8.8, 9.8, 10.8, 11.8} 2. 6(x + 2) = 18; {0, 1, 2, 3, 4, 5}

3. 4x + 1 = 17; {0, 1, 2, 3, 4, 5} 4. 4.9 - x = 2.2; {2.6, 2.7, 2.8, 2.9, 3.0}

5. 2.6x = 16.9; {6.1, 6.3, 6.5, 6.7, 6.9} 6. 12x - 8 = 22; {2.1, 2.2, 2.3, 2.4, 2.5, 2.6}

Use a spreadsheet to find the solution for 4(x - 3) = 32 if the replacement set is {7, 8, 9, 10, 11, 12}.

You can solve the open sentence by replacing x with each value in the replacement set.

Step 1 Use the first column of the spreadsheet for the replacement set. Enter the numbers using the formula bar. Click on a cell of the spreadsheet, type the number and press ENTER.

Step 2 The second column contains the formula for the left side of the open sentence. To enter a formula, enter an equals sign followed by the formula. Use the name of the cell containing each replacement value to evaluate the formula for that value. For example, in cell B2, the formula contains A2 in place of x.

The solution is the value of x for which the formula in column B returns 32. The solution is 11.

A 1

4 5 6 7 8

2 3

B C 4(x - 3) =4*(A2-3) =4*(A3-3) =4*(A4-3) =4*(A5-3) =4*(A6-3) =4*(A7-3)

x 7 8 9

10 11 12

Sheet 1 Sheet 2 Sheet 3

A 1

4 5 6 7 8

2 3

B C 4(x - 3) x

7 8 9

10 11 12

16 20 24 28 32 36

Sheet 1 Sheet 2 Sheet 3

1-5 Spreadsheet ActivitySolving Open Sentences

Example



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Study Guide and InterventionRelations

1-6

Represent a Relation A relation is a set of ordered pairs. A relation can be represented by a set of ordered pairs, a table, a graph, or a mapping. A mapping illustrates how each element of the domain is paired with an element in the range. The set of first numbers of the ordered pairs is the domain. The set of second numbers of the ordered pairs is the range of the relation.

a. Express the relation {(1, 1), (0, 2), (3, -2)} as a table, a graph, and a mapping.

x y

1 1

0 2

3 -2

x

y

O

X Y

103

12

-2

b. Determine the domain and the range of the relation. The domain for this relation is {0, 1, 3}. The range for this relation is {-2, 1, 2}.

Exercises 1A. Express the relation

{(-2, -1), (3, 3), (4, 3)} asa table, a graph, and a

mapping.

1B. Determine the domain and the range of the relation.

Example

x

y

O

X Yx y


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Graphs of a Relation The value of the variable in a relation that is subject to choice is called the independent variable. The variable with a value that is dependent on the value of the independent variable is called the dependent variable. These relations can be graphed without a scale on either axis, and interpreted by analyzing the shape.

The graph below represents the height of a football after it is kicked downfield. Identify the independent and the dependent variable for the relation. Then describe what happens in the graph.

The independent variable is time, and the dependent variable is height. The football starts on the ground when it is kicked. It gains altitude until it reaches a maximum height, then it loses altitude until it falls to the ground.

Time

Height

The graph below represents the price of stock over time. Identify the independent and dependent variable for the relation. Then describe what happens in the graph.

The independent variable is time and the dependent variable is price. The price increases steadily, then it falls, then increases, then falls again.

Time

Price

ExercisesIdentify the independent and dependent variables for each relation. Then describe what is happening in each graph.

1. The graph represents the speed of a car as it travels to the grocery store.

2. The graph represents the balance of a savings account over time.

3. The graph represents the height of a baseball after it is hit.

Time

Height

Time

AccountBalance(dollars)

Time

Speed


Relations

1-6

Example 1 Example 2


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Skills PracticeRelations

1-6

Express each relation as a table, a graph, and a mapping. Then determine the domain and range.

1. {(-1, -1), (1, 1), (2, 1), (3, 2)}

x

y

O

2. {(0, 4), (-4, -4), (-2, 3), (4, 0)}

3. {(3, -2), (1, 0), (-2, 4), (3, 1)}

x

y

O

Identify the independent and dependent variables for each relation.

4. The more hours Maribel works at her job, the larger her paycheck becomes.

5. Increasing the price of an item decreases the amount of people willing to buy it.

x

y

O

x y

x y

x y


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1-6 Practice Relations

1. Express {(4, 3), (-1, 4), (3, -2), (-2, 1)} as a table, a graph, and a mapping. Then determine the domain and range.

x

y

O

Describe what is happening in each graph.

2. The graph below represents the height of a 3. The graph below represents a tsunami as it travels across an ocean. student taking an exam.

Express the relation shown in each table, mapping, or graph as a set of ordered pairs.

4. X Y

0 9

-8 3

2 -6

1 4

5. X Y

5-5

37

9-6

48

6.

x

y

O

7. BASEBALL The graph shows the number of home runs hit by Andruw Jones of the Atlanta Braves. Express the relation as a set of ordered pairs. Then describe the domain and range.

Time

Number ofQuestionsAnswered

Time

Height

24

32

28

36

40

44

48

52

’02 ’03 ’04 ’05 ’06 ’070

Andruw Jones’ Home Runs

Ho

me

Ru

ns

Year


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1. HEALTH The American Heart Association recommends that your target heart rate during exercise should be between 50% and 75% of your maximum heart rate. Use the data in the table below to graph the approximate maximum heart rates for people of given ages.

Source: American Heart Association

Age

Maximum Heart Rate

200 25 35 40

y

x30

Hea

rt R

ate

180

190

170

160

200

2. NATURE Maple syrup is made by collecting sap from sugar maple trees and boiling it down to remove excess water. The graph shows the number of gallons of tree sap required to make different quantities of maple syrup. Express the relation as a set of ordered pairs.

Gallons of Syrup10 2 4 5

y

x3 7 8 96

Gal

lon

s o

f Sa

p

160

200

120

80

240

280

320

Maple Sap to Syrup

Source: Vermont Maple Sugar Makers’ Association

3. BAKING Identify the graph that best represents the relationship between the number of cookies and the equivalent number of dozens.

Number of dozens

Nu

mb

er o

f co

oki

es

y

x

Graph A

Number of dozens

Nu

mb

er o

f co

oki

es

y

x

Graph B

Number of dozens

Nu

mb

er o

f co

oki

es

y

x

Graph C

4. DATA COLLECTION Margaret collected data to determine the number of books her schoolmates were bringing home each evening. She recorded her data as a set of ordered pairs. She let x be the number of textbooks brought home after school, and y be the number of students with x textbooks. The relation is shown in the mapping.

a. Express the relation as a set of ordered pairs.

b. What is the domain of the relation?

c. What is the range of the relation?

x y

811122328

012345

Age (years) 20 25 30 35 40

Maximum Heart Rate

(beats per minute)200 195 190 185 180

1-6 Word Problem PracticeRelations


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Even and Odd FunctionsWe know that numbers can be either even or odd. It is also true that functions can be defined as even or odd. For a function to be even means that it is symmetric about the y-axis. That is, if you fold the graph along the y-axis, the two halves of the graph match exactly. For a function to be odd means that the function is symmetric about the origin. This means if you rotate the graph using the origin as the center, it will match its original position before completing a full turn.

The function y = x2 is an even function. The function y = x5 is an odd function. If you rotate the graph 180º the graph will lie on itself.

y

xO

1. The table below shows the ordered pairs of an even function. Complete the table. Plot the points and sketch the graph.

2. The table below shows the ordered pairs of an odd function. Complete the table. Plot the points and sketch the graph.

y

xO

y

xO2 4 6 8 10 12-4-6-8-10-12 -2

456

321

-1-2-3-4-5-6

y

xO

2 4 6 8 10-4-6-8-10 -2

810

642

-2-4-6-8

-10

Enrichment

x -12 -5 -1 1 5 12

y 6 3 1

x -10 -4 -2 2 4 10

y 8 4 2

1-6


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Identify Functions Relations in which each element of the domain is paired with exactly one element of the range are called functions.

Determine whether the relation {(6, -3), (4, 1), (7, -2), (-3, 1)} is a function. Explain.

Since each element of the domain is paired with exactly one element of the range, this relation is a function.

Determine whether 3x - y = 6 is a function.

Since the equation is in the form Ax + By = C, the graph of the equation will be a line, as shown at the right.

If you draw a vertical line through each value of x, the vertical line passes through just one point of the graph. Thus, the line represents a function.

ExercisesDetermine whether each relation is a function.

1. 2. 3.

4. 5. 6.

7. {(4, 2), (2, 3), (6, 1)} 8. {(-3, -3), (-3, 4), (-2, 4)} 9. {(-1, 0), (1, 0)}

10. -2x + 4y = 0 11. x2 + y2 = 8 12. x = -4

x

y

Ox

y

Ox

y

O

X Y

4567

-1012

x

y

Ox

y

O

x

y

O

1-7 Study Guide and InterventionFunctions

Example 1 Example 2


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Functions

1-7

Find Function Values Equations that are functions can be written in a form called function notation. For example, y = 2x -1 can be written as f(x) = 2x - 1. In the function, x represents the elements of the domain, and f(x) represents the elements of the range. Suppose you want to find the value in the range that corresponds to the element 2 in the domain. This is written f(2) and is read “f of 2.” The value of f(2) is found by substituting 2 for x in the equation.

If f(x) = 3x - 4, find each value.

a. f(3) f (3) = 3(3) - 4 Replace x with 3.

= 9 - 4 Multiply.

= 5 Simplify.

b. f(-2) f (-2) = 3(-2) - 4 Replace x with -2.

= -6 - 4 Multiply.

= -10 Simplify.

ExercisesIf f(x) = 2x - 4 and g(x) = x2 - 4x, find each value.

1. f (4) 2. g(2) 3. f (-5)

4. g(-3) 5. f (0) 6. g(0)

7. f (3) - 1 8. f ( 1 − 4 ) 9. g ( 1 −

4 )

10. f (a2) 11. f (k + 1) 12. g(2n)

13. f (3x) 14. f (2) + 3 15. g(-4)

Example


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1-7 Skills PracticeFunctions

Determine whether each relation is a function.

1. 2. 3.

4. x y

4 -5

-1 -10

0 -9

1 -7

9 1

5. x y

2 7

5 -3

3 5

-4 -2

5 2

6. x y

3 7

-1 1

1 0

3 5

7 3

7. {(2, 5), (4, -2), (3, 3), (5, 4), (-2, 5)} 8. {(6, -1), (-4, 2), (5, 2), (4, 6), (6, 5)}

9. y = 2x - 5 10. y = 11

11. 12. 13.

If f(x) = 3x + 2 and g(x) = x2 - x, find each value.

14. f(4) 15. f(8)

16. f(-2) 17. g(2)

18. g(-3) 19. g(-6)

20. f(2) + 1 21. f(1) - 1

22. g(2) - 2 23. g(-1) + 4

24. f(x + 1) 25. g(3b)

x

y

Ox

y

Ox

y

O

X Y

467

2-1

35

X Y

41

-2

520

-3

X Y

41

-3-5

-6-2

13


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1-7 PracticeFunctions

Determine whether each relation is a function.

1. 2. X Y

1 -5

-4 3

7 6

1 -2

3.

4. {(1, 4), (2, -2), (3, -6), (-6, 3), (-3, 6)} 5. {(6, -4), (2, -4), (-4, 2), (4, 6), (2, 6)}

6. x = -2 7. y = 2

If f(x) = 2x - 6 and g(x) = x - 2x2, find each value.

8. f(2) 9. f (- 1 − 2 ) 10. g(-1)

11. g (- 1 − 3 ) 12. f(7) - 9 13. g(-3) + 13

14. f(h + 9) 15. g(3y) 16. 2[g(b) + 1]

17. WAGES Martin earns $7.50 per hour proofreading ads at a local newspaper. His weekly wage w can be described by the equation w = 7.5h, where h is the number of hours worked.

a. Write the equation in function notation.

b. Find f(15), f(20), and f(25).

18. ELECTRICITY The table shows the relationship between resistance R and current I in a circuit.

Resistance (ohms) 120 80 48 6 4

Current (amperes) 0.1 0.15 0.25 2 3

a. Is the relationship a function? Explain.

b. If the relation can be represented by the equation IR = 12, rewrite the equation in function notation so that the resistance R is a function of the current I.

c. What is the resistance in a circuit when the current is 0.5 ampere?

x

y

O

X Y

03

-2

-3-2

15


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1. TRANSPORTATION The cost of riding in a cab is $3.00 plus $0.75 per mile. The equation that represents this relation is y = 0.75x + 3, where x is the number of miles traveled and y is the cost of the trip. Look at the graph of the equation and determine whether the relation is a function.

Distance (miles)210 43

y

x5 6 7 8 9 10

Co

st (

$)

6

8

4

2

10

16

14

12

2. TEXT MESSAGING Many cell phones have a text messaging option in addition to regular cell phone service. The function for the monthly cost of text messaging service from Noline Wireless Company is f (x) = 0.10x + 2, where x is the number of text messages that are sent. Find f (10) and f (30), the cost of 10 text messages in a month and the cost of 30 text messages in a month.

3. GEOMETRY The area for any square is given by the function y = x2, where x is the length of a side of the square and y is the area of the square. Write the equation in function notation and find the area of a square with a side length of 3.5 inches.

4. TRAVEL The cost for cars entering President George Bush Turnpike at Beltline road is given by the relation x = 0.75, where x is the dollar amount for entrance to the toll road and y is the number of passengers. Determine if this relation is a function. Explain.

5. CONSUMER CHOICES Aisha just received a $40 paycheck from her new job. She spends some of it buying music online and saves the rest in a bank account. Her savings is given by f (x) =

40 – 1.25x, where x is the number of songs she downloads at $1.25 per song.

a. Graph the function.

b. Find f(3), f(18), and f(36). What do these values represent?

c. How many songs can Aisha buy if she wants to save $30?

1-7 Word Problem Practice Functions


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Composite Functions Three things are needed to have a function—a set called the domain, a set called the range, and a rule that matches each element in the domain with only one element in the range. Here is an example.

Rule: f(x) = 2x + 1

3

-5

f(x)

5

x

21

-3

f(x) = 2x + 1

f(1) = 2(1) + 1 = 2 + 1 = 3

f(2) = 2(2) + 1 = 4 + 1 = 5

f(-3) = 2(-3) + 1 = -6 + 1 = -5

Suppose we have three sets A, B, and C and two functions described as shown below.

Rule: f(x) = 2x + 1 Rule: g( y) = 3y - 4 A B C

f(x)

3 5

x

1

g[f(x)]

g( y) = 3y - 4

g(3) = 3(3) - 4 = 5

Let’s find a rule that will match elements of set A with elements of set C without finding any elements in set B. In other words, let’s find a rule for the composite function g[f(x)].

Since f(x) = 2x + 1, g[ f(x)] = g(2x + 1).

Since g( y) = 3y - 4, g(2x + 1) = 3(2x + 1) - 4, or 6x - 1.

Therefore, g[ f(x)] = 6x - 1.

Find a rule for the composite function g[f(x)].

1. f(x) = 3x and g( y) = 2y + 1 2. f(x) = x2 + 1 and g( y) = 4y

3. f(x) = -2x and g( y) = y2 - 3y 4. f(x) = 1 − x - 3

and g( y) = y-1

5. Is it always the case that g[ f(x)] = f[ g(x)]? Justify your answer.

Enrichment 1-7


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1-8 Study Guide and InterventionInterpreting Graphs of Functions

Interpret Intercepts and Symmetry The intercepts of a graph are points where the graph intersects an axis. The y-coordinate of the point at which the graph intersects the y-axis is called a y-intercept. Similarly, the x-coordinate of the point at which a graph intersects the x-axis is called an x-intercept. A graph possesses line symmetry in a line if each half of the graph on either side of the line matches exactly.

ARCHITECTURE The graph shows a function that approximates the shape of the Gateway Arch, where x is the distance from the center point in feet and y is theheight in feet. Identify the function as linear or nonlinear. Then estimate and interpret the intercepts, and describe and interpret any symmetry.

Linear or Nonlinear: Since the graph is a curve and not a line, the graph is nonlinear.y-Intercept: The graph intersects the y-axis at about (0, 630), so the y-intercept of the graph is about 630. This means that the height of the arch is 630 feet at the center point.x-Intercept(s): The graph intersects the x-axis at about (-320, 0) and (320, 0). So the x-intercepts are about -320 and 320. This means that the object touches the ground to the left and right of the center point.Symmetry: The right half of the graph is the mirror image of the left half in the y-axis. In the context of the situation, the symmetry of the graph tells you that the arch is symmetric. The height of the arch at any distance to the right of the center is the same as its height that same distance to the left.

Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph and any symmetry.

1. Right Whale Population

Popu

latio

n

80

0

160

240

Generations Since 20074 8 12

y

x

2. Stock Price

Pric

e Va

riatio

n (p

oint

s)

-2

2

0

Time Since Opening Bell (h)

2 4 6

y

x

3.

y

x

Average GasolinePrice

Pric

e ($

per

gal

lon)

2

3

1

0

4

5

6

Years Since 198715105 2520 30

Example

O

y

x

y -intercept

x -intercept

Gateway Arch

Heig

ht (f

t)

0Distance (ft)

80-80-240 240

160

240

80

320

400

480

560y

x


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Interpreting Graphs of Functions

1-8

Interpret Extrema and End Behavior Interpreting a graph also involves estimating and interpreting where the function is increasing, decreasing, positive, or negative, and where the function has any extreme values, either high or low.

Example

HEALTH The outbreak of the H1N1 virus can be modeled by the function graphed at the right. Estimate and interpret where the function is positive, negative, increasing, and decreasing, the x-coordinates of any relative extrema, and the end behavior of the graph.

Positive: for x between 0 and 42 Negative: no parts of domainThis means that the number of reported cases was always positive. This is reasonable because a negative number of cases cannot exist in the context of the situation.Increasing: for x between 0 and 42 Decreasing: no parts of domainThe number of reported cases increased each day from the first day of the outbreak. Relative Maximum: at about x = 42 Relative Minimum: at x = 0The extrema of the graph indicate that the number of reported cases peaked at about day 42.End Behavior: As x increases, y appears to approach 11,000. As x decreases, y decreases. The end behavior of the graph indicates a maximum number of reported cases of 11,000.

Estimate and interpret where the function is positive, negative, increasing, and decreasing, the x-coordinate of any relative extrema, and the end behavior of the graph.

1. Right Whale Population

Popu

latio

n

80

0

160

240

Generations Since 20074 8 12

y

x

2. Stock Price

Pric

e Va

riatio

n (p

oint

s)

-2

2

0

Time Since Opening Bell (h)

2 4 6

y

x

3.

y

x

Average GasolinePrice

Pric

e ($

per

gal

lon)

2

3

1

0

4

5

6

Years Since 198715105 2520 30

y

x

Worldwide H1N1

Repo

rted

Cas

es

4000

0

8000

12,000

Days Since Outbreak21147 3528 42


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Skills PracticeInterpreting Graphs of Functions

1-8

Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the x-coordinate of any relative extrema, and the end behavior of the graph.

1. David’s Savings for Car

Savi

ngs

($)

1400

1200

0

1600

1800

2000

2200

Weeks2 4 6 8 10

y

x

3.

y

x

Height of Golf Ball

Heig

ht (f

t)

40

0

80

120

160

Distance from Tee (yd)40 80 120 160

2.

y

x

Baking Supplies

Flou

r (c)

4

0

8

12

16

20

Batches of Cookies4 8 12

4. Solar Reflector

Heig

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Width (ft)

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16

8

−8−16

−8

−16

8 16

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PracticeInterpreting Graphs of Functions

1-8

Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the x-coordinate of any relative extrema, and the end behavior of the graph.

1.

y

x

Wholesale T-Shirt Order

Tota

l Cos

t ($)

200

0

400

600

800

1000

Shirts (dozens)2 4 6 8 10

3.

y

x

Height of Diver

Heig

ht A

bove

Wat

er (m

)

2

0

4

6

8

10

12

Time (s)0.5 1 1.5 2 2.5

2.

y

x

Water Level

Wat

er L

evel

(cm

)

28

0

32

36

40

44

Time (seconds)40 80 120 160 200 240

4.

y

x

Boys’ Average Height

Heig

ht (i

n.)

24

0

48

72

Age (yr)4 8 12 16 20


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1-8 Word Problem PracticeInterpreting Graphs of Functions

1. HEALTH The graph shows the Calories yburned by a 130-pound person swimming freestyle laps as a function of time x. Identify the function as linear or nonlinear. Then estimate and interpret the intercepts.

y

x

Calories BurnedSwimming

Calo

ries

(kC)

800

1200

400

0

1600

2000

2400

2800

Time (h)321 5 74 6 8

2. TECHNOLOGY The graph below shows the results of a poll that asks Americans whether they used the Internet yesterday. Estimate and interpret where the function is positive, negative, increasing, and decreasing, the x-coordinates of any relative extrema, and the end behavior of the graph.

y

x

Did you use theInternet yesterday?

Yes

Resp

onse

s(p

erce

nt o

f pol

led)

60

0

70

Months Since January 200512 24 36 48 60

3. GEOMETRY The graph shows the area yin square centimeters of a rectangle with perimeter 20 centimeters and width xcentimeters. Describe and interpret any symmetry in the graph.

Area (cm2)

Area

(cm

2 )

Width (cm)

10

-10

20

30

0 2 4 6 8 10

y

x

4. EDUCATION Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the x-coordinate of any relative extrema, and the end behavior of the graph.

U.S. Education Spending

Spen

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of $

)

200

0

400

600

800

1000

Years Since 1949302010 50 7040 60

y

x


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1-8 Enrichment Symmetry in Graphs of Functions

You have seen that the graphs of some functions have line symmetry. Functions that have line symmetry in the y-axis are called even functions. The graph of a function can also have point symmetry. Recall that a figure has point symmetry if it can be rotated less than 360° about the point so that the image matches the original figure. Functions that are symmetric about the origin are called odd functions.

Even Functions Odd Functions Neither Even nor Odd

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

The graph of a function cannot be symmetric about the x-axis because the graph would fail the Vertical Line Test.

ExercisesIdentify the function graphed as even, odd, or neither.

1. y

xO

2. y

x

3. y

xO

4. y

xO

5. y

xO

6. y

xO

7. y

xO

8. y

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1 Student Recording SheetUse this recording sheet with pages 70–71 of the Student Edition.

Read each question. Then fill in the correct answer.

1. A B C D

2. F G H J

3. A B C D

4. F G H J

5. A B C D

6. F G H J

7. A B C D

Multiple Choice

Record your answers for Question 12 on the back of this paper.

Extended Response

8a.

8b.

8c.

9a.

9b.

10. (grid in)

11a.

11b.

11c.

10.

9

8

7

6

5

4

3

2

1

0

9

8

7

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1

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9

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3

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. . . . .

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

Record your answer in the blank.

For gridded response questions, also enter your answer in the grid by writing each number or symbol in a box. Then fill in the corresponding circle for that number or symbol.

Short Response/Gridded Response

055_067_ALG1_A_CRM_C01_AS_660498.indd 55055_067_ALG1_A_CRM_C01_AS_660498.indd 55 12/21/10 5:22 PM12/21/10 5:22 PM

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1


Rubric for Scoring Extended Response

General Scoring Guidelines

• If a student gives only a correct numerical answer to a problem but does not show how he or she arrived at the answer, the student will be awarded only 1 credit. All extended response questions require the student to show work.

• A fully correct answer for a multiple-part question requires correct responses for all parts of the question. For example, if a question has three parts, the correct response to one or two parts of the question that required work to be shown is not considered a fully correct response.

• Students who use trial and error to solve a problem must show their method. Merely showing that the answer checks or is correct is not considered a complete resopnse for full credit.

Exercise 12 Rubric

Score Specific Criteria

4 In part a, the student correctly writes the expression for the volume of a sphere as 4 − 3 πr3. In part b, the student substitutes 6 for the variable r. The student then takes

6 to the third power. The result is multiplied by 4 and then divided by three to give 288π cm3. Pi is irrational so it appears in the answer.

3 A generally correct solution, but may contain minor flaws in reasoning or computation.

2 A partially correct interpretation and/or solution to the problem.

1 A correct solution with no evidence or explanation.

0 An incorrect solution indicating no mathematical understanding of the concept or task, or no solution is given.


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SCORE

1.

2.

3.

4.

5.

1. Write a verbal expression for the algebraic expression 2 + 5p.

2. Write an algebraic expression for the verbal expression 8 to the fourth power increased by 6.

Evaluate each expression. 3. 62 - 32

· 8 + 11

4. 43 ÷ 8

5. MULTIPLE CHOICE Evaluate a(4b + c2) if a = 2, b = 5, and c = 1.

A 41 B 42 C 44 D 45

1. Name the property that is used in 5 · n · 2 = 0. Then find the value of n.

2. The equation 2 − 3 [3 ÷ (10 - 8)] = 2 −

3 (3 ÷ 2) is an example of

which property of equality?

3. Evaluate 7 · 2 · 7 · 5 using properties of numbers. Name the property used in each step.

4. Use the Distributive Property to rewrite 7 · 98. Then evaluate.

5. MULTIPLE CHOICE Simplify 16a2 - 7b2

+ 3b - 2a2.

A 14 - 4b B 14a2 - 7b2

+ 3b C 10b D simplified

1.

2.

3.

4.

5.

1 Chapter 1 Quiz 2(Lessons 1-3 and 1-4)


SCORE


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SCORE

1.

2.

3.

4.

1. Find the solution of 1 − 2 (x - 3) = 4 if the replacement set is

{8, 9, 10, 11, 12}.

2. MULTIPLE CHOICE Solve r = 7(16 - 5) −

3 + 4(2) .

A 5 1 − 2 B 7 C 11 D 77

3. Candice is typing an average of 40 words per minute. Write and solve an equation to find the time it will take her to type 1000 words.

4. Express the relation {(3, 5), (-4, 6), (3, 8), (2, 4), (1, 3)} as a mapping. Then determine the domain and range.

1. Determine whether the relation is a function.

2. If g(x) = x2 - 3x + 2, find g(-4).

3. MULTIPLE CHOICE Which represents For every hour that Samuel works, he earns $8.50?

A f (h) = 8.5h C f (h) = 8.5 - h

B f (h) = 8.5 + h D f (h) = h ÷ 8.5

4. Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph.

Online Music

Have

Lis

tene

d O

nlin

e(p

erce

nt o

f pol

led)

20

0

40

60

Months SinceAugust 2000

40 80 120

y

x


X Y


x y

0 1

−2 −1

− 4 1

1.

2.

3.

4.

SCORE


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SCORE

Part I Write the letter for the correct answer in the blank at the right of each question.

1. Write an algebraic expression for 12 less than a number times 7. A 12 < 7n B 12 > 7n C 12 - 7n D 7n - 12

2. Evaluate 20 + 3(8 - 5). F 29 G 39 H 180 J 26

Evaluate each expression if a = 4, b = 6, and c = 2.

3. ab - c A 12 B 16 C 22 D 8

4. 3a + b2c F 36 G 84 H 96 J 240

5. Simplify 4(w - 9). A 4w - 9 B 4w - 13 C w - 5 D 4w - 36

6. Simplify 3r + 2(t + 5r). F 15r + 2t G 8r + 2t H 15r J 13r + 2t

7. Name the property used in (5 + 2) + n = 7 + n. A Additive Identity C Reflexive Property B Multiplicative Identity D Substitution Property

Part II

Evaluate each expression using properties of numbers. Name the property used in each step.

8. 6.4 + 2.7 + 1.6 + 5.3 9. 4 − 3 � 7 � 3 � 10

For Questions 10 and 11, write a verbal expression for each algebraic expression.

10. 18p 11. x2 - 5

12. Name two properties used to evaluate 7 � 1 - 4 � 1 − 4 .

13. Rewrite 6(10 + 2) using the Distributive Property. Then simplify.

14. Simplify 6b + 7b + 2b2.

15. Felicity put down $800 on a used car. She took out a loan to pay off the balance of the cost of the car. Her monthly payment will be $175. After 9 months how much will she have paid for the car?

8.

9.

10.

11.

12.

13.

14.

15.

1.

2.

3.

4.

5.

6.

7.

Chapter 1 Mid-Chapter Test(Lessons 1-1 through 1-4)

1


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SCORE

Choose a term from the vocabulary list above to complete the sentence. 1. In the algebraic expression 8q, the letter q is called a(n) .

2. An expression like c3 is an example of a(n) and is read “c cubed.”

3. A function graphed with a line or smooth curve is called a(n) .

4. The process of finding a value for a variable that results in a true sentence is called solving the .

5. are terms that contain the same variables,with corresponding variables having the same power.

6. The of a term is the numerical factor.

7. The set of the first number of the ordered pairs of a function is the .

8. In a(n) , there is exactly one output for each input.

9. The set of second numbers of the ordered pairs in a relation is the of the relation.

Define each term in your own words.

10. end behavior

11. solution set

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

algebraic expression

coefficient

continuous function

coordinate system

dependent variable

discrete function

domain

end behavior

exponent

factors

function

identity

independent variable

intercept

like terms

multiplicative inverses

open sentences

order of operations

power

range

replacement set

reciprocal

solution set

symmetry

variable

Chapter 1 Vocabulary Test1


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SCORE

Write the letter for the correct answer in the blank at the right of each question. 1. Write an algebraic expression for the sum of a number and 8. A 8x B x - 8 C x + 8 D x ÷ 8

2. Write an algebraic expression for 27 decreased by a number.

F 27 + m G 27 - m H m - 27 J 27 − m

3. Write a verbal expression for 19a. A the sum of 19 and a number C the quotient of 19 and a number

B the difference of 19 and a number D the product of 19 and a number

4. Write a verbal expression for x + y. F the sum of x and y H the difference of x and y

G the quotient of x and y J the product of x and y

5. Evaluate 6(8 - 3). A 45 B 30 C 11 D 66

6. Evaluate 2k + m if k = 11 and m = 5. F 32 G 216 H 27 J 18

7. Name the property used in n + 0 = 7. A Multiplicative Inverse Property C Additive Identity Property B Substitution Property D Multiplicative Identity Property

8. Evaluate 13 + 6 + 7 + 4. F 2184 G 29 H 20 J 30

9. Simplify 7b + 2b + 3c. A 12bc B 9b + 3c C 7b + 5c D 5b + 3c

10. Simplify 5(2g + 3). F 10g + 3 G 7g + 3 H 10g + 15 J 7g + 8

11. Evaluate 4 · 1 + 6 · 16 + 0. A 100 B 0 C 8 D 185

12. Which of the following uses the Distributive Property to determine the product 12(185)?

F 12(100) + 12(13) H 12(18) + 12(5) G 12(1) + 12(8) + 12(5) J 12(100) + 12(80) + 12(5)

13. Find the solution of x + 4 = 7 if the replacement set is {1, 2, 3, 4, 5}. A 1 B 3 C 4 D 2

14. A car rental company charges a rental fee of $20 per day in addition to a charge of $0.30 per mile driven. How much does it cost to rent a car for a day and drive it 25 miles?

F $45.30 G $20.30 H $27.50 J $26.00

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2.

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Chapter 1 Test, Form 11


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15. Which statement best describes the graph of the price of one share of a company’s stock shown at the right?

A The price increased more in the morning than in the afternoon.

B The price decreased more in the morning than in the afternoon.

C The price increased more in the afternoon than in the morning.

D The price decreased more in the afternoon than in the morning.

16. What is the domain of the relation? F {–1, 0, 1, 3} H {–2, –1, 0, 1, 2, 3} G {–2, 0, 1, 3} J {0, 1, 2, 3}

17. Determine which relation is a function. A X Y

2

4

-2

1

3

5

C x 3 4 4 5

y –1 2 3 6

B y = 1 −

5 x + 2 D {(3, 0), (– 2, – 2), (7, – 2), (– 2, 0)}

18. If h(r) = 2 − 3 r – 6, what is the value of h(–9)?

F 12 G 0 H - 6 2 − 3 J -12

For Questions 19 and 20, use the graph.

19. Interpret the y-intercept of the graph.

A All those polled used a social networking site 8 months after February 2005.

B About 8% of those polled used a social networking site in February 2005.

C No one used a social networking site in February 2005.

D There were 8 social networking sites in February 2005.

20. Interpret the end behavior of the function in terms of social networking. F expected to decrease H expected to level off at 55%

G expected to increase J expected to level off at 8%

Bonus Simplify (4x + 2)3.

Time of DayA.M. Noon P.M.

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Chapter 1 Test, Form 1 (continued)

15.

16.

17.

18.

19.

20.

1

y

x

Social Networking

Used

Soc

ial N

etw

orki

ng S

ite(p

erce

nt o

f pol

led)

10

0

20

30

40

Months Since February 200512 24 36 48

B:


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Write the letter for the correct answer in the blank at the right of each question.

1. Write an algebraic expression for nine times of the square of a number. A 9 + x2 B 9 - x2 C 9x2 D x2

- 9

2. Write a verbal expression for 2n + 7. F the product of 2, n, and 7 H 7 less than a number times 2 G 7 more than twice a number J 7 more than n and 2

3. Evaluate 6 + 2 · 3 - 1. A 23 B 10 C 16 D 11

4. Evaluate 2(11 - 5) + 9 ÷ 3. F 18 G 15 H 30 J 11

5. Evaluate x2 + xyz if x = 3, y = 5, and z = 4. A 69 B 63 C 85 D 21

6. Which equation illustrates the Multiplicative Inverse Property? F 0 · 16 = 0 H 3 · 1 −

3 =1

G 1(48) = 48 J 9(1 + 0) = 9(1)

7. Evaluate 29 · 1 + 2(20 ÷ 4 - 5). A 0 B 30 C 29 D 28

8. Simplify r2 - 2r3

+ 3r2. F 4r2 - 2r3 G 2r H 3r2 - 2r3 J 4r2

9. Simplify 3(2x + 4y - y). A 5x + 6y B 6x + 9y C 6x + 3y D 5x + 11y

10. Use the Distributive Property to find 6(14 + 7). F 91 G 126 H 42 J 56

11. Simplify 2(a + 3b) + 3(4a + b). A 6a + 6b B 14a + 9b C 14a + 4b D 6a + 7b

12. Evaluate 3 2 − 5 + 7 + 4 1 −

5 .

F 7 3 − 2 + 7 G 14 3 −

10 H 84 3 −

5 J 14 3 −

5

13. Find the solution of n − 2 - 11 = 3 if the replacement set is {26, 28, 29, 30, 31}.

A 26 B 28 C 30 D 31

14. Somerville High School raised $740 to buy winter coats for the homeless at $46.25 each. How many coats can they buy?

F 12 G 16 H 24 J 34,225

Chapter 1 Test, Form 2A

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5.

6.

7.

8.

9.

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11.

12.

13.

14.

1


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15. Which statement best describes a daily stock price? A The price increased. B The price decreased. C The price did not change. D The price increased then decreased.

For Questions 16 and 17, use the graph.16. What is the domain of the relation? F {-4, -1, 0, 2, 4} H {-4, -2, -1, 0, 1, 2, 4}

G {-4, -2, -1, 1, 4} J {-1, 1}

17. Which is a true statement about the relation? A The relation is a linear function. B The value of x increases as y decreases. C The value of x increases as y increases. D The relation is not a function.

18. Determine which relation is not a function. F y

xO

G x y

–2 0

0 0

1 2

3 1

H X Y

-4

-3

5

0

2

9

J x y

–4 0

–3 9

5 2

6 9


19. Interpret the y-intercept of the graph. A 0 bracelets cost about $30. B 1 dozen bracelets cost about $30. C 28 dozen bracelets cost $0. D Each dozen bracelets costs about $5.

20. Interpret the end behavior of the function. F The total cost decreases. G The cost per dozen decreases. H The total cost increases. J The cost per dozen increases.

Bonus Find the value of f in the equation f = 4 − 5 (200 - m) + a

if m = 100 and a = 132.

y

xO

15.

16.

17.

18.

19.

20.


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1 Chapter 1 Test, Form 2A (continued)

y

x

Wholesale Bracelets

Tota

l Cos

t ($)

40

60

20

0

80

100120

Bracelets (dozens)42 8 106 12

B:


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SCORE

Write the letter for the correct answer in the blank at the right of each question.

1. Write an algebraic expression for 3 times x squared minus 4 times x. A 3(2x) - 4x B 4 - 3x C 3x2 - 4x D 3(x2 - 4x)

2. Write a verbal expression for 3n - 8. F the product of 3, n, and 8 H 3 times n less than 8 G 8 less than the product of 3 and n J n minus 8 times 3

3. Evaluate 4 + 5 � 7 - 1. A 139 B 15 C 34 D 38

4. Evaluate 3(16 - 9) + 12 ÷ 3. F 33 G 25 H 41 J 28

5. Evaluate m2 + mtp if m = 3, t = 4, and p = 7.

A 93 B 87 C 100 D 23

6. Which equation illustrates the Additive Identity Property? F 8(9 + 0) = 8(9) H 8 � 1 = 8

G 4(0) = 0 J 1 − 4 � 4 = 1

7. Evaluate 16 � 1 + 4(18 ÷ 2 - 9). A 20 B 0 C 16 D 80

8. Simplify 7x2 + 10x2

+ 5y3. F 22 x2y3 G 17x2 + 5y3 H 22 x4 + y3 J 17x4y3 + 5

9. Simplify 2(7n + 5m - 3m). A 14n + 2m B 9n + 7m C 9n + m D 14n + 4m

10. Use the Distributive Property to find 7(11 - 8). F 133 G 21 H 69 J 85

11. Simplify 3(5a + b) + 4(a + 2b). A 9a + 5b B 19a + 3b C 19a + 11b D 9a + 9b

12. Evaluate 4 1 − 5 + 9 + 2 3 −

5 .

F 15 4 − 5 G 15 2 −

5 H 17 4 −

5 J 17 3 −

10

13. Find the solution of 3n - 13 = 38 if the replacement set is {12, 14, 15, 17, 18}. A 12 B 15 C 17 D 18

14. Ari is jogging at an average rate of 2.25 meters per second. Find the time it will take him to jog 270 meters.

F 1 minute G 2 minutes H 3 minutes J 12 minutes

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

1 Chapter 1 Test, Form 2B


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15. Which statement best describes a daily stock price? A The price was unchanged then increased sharply. B The price was unchanged then decreased sharply. C The price rose sharply then leveled off. D The price declined sharply then leveled off.


16. What is the domain of the relation? F {–4, –2, –1, 0, 1, 2, 3, 4} H {–4, –2, –1, 0, 1, 4} G {–4, –1, 0, 2, 3, 4} J {–4, 4}

17. Which is a true statement about the relation? A The relation is not a function. B The value of x increases as y decreases. C The value of x increases as y increases. D The relation is a linear function.

18. Determine which relation is a function. F G H J

For Questions 19 and 20, use the graph. 19. Interpret the y-intercept of the graph. A Anna owes $10 before any payments. B Each payment Anna makes is $50. C Anna owes $500 before any payments. D Anna pays off the loan in 10 payments.

20. Interpret the end behavior of the function. F The amount owed decreases. G The payment amount decreases. H The amount owed increases. J The payment amount increases.

Bonus Simplify 8(a2 + 3b2) - 24b2.


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-32

-415

3

-1

2

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x y

–2 7

0 0

1 –2

1 3

Chapter 1 Test, Form 2B (continued)

15.

16.

17.

18.

19.

20.

1

y

x

Anna’s Loan

Loan

Bal

ance

($)

200

300

100

0

400

500600

Weekly Payments2 4 6 8 1210

B:


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1. the sum of the square of a number and 34

2. the product of 5 and twice a number

3. Write a verbal expression for 4n3 +

6.

4. Evaluate 23[(15 - 7) (4 ÷ 2)].

5. Evaluate 3w + (8 - v)t if w = 4, v = 5 and t = 2.

For Questions 6 and 7, name the property used in each equation. Then find the value of n.

6. 5 + 0 = n

7. 7 + (4 + 6) = 7 + n

8. Evaluate 4(5 · 1 ÷ 20). Name the property used in each step.

9. Rewrite 3(14 - 5) using the Distributive Property. Then simplify.

Simplify each expression.

10. 15w - 6w + 14w2

11. 7(2y + 1) + 3y

For Questions 12 and 13, evaluate each expression.

12. 32 + 5 + 8 + 15

13. 1 − 3 · 4 · 9 · 1 −

2

14. Find the solution of 5b - 13 = 22 if the replacement set is {5, 6, 7, 8, 9}.

15. Solve 6 + 3 2 (4)

− 7

- 1 = y.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

Chapter 1 Test, Form 2C1


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Chapter 1 Test, Form 2C (continued)

For Questions 16 and 17, use the graph that shows temperature as a functionof time.

16. Identify the independent and dependent variables.

17. Name the ordered pair at point C and explain what it represents.

For Questions 18–20, use thetable that shows airmail letter rates to Greenland.

18. Write the data as a set of ordered pairs.

19. Draw a graph that shows the relationship between the weight of a letter sent airmail and the total cost.

20. Interpret the end behavior of the function.

Bonus Use grouping symbols, exponents, and symbols for addition, subtraction, multiplication, and division with the digits 1, 9, 8, and 7 (in that order) to form expressions that will yield each value.

a. 6 b. 7 c. 9

B: a.

b.

c.

1

Time

Tem

per

atu

re (

°F)

0

81

82

83

84

85

86

87

88

89

90

6 A.M. 7 A.M. 8 A.M. 9 A.M. 10 A.M.

A

E

B

CD

16.

17.

18.

19.

Weight (oz)

Rat

e ($

)

0

1

2

3

4

5

6

7

5.0 6.0 7.0 8.0

20.

Source: World Almanac

Weight (oz) Rate ($)

5.0 4.20

6.0 5.05

7.0 5.90

8.0 6.75


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1. the sum of one-third of a number and 27

2. the product of a number squared and 4

3. Write a verbal expression for 5n3 + 9.

4. Evaluate 32[(12 - 4) ÷ 2].

5. Evaluate 4w + (v - 5)t if w = 2, v = 8, and t = 4.

Name the property used in each equation. Then find the value of n.

6. 11 � n = 1

7. 7 + n = 7 + 3

8. Evaluate 6(6 � 1 ÷ 36). Name the property used in each step.

9. Rewrite (10 + 3)5 using the Distributive Property. Then simplify.


10. 4w2 + 7w2

+ 7z2

11. 3x + 4(5x + 2)


12. 5 � 13 � 4 � 1

13. 17 + 6 + 3 + 14

14. Find the solution of 3x - 8 = 16 if the replacement set is {5, 6, 7, 8, 9}.

15. Solve 6 + 4 2 · 3

− 10 - 1

= y.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

1 Chapter 1 Test, Form 2D


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Chapter 1 Test, Form 2D (continued)

Use the graph that shows Robert’s bowling scores for his last four games.


17. Describe what may have happened between the first and fourth games.

For Questions 18–20, use the table that shows 2006 airmail letter rates to New Zealand.

18. Write the data as a set of ordered pairs.

19. Draw a graph that shows therelationship between the weight of a letter sent airmail and the total cost.

20. Interpret the end behavior of the function.

Bonus Insert brackets, parentheses, and the symbols for addition, subtraction, and division in the following sequence of numbers to create an expression whose value is 4.

2 5 1 4 1

Game

Sco

re

020406080

100120140

200180160

1 2 3 4

(1, 72)(4, 87)

(2, 103)

(3, 122)

16.

17.

18.

19.

20.

Weight (oz)

Rat

e ($

)

0

1

2

3

4

5

6

1.0 2.0 3.0 4.0 5.0

B:

1

Source: World Almanac

Weight (oz) Rate ($)

2.0 1.80

3.0 2.75

4.0 3.70

5.0 4.65


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SCORE


1. the sum of the cube of a number and 12

2. 42 decreased by twice some number

3. Write a verbal expression for 6g2

− 5 .

4. Evaluate 4[ 3 3 - 5(8 - 6)]

− 3 2 - 7

+ 11.

Evaluate each expression if w = 4, n = 8, v = 5, and t = 2.

5. w2 + n(v2

-t) 6. 3nw - w2 + t3

For Questions 7 and 8, name the property used in each equation. Then find the value of n.

7. 7y + y = 7y + ny 8. (6 + n)x = 15x

9. Evaluate 2 − 3 (3 ÷ 2) + (32

- 9). Name the property used

in each step.

10. Rewrite 2(x + 3y - 2z) using the Distributive Property. Then simplify.


11. 3 + 6(5a + 4an) + 9na

12. 7a + 7a2 + 14b2


13. 6 � 8 + 29 + 7 + 3 � 7

14. 32 + 6 � 4 + 7 � 4 + 16

15. Solve 5 · 2 3 - 4 · 3 2 − 1 + 3

= x.

16. Find the solution of 2b + 1 − 2 = 3 if the replacement

set is { 1 − 2 , 3 −

4 , 1, 5 −

4 , 3 −

2 , 7 −

4 } .

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

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15.

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Chapter 1 Test, Form 31


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17. Some warehouse stores charge members an annual fee to shop there. On his first trip to a warehouse store, Mr. Marshpays a $50 membership fee. Cases of bottled water cost $4 at the warehouse store. Write and solve an equation to find the total amount Mr. Marsh spent on his first trip before tax if he bought 8 cases of water.

18. The graph shown represents a puppy exploring a trail. Describe what is happening in the graph. Is the function discrete or continuous?

For Questions 19 and 20, use the graph that shows the average daily circulation of the Evening Telegraph.


20. Write a description of what the graph displays.

21. Each day David drives to work in the morning, returns home for lunch, drives back to work, and then goes to a gym to exercise before he returns home for the evening. Draw a reasonable graph to show the distance David is from hishome for a two-day period.

22. Determine whether - 1 − 2 x + 4y = 6 represents a function.

23. If f (x) = -3x2 - 2x + 1, find 2[f (r)].

For Questions 24 and 25, use the graph at the right.

24. Interpret the y-intercept of the graph.

25. Interpret the end behavior of the function

Bonus Simplify 62 + (3 + 4)2 - (21 ÷ 3 + 4 · 2)

−− 14 - 3 · 14

+ 23 - (5 + 1) · 2 .

y

100

20304050607080

2006 2007 2008 2009 2010

New

spap

ers

Sold

(th

ou

san

ds)

Year

Time

Distance fromTrailhead

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:

Chapter 1 Test, Form 3 (continued)1

y

x

Ohio Population

Popu

latio

n (m

illio

ns)

105

0

15

3025

20

Years Since 190025 50 75 100 125150


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Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.

1. a. Write an algebraic expression that includes a sum and a product. Write a verbal expression for your algebraic expression.

b. Write a verbal expression that includes a difference and a quotient. Write an algebraic expression for your verbal expression.

2. Explain how a replacement set and a solution set are used with an open sentence.

3. a. Write an equation that demonstrates one of the identity properties. Name the property used in the equation.

b. Explain how to use the Distributive Property to find 7 · 23. c. Describe how to use the Commutative and Associative Properties

to simplify the evaluation of 18 + 33 + 82 + 67.

4. Think of a situation that could be modeled by this graph. Then label the axes of the graph and write several sentences describing the situation.

5. Use the set {–1, 0, 1, 2} as a domain and the set {–3, –1, 4, 5} as a range.

a. Create a relation. Express the relation as a set of ordered pairs.

b. Create a relation that is not a function. Express the relation as a table, a graph, and a mapping.

c. Explain why the relation created for part b is not a function.

6. Identify the function graphed as linear or nonlinear. Then estimate and interpret key features of the graph.

1 Chapter 1 Extended-Response Test

y

xO

y

x

How often do you use theInternet away from home?

Seve

ral T

imes

a D

ay (p

erce

nt o

f pol

led)

2

3

1

0

4

5

6

7

8

9

10

11

12

Months Since March 200412 186 24 30 36 42 48 54 60 66 72


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SCORE

1. Write an algebraic expression to represent the number of pens that can be bought with 30 cents if each pen costs c cents. (Lesson 1-1)

A 30 - c B 30 − c C 30 + c D 30c

2. Evaluate 7a + b − b + c

if a = 2, b = 6, and c = 4. (Lesson 1-2)

F 3 1 − 3 G 1 1 −

2 H 3 J 2

3. Find the solution of 3(y + 7) ≤ 39 if the replacement set is {2, 4, 6, 8, 10, 12}. (Lesson 1-5)

A {2, 4} B {6, 8, 10, 12} C {8, 10, 12} D {2, 4, 6}

4. The equation 4 + 9 = 4 + 9 is an example of which property of equality? (Lesson 1-3)

F Substitution G Reflexive H Symmetric J Transitive

5. Simplify 7x2 + 5x + 4x. (Lesson 1-4)

A 7x2 + 9x B 16x4 C 12x3

+ 4x D 7x2 + x

6. Simplify 7(2x + y) + 6(x + 5y). (Lesson 1-4)

F 20x + 37y G 20x + 6y H 13x + 42y J 15x + 6y

For Questions 7 and 8, use the following statement.If x is a multiple of 2, then x is divisible by 4.

7. Identify the hypothesis of the statement. (Lesson 1-8)

A x is a multiple of 2 C x is divisible by 4 B x = 2 D x = 4

8. Which number is a counterexample for the statement? (Lesson 1-8)

F 20 G 4 H 32 J 10

9. The distance an airplane travels increases as the duration of the flight increases. Identify the dependent variable. (Lesson 1-6)

A time B direction C airplane D distance

10. Omari drives a car that gets 18 miles per gallon of gasoline. The car’s gasoline tank holds 15 gallons. The distance Omari drives before refueling is a function of the number of gallons of gasoline in the tank. Identify a reasonable domain for this situation. (Lesson 1-6)

F 0 to 18 miles H 0 to 270 miles G 0 to 15 gallons J 0 to 60 mph

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. F G H J

A B C D

F G H J

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

1 Standardized Test Practice(Chapter 1)

A B C D

Part 1: Multiple Choice

Instructions: Fill in the appropriate circle for the best answer.


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11. Evaluate x2 + y2 + z, if x = 7, y = 6, and z = 4. (Lesson 1-2)

A 17 B 101 C 89 D 59

12. Find the solution of 20 = 5(7 - x) if the replacement set is {0, 1, 2, 3, 4, 5, 6}. (Lesson 1-5)

F 0 G 1 H 2 J 3

13. Using the Distributive Property to find 9 (5 2 − 3 ) would give

which expression? (Lesson 1-4)

A 9(5) + 2 − 3 B 9 ( 17 −

3 ) C 9(5) + 9 ( 2 −

3 ) D 9(5) ( 2 −

3 )

14. Which sentence best describes the end behavior of the function shown? (Lesson 1-8)

F As x increases, y decreases, and as x decreases, y decreases.

G As x increases, y increases, and as x decreases, y decreases.

H As x increases, y decreases, and as x decreases, y increases.

J As x increases, y increases, and as x decreases, y increases.

15. If g(x) = x 2 + 5, find g(3). (Lesson 1-7)

A 8 B 9 C 11 D 14

16. Evaluate 4(16 ÷ 2 + 6). 17. Evaluate 2 + x(2y + z) if (Lesson 1-2) x = 5, y = 3, and z = 4.

(Lesson 1-2)

11.

12.

13.

14.

15.

F G H J

1 Standardized Test Practice (continued)

A B C D

A B C D

F G H J

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

Part 2: Gridded Response

Instructions: Enter your answer by writing each digit of the answer in a column box and

then shading in the appropriate circle that corresponds to that entry.

A B C D

y

xO

−20

−10

−2−3−4

20

10

1 2 3 4


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

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-Hill C

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NAME DATE PERIOD

PDF Pass


Find each product or quotient.(Prerequisite Skill)

18. 17 · 8 19. 84 ÷ 7

20. 0.9 · 5.6 21. 8 − 9 ÷ 16 −

3

22. Write an algebraic expression for six less than twice a number. (Lesson 1-1)

23. Write a verbal expression for 4m2 + 2. (Lesson 1-1)

24. Evaluate 13 - 1 − 3 (11 - 5). (Lesson 1-2)

25. Evaluate 2b + c2

− a , if a = 2, b = 4, and c = 6. (Lesson 1-2)

26. Evaluate 3(5 · 2 - 9) + 2 · 1 − 2 . (Lesson 1-2)

27. Evaluate 1 − 3 . 20 . 6 . 1 −

5 using the properties of numbers.

(Lesson 1-3)


28. 7n + 4n 29. 5y + 3(2y + 1) (Lesson 1-4) (Lesson 1-4)

30. Solve 2(7) + 4 = x. (Lesson 1-5)

31. Find the solution of 3x - 4 = 2 if the replacement set is{0, 1, 2, 3, 4, 5}. (Lesson 1-5)

32. Alvin is mowing his front lawn. His mailbox is on the edge of the lawn. Draw a reasonable graph that shows the distance Alvin is from the mailbox as he mows. Let the horizontal axis show the time and the vertical axis show the distance from the mailbox. (Lesson 1-6)

33. Identify and interpret

y

x

Computer Virus

Affe

cted

Com

pute

rs

40006000

2000

0

800010,000

Time (minutes)40 6020 80 100

each feature of the graph shown. (Lesson 1-8)

a. intercept(s)

b. end behavior

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33a.

33b.

Part 3: Short Response

Instructions: Write your answers in the space.

1 Standardized Test Practice (continued)


An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass

Chapter 1 A1 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DAT

E

P

ER

IOD

Lesson 1-1

Cha

pte

r 1

5 G

lenc

oe A

lgeb

ra 1

Wri

te V

erb

al E

xpre

ssio

ns

An

alg

ebra

ic e

xpre

ssio

n c

onsi

sts

of o

ne

or m

ore

nu

mbe

rs a

nd

vari

able

s al

ong

wit

h o

ne

or m

ore

arit

hm

etic

ope

rati

ons.

In

alg

ebra

, var

iab

les

are

sym

bols

use

d to

rep

rese

nt

un

spec

ifie

d n

um

bers

or

valu

es. A

ny

lett

er m

ay b

e u

sed

as a

va

riab

le.

W

rite

a v

erb

al e

xpre

ssio

n f

or e

ach

alg

ebra

ic e

xpre

ssio

n.

a. 6

n2

the

prod

uct

of

6 an

d n

squ

ared

b.

n3

- 1

2mth

e di

ffer

ence

of

n c

ube

d an

d tw

elve

tim

es m

Exer

cise

sW

rite

a v

erb

al e

xpre

ssio

n f

or e

ach

alg

ebra

ic e

xpre

ssio

n.

1. w

- 1

2.

1 −

3 a3

3. 8

1 +

2x

4. 1

2d

5. 8

4 6.

62

7. 2

n2

+ 4

8.

a3

․

b3

9. 2

x3 -

3

10.

6k3

−

5

11.

1 −

4 b2

12. 7

n5

13. 3

x +

4

14.

2 −

3 k5

15. 3

b2 +

2a3

16

. 4(n

2 +

1)

1-1

Stud

y G

uide

and

Inte

rven

tion

Vari

ab

les a

nd

Exp

ressio

ns

Exam

ple

1–16

. Sam

ple

an

swer

s ar

e g

iven

.

on

e th

ird

th

e cu

be

of

a

12 t

imes

d

the

squ

are

of

6

the

sum

of

4 an

d t

wic

e th

e sq

uar

e o

f n

th

e d

iffer

ence

of

twic

e a

nu

mb

er c

ub

ed a

nd

3

th

e su

m o

f th

ree

tim

es a

nu

mb

er a

nd

4

3

tim

es b

sq

uar

ed

plu

s 2

tim

es a

cu

bed

4

tim

es t

he

sum

o

f th

e sq

uar

e o

f n

an

d 1

on

e le

ss t

han

w

eig

hty

-on

e in

crea

sed

by

twic

e x

eig

ht

to t

he

fou

rth

po

wer

a c

ub

ed t

imes

b c

ub

ed

6 ti

mes

th

e cu

be

of

k d

ivid

ed b

y 5

two

-th

ird

s th

e fi

fth

po

wer

of

k

on

e-fo

urt

h t

he

squ

are

of

bse

ven

tim

es t

he

fi ft

h p

ow

er o

f n

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Chapter Resources


NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

3 G

lenc

oe A

lgeb

ra 1

B

efor

e yo

u b

egin

Ch

ap

ter

1

•

Rea

d ea

ch s

tate

men

t.

•

Dec

ide

wh

eth

er y

ou A

gree

(A

) or

Dis

agre

e (D

) w

ith

th

e st

atem

ent.

•

Wri

te A

or

D i

n t

he

firs

t co

lum

n O

R i

f yo

u a

re n

ot s

ure

wh

eth

er y

ou a

gree

or

disa

gree

, wri

te N

S (

Not

Su

re).

Aft

er y

ou c

omp

lete

Ch

ap

ter

1

•

Rer

ead

each

sta

tem

ent

and

com

plet

e th

e la

st c

olu

mn

by

ente

rin

g an

A o

r a

D.

•

Did

an

y of

you

r op

inio

ns

abou

t th

e st

atem

ents

ch

ange

fro

m t

he

firs

t co

lum

n?

•

For

th

ose

stat

emen

ts t

hat

you

mar

k w

ith

a D

, use

a p

iece

of

pape

r to

wri

te a

n

exam

ple

of w

hy

you

dis

agre

e.

1A

ntic

ipat

ion

Gui

deE

xp

ressio

ns, E

qu

ati

on

s, an

d F

un

cti

on

s

Step

1

Step

2

ST

EP

1A

, D, o

r N

SS

tate

men

tS

TE

P 2

A o

r D

1.

An

alg

ebra

ic e

xpre

ssio

n c

onta

ins

one

or m

ore

nu

mbe

rs,

vari

able

s, a

nd

arit

hm

etic

ope

rati

ons.

2.

Th

e ex

pres

sion

x4

mea

ns

x +

x +

x +

x.

3.

Acc

ordi

ng

to t

he

orde

r of

ope

rati

ons,

all

mu

ltip

lica

tion

an

d di

visi

on s

hou

ld b

e do

ne

befo

re a

nyt

hin

g el

se.

4.

Sin

ce 2

mak

es t

he

equ

atio

n 3

t -

1 =

5 t

rue,

{2}

is

the

solu

tion

se

t fo

r th

e eq

uat

ion

.

5.

Bec

ause

of

the

Ref

lexi

ve P

rope

rty

of E

qual

ity,

if

a +

b =

c t

hen

c

= a

+ b

.

6.

Th

e m

ult

ipli

cati

ve i

nve

rse

of 2

3 is

1 −

23 .

7.

Th

e D

istr

ibu

tive

Pro

pert

y st

ates

th

at a

(b +

c)

wil

l eq

ual

ab

+ c

.

8.

Th

e or

der

in w

hic

h y

ou a

dd o

r m

ult

iply

nu

mbe

rs d

oes

not

ch

ange

th

eir

sum

or

prod

uct

.

9.

A g

raph

has

sym

met

ry i

n a

lin

e if

eac

h h

alf

of t

he

grap

h o

n

eith

er s

ide

of t

he

lin

e m

atch

es e

xact

ly.

10.

In t

he

coor

din

ate

plan

e, t

he

x-ax

is i

s h

oriz

onta

l an

d th

e y-

axis

is

ver

tica

l.

A D D A D A A AD A

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Answers (Anticipation Guide and Lesson 1-1)

A01_A14_ALG1_A_CRM_C01_AN_660498.indd A1A01_A14_ALG1_A_CRM_C01_AN_660498.indd A1 12/21/10 6:44 PM12/21/10 6:44 PM

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

6 G

lenc

oe A

lgeb

ra 1

Wri

te A

lgre

bra

ic E

xpre

ssio

ns

Tra

nsl

atin

g ve

rbal

exp

ress

ion

s in

to a

lgeb

raic

ex

pres

sion

s is

an

im

port

ant

alge

brai

c sk

ill.

W

rite

an

alg

ebra

ic e

xpre

ssio

n f

or e

ach

ver

bal

exp

ress

ion

.

a. f

our

mor

e th

an a

nu

mb

er n

Th

e w

ords

mor

e th

an i

mpl

y ad

diti

on.

fou

r m

ore

than

a n

um

ber

n4

+ n

Th

e al

gebr

aic

expr

essi

on i

s 4

+ n

.

b.

the

dif

fere

nce

of

a n

um

ber

sq

uar

ed a

nd

8T

he e

xpre

ssio

n di

ffer

ence

of

impl

ies

subt

ract

ion.

the

diff

eren

ce o

f a

nu

mbe

r sq

uar

ed a

nd

8n

2 -

8T

he

alge

brai

c ex

pres

sion

is

n2

- 8

.

Exer

cise

sW

rite

an

alg

ebra

ic e

xpre

ssio

n f

or e

ach

ver

bal

exp

ress

ion

.

1. a

nu

mbe

r de

crea

sed

by 8

2. a

nu

mbe

r di

vide

d by

8

3. a

nu

mbe

r sq

uar

ed

4. f

our

tim

es a

nu

mbe

r

5. a

nu

mbe

r di

vide

d by

6

6. a

nu

mbe

r m

ult

ipli

ed b

y 37

7. t

he

sum

of

9 an

d a

nu

mbe

r

8. 3

les

s th

an 5

tim

es a

nu

mbe

r

9. t

wic

e th

e su

m o

f 15

an

d a

nu

mbe

r

10. o

ne-

hal

f th

e sq

uar

e of

b

11. 7

mor

e th

an t

he

prod

uct

of

6 an

d a

nu

mbe

r

12. 3

0 in

crea

sed

by 3

tim

es t

he

squ

are

of a

nu

mbe

r

1-1

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Vari

ab

les a

nd

Exp

ressio

ns

Exam

ple

b -

8

h

−

8

n2 4n

n

−

6

37n

9 +

n

5n -

3

2(15

+ n

)

1 −

2 b2

6n +

7

30 +

3n

2

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NA

ME

DAT

E

P

ER

IOD

Lesson 1-1

Cha

pte

r 1

7 G

lenc

oe A

lgeb

ra 1

Wri

te a

ver

bal

exp

ress

ion

for

eac

h a

lgeb

raic

exp

ress

ion

.

1. 9

a2 2.

52

3. c

+ 2

d

4. 4

- 5

h

5. 2

b2 6.

7x3

- 1

7. p

4 +

6r

8. 3

n2

- x

Wri

te a

n a

lgeb

raic

exp

ress

ion

for

eac

h v

erb

al e

xpre

ssio

n.

9. t

he

sum

of

a n

um

ber

and

10

10. 1

5 le

ss t

han

k

11. t

he

prod

uct

of

18 a

nd

q

12. 6

mor

e th

an t

wic

e m

13. 8

in

crea

sed

by t

hre

e ti

mes

a n

um

ber

14. t

he

diff

eren

ce o

f 17

an

d 5

tim

es a

nu

mbe

r

15. t

he

prod

uct

of

2 an

d th

e se

con

d po

wer

of

y

16. 9

les

s th

an g

to

the

fou

rth

pow

er

1-1

Skill

s Pr

acti

ceVari

ab

les a

nd

Exp

ressio

ns

x

+ 1

0

1

8q

8

+ 3

x

2

y2

t

he

pro

du

ct o

f 9

and

a

5 sq

uar

ed

sq

uar

ed

t

he

sum

of

c a

nd

tw

ice

d

the

dif

fere

nce

of

4 an

d 5

tim

es h

2

tim

es b

sq

uar

ed

1 le

ss t

han

7 t

imes

x

cub

ed

p

to

th

e fo

urt

h p

ow

er p

lus

6 ti

mes

r

3 t

imes

n s

qu

ared

m

inu

s x

k

- 1

5

2

m +

6

1

7 -

5x

g

4 -

9

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Answers (Lesson 1-1)


An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

8 G

lenc

oe A

lgeb

ra 1

Wri

te a

ver

bal

exp

ress

ion

for

eac

h a

lgeb

raic

exp

ress

ion

.

1. 2

3f

2. 7

3

3. 5

m2

+ 2

4.

4d

3 -

10

5. x

3 ․

y4

6.

b2

- 3

c3

7.

k5 −

6 8.

4n2

−

7

Wri

te a

n a

lgeb

raic

exp

ress

ion

for

eac

h v

erb

al e

xpre

ssio

n.

9. t

he

diff

eren

ce o

f 10

an

d u

10. t

he

sum

of

18 a

nd

a n

um

ber

11. t

he

prod

uct

of

33 a

nd

j

12. 7

4 in

crea

sed

by 3

tim

es y

13. 1

5 de

crea

sed

by t

wic

e a

nu

mbe

r

14. 9

1 m

ore

than

th

e sq

uar

e of

a n

um

ber

15. t

hre

e fo

urt

hs

the

squ

are

of b

16. t

wo

fift

hs

the

cube

of

a n

um

ber

17. B

OO

KS

A u

sed

book

stor

e se

lls

pape

rbac

k fi

ctio

n b

ooks

in

exc

elle

nt

con

diti

on f

or

$2.5

0 an

d in

fai

r co

ndi

tion

for

$0.

50. W

rite

an

exp

ress

ion

for

th

e co

st o

f bu

yin

g x

exce

llen

t-co

ndi

tion

pap

erba

cks

and

f fa

ir-c

ondi

tion

pap

erba

cks.

18. G

EOM

ETRY

Th

e su

rfac

e ar

ea o

f th

e si

de o

f a

righ

t cy

lin

der

can

be

fou

nd

by m

ult

iply

ing

twic

e th

e n

um

ber

π b

y th

e ra

diu

s ti

mes

th

e h

eigh

t. I

f a

circ

ula

r cy

lin

der

has

rad

ius

r an

d h

eigh

t h

, wri

te a

n e

xpre

ssio

n t

hat

rep

rese

nts

th

e su

rfac

e ar

ea o

f it

s si

de.

1-1

Prac

tice

Vari

ab

les a

nd

Exp

ressio

ns

the

pro

du

ct o

f 23

an

d f

seve

n c

ub

ed

2 m

ore

th

an 5

tim

es m

sq

uar

ed

4 ti

mes

d c

ub

ed m

inu

s 10

x c

ub

ed t

imes

y t

o t

he

b

sq

uar

ed m

inu

s 3

tim

es c

cu

bed

fou

rth

po

wer

1– 8

. Sam

ple

an

swer

s ar

e g

iven

.

o

ne

sixt

h o

f th

e fi

fth

po

wer

of

k

on

e se

ven

th o

f 4

tim

es n

sq

uar

ed

2.50

x +

0.5

0f 2πrh

10

- u

33j

15

- 2

x

3 −

4 b2

18 +

x

74 +

3y

x2

+ 9

1

2 −

5 x3

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NA

ME

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Lesson 1-1

Cha

pte

r 1

9 G

lenc

oe A

lgeb

ra 1

1. S

OLA

R S

YST

EM I

t ta

kes

Ear

th a

bou

t 36

5 da

ys t

o or

bit

the

Su

n. I

t ta

kes

Ura

nu

s ab

out

85 t

imes

as

lon

g. W

rite

a

nu

mer

ical

exp

ress

ion

to

desc

ribe

th

e n

um

ber

of d

ays

it t

akes

Ura

nu

s to

orb

it

the

Su

n.

2. T

ECH

NO

LOG

Y T

her

e ar

e 10

24 b

ytes

in

a

kilo

byte

. Wri

te a

n e

xpre

ssio

n t

hat

de

scri

bes

the

nu

mbe

r of

byt

es i

n a

co

mpu

ter

chip

wit

h n

kil

obyt

es.

3. T

HEA

TER

H. H

owar

d H

ugh

es, P

rofe

ssor

E

mer

itu

s of

Tex

as W

esle

yan

Col

lege

an

d h

is w

ife

Eri

n C

onn

or H

ugh

es a

tten

ded

a re

cord

613

6 th

eatr

ical

sh

ows.

Wri

te a

n

expr

essi

on f

or t

he

aver

age

nu

mbe

r of

sh

ows

they

att

ende

d pe

r ye

ar i

f th

ey

accu

mu

late

d th

e re

cord

ove

r y

year

s.

4. T

IDES

Th

e di

ffer

ence

bet

wee

n h

igh

an

d lo

w t

ides

alo

ng

the

Mai

ne

coas

t in

N

ovem

ber

is 1

9 fe

et o

n M

onda

y an

d x

feet

on

Tu

esda

y. W

rite

an

exp

ress

ion

to

show

th

e av

erag

e ri

se a

nd

fall

of

the

tide

fo

r M

onda

y an

d T

ues

day.

5. B

LOC

KS

A t

oy m

anu

fact

ure

r pr

odu

ces

a se

t of

blo

cks

that

can

be

use

d by

ch

ildr

en

to b

uil

d pl

ay s

tru

ctu

res.

Th

e pr

odu

ct

pack

agin

g te

am i

s an

alyz

ing

diff

eren

t ar

ran

gem

ents

for

pac

kagi

ng

thei

r bl

ocks

. O

ne

idea

th

ey h

ave

is t

o ar

ran

ge t

he

bloc

ks i

n t

he

shap

e of

a c

ube

, wit

h

b bl

ocks

alo

ng

one

edge

.

a. W

rite

an

exp

ress

ion

rep

rese

nti

ng

the

tota

l n

um

ber

of b

lock

s pa

ckag

ed i

n a

cu

be m

easu

rin

g b

bloc

ks o

n o

ne

edge

.

b.

Th

e pa

ckag

ing

team

dec

ides

to

take

on

e la

yer

of b

lock

s of

f th

e to

p of

th

is

pack

age.

Wri

te a

n e

xpre

ssio

n

repr

esen

tin

g th

e n

um

ber

of b

lock

s in

th

e to

p la

yer

of t

he

pack

age.

c. T

he

team

fin

ally

dec

ides

th

at t

hei

r fa

vori

te p

acka

ge a

rran

gem

ent

is t

o ta

ke 2

lay

ers

of b

lock

s of

f th

e to

p of

a

cube

mea

suri

ng

b bl

ocks

alo

ng

one

edge

. Wri

te a

n ex

pres

sion

rep

rese

ntin

g th

e n

um

ber

of b

lock

s le

ft b

ehin

d af

ter

the

top

two

laye

rs a

re r

emov

ed.

b

b

b

1-1

Wor

d Pr

oble

m P

ract

ice

Vari

ab

les a

nd

Exp

ressio

ns

365

× 8

5

1024

× n

or

1024

n

6136

−

y

b3

b2

19 +

x

−

2

b3

- 2

b2

or

(b -

2)

× b

2

001_

012_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

912

/21/

10

5:20

PM



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

10

Gle

ncoe

Alg

ebra

1

Too

thp

ick T

rian

gle

sV

aria

ble

expr

essi

ons

can

be

use

d to

rep

rese

nt

patt

ern

s an

d h

elp

solv

e pr

oble

ms.

Con

side

r th

e pr

oble

m o

f cr

eati

ng

tria

ngl

es o

ut

of t

ooth

pick

s sh

own

bel

ow. F

igu

re 3

Fig

ure

2F

igu

re 1

1. H

ow m

any

toot

hpi

cks

does

it

take

to

crea

te e

ach

fig

ure

?

2. H

ow m

any

toot

hpi

cks

does

it

take

to

mak

e u

p th

e pe

rim

eter

of

each

im

age?

3. S

ketc

h t

he

nex

t th

ree

figu

res

in t

he

patt

ern

.

Fig

ure

4F

igu

re 5

Fig

ure

6

4. C

onti

nu

e th

e pa

tter

n t

o co

mpl

ete

the

tabl

e.

5. L

et t

he

vari

able

n r

epre

sen

t th

e fi

gure

nu

mbe

r. W

rite

an

exp

ress

ion

th

at c

an b

e u

sed

to

fin

d th

e n

um

ber

of t

ooth

pick

s n

eede

d to

cre

ate

figu

re n

.

6. L

et t

he

vari

able

n r

epre

sen

t th

e fi

gure

nu

mbe

r. W

rite

an

exp

ress

ion

th

at c

an b

e u

sed

to

fin

d th

e n

um

ber

of t

ooth

pick

s in

th

e pe

rim

eter

of

figu

re n

.

1-1

Enri

chm

ent

Imag

e N

um

ber

12

34

56

78

910

Nu

mb

er o

f to

oth

pic

ks3

57

Nu

mb

er o

f to

oth

pic

ks in

P

erim

eter

34

5

3; 5

; 7

3; 4

; 5

9

11

13

15

17

19

21

6

7

8

9

1

0

11

12

2n +

1

n +

2

001_

012_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

1012

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-2

Cha

pte

r 1

11

Gle

ncoe

Alg

ebra

1

Eval

uat

e N

um

eric

al E

xpre

ssio

ns

Nu

mer

ical

exp

ress

ion

s of

ten

con

tain

mor

e th

an

one

oper

atio

n. T

o ev

alu

ate

them

, use

th

e ru

les

for

orde

r of

ope

rati

ons

show

n b

elow

.

Ord

er o

fO

per

atio

ns

Ste

p 1

Eva

lua

te e

xp

ressio

ns in

sid

e g

rou

pin

g s

ym

bo

ls.

Ste

p 2

Eva

lua

te a

ll p

ow

ers

.

Ste

p 3

Do

all

mu

ltip

lica

tio

n a

nd

/or

div

isio

n f

rom

le

ft t

o r

igh

t.

Ste

p 4

Do

all

ad

ditio

n a

nd

/or

su

btr

actio

n f

rom

le

ft t

o r

igh

t.

E

valu

ate

each

exp

ress

ion

.

a. 3

4 34 =

3 ․

3 ․

3 ․

3

Use 3

as a

facto

r 4 t

imes.

=

81

Multip

ly.

b.

63 63 =

6 ․

6 ․

6

Use 6

as a

facto

r 3 t

imes.

=

216

M

ultip

ly.

E

valu

ate

each

exp

ress

ion

.

a. 3

[2 +

(12

÷ 3

)2 ]3[

2 +

(12

÷ 3

)2 ] =

3(2

+ 4

2 ) D

ivid

e 1

2 b

y 3

.

=

3(2

+ 1

6) Fi

nd 4

square

d.

=

3(1

8)

Add 2

and 1

6.

=

54

Multip

ly 3

and 1

8.

b.

3 +

23

−

42 · 3

3 +

23

−

42 · 3 =

3 +

8

−

42 · 3

E

valu

ate

pow

er

in n

um

era

tor.

=

11

−

42 · 3

A

dd 3

and 8

in t

he n

um

era

tor.

=

11

−

16 · 3

E

valu

ate

pow

er

in d

enom

inato

r.

=

11

−

48

Multip

ly.

Exer

cise

sE

valu

ate

each

exp

ress

ion

.

1. 5

2 2.

33

3. 1

04

4. 1

22 5.

83

6. 2

8

7. (

8 -

4)

․

2

8. (

12 +

4)

․

6

9. 1

0 +

8 ․

1

10. 1

5 -

12

÷ 4

11

. 12(

20 -

17)

- 3

․ 6

12

. 24

÷ 3

․ 2

- 3

2

13. 3

2 ÷

3 +

22

․

7 -

20

÷ 5

14

. 4

+ 32

−

12 +

1

15. 2

50 ÷

[5(

3 ․

7 +

4)]

16.

2 · 4

2 -

8 ÷

2

−

(5

+ 2)

· 2

17

. 4(

52 ) -

4

· 3

−

4(4

· 5 +

2)

18.

52

- 3

−

20(3)

+

2(

3)

1-2

Stud

y G

uide

and

Inte

rven

tion

Ord

er

of

Op

era

tio

ns

Exam

ple

1Ex

amp

le 2

896

1218

27

2

1 −

3

25

27

10,0

00

144

512

256

18

7

1

21

001_

012_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

1112

/21/

10

5:20

PM

Answers (Lesson 1-1 and Lesson 1-2)


An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

12

Gle

ncoe

Alg

ebra

1

Eval

uat

e A

lgeb

raic

Exp

ress

ion

s A

lgeb

raic

exp

ress

ion

s m

ay c

onta

in m

ore

than

on

e op

erat

ion

. Alg

ebra

ic e

xpre

ssio

ns

can

be

eval

uat

ed i

f th

e va

lues

of

the

vari

able

s ar

e kn

own

. F

irst

, rep

lace

th

e va

riab

les

wit

h t

hei

r va

lues

. Th

en u

se t

he

orde

r of

ope

rati

ons

to c

alcu

late

th

e va

lue

of t

he

resu

ltin

g n

um

eric

al e

xpre

ssio

n.

E

valu

ate

x3 +

5(y

- 3

) if

x =

2 a

nd

y =

12.

x3 +

5(y

- 3

) =

23

+ 5

(12

- 3

)

R

epla

ce x

with 2

and y

with 1

2.

= 8

+ 5

(12

- 3

) E

valu

ate

23.

= 8

+ 5

(9)

Subtr

act

3 f

rom

12.

= 8

+ 4

5 M

ultip

ly 5

and 9

.

= 5

3 A

dd 8

and 4

5.

Th

e so

luti

on i

s 53

.

Exer

cise

sE

valu

ate

each

exp

ress

ion

if

x =

2, y

= 3

, z =

4, a

= 4 −

5 , an

d b

= 3 −

5 .

1. x

+ 7

2.

3x

- 5

3.

x +

y2

4. x

3 +

y +

z2

5.

6a

+ 8

b

6. 2

3 -

(a

+ b

)

7.

y2 −

x2

8. 2

xyz

+ 5

9.

x(2

y +

3z)

10. (

10x)

2 +

100

a

11.

3xy

- 4

−

7x

12

. a2

+ 2

b

13.

z2 -

y2

−

x2

14. 6

xz +

5xy

15

. (z

- y )

2 −

x

16.

25ab

+ y

−

xz

17.

5 a 2 b

−

y

18.

(z ÷

x)2

+ a

x

19. (

x −

z ) 2 +

(

y −

z ) 2

20.

x +

z

−

y +

2z

21

. ( z

÷ x

−

y )

+ (

y ÷

x −

z )

1-2

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Ord

er

of

Op

era

tio

ns

Exam

ple 9

111

2721

3 −

5

9 −

4 53

36

480

1 21

−

25

7 −

4 78

1 −

2

1 7 −

8 16

−

25

5 3 −

5

13

−

16

6 −

11

1 1

−

24

19 3 −

5

001_

012_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

1212

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-2

Cha

pte

r 1

13

Gle

ncoe

Alg

ebra

1

Eva

luat

e ea

ch e

xpre

ssio

n.

1. 8

2 2.

34

3. 5

3 4.

33

5. (

5 +

4)

� 7

6.

(9

- 2

) � 3

7. 4

+ 6

� 3

8.

12

+ 2

� 2

9. (

3 +

5)

� 5

+ 1

10

. 9 +

4(3

+ 1

)

11. 3

0 -

5 �

4 +

2

12. 1

0 +

2 �

6 +

4

13. 1

4 ÷

7 �

5 -

32

14

. 4[3

0 -

(10

- 2

) � 3

]

15. 5

+ [

30 -

(6

- 1

)2 ]

16. 2

[12

+ (

5 -

2)2 ]

Eva

luat

e ea

ch e

xpre

ssio

n i

f x

= 6

, y =

8, a

nd

z =

3.

17. x

y+

z

18. y

z -

x

19. 2

x +

3y

- z

20

. 2(x

+ z

) -

y

21. 5

z +

(y

- x

)

22. 5

x -

(y

+ 2

z)

23. x

2 +

y2

- 1

0z

24. z

3 +

(y2

- 4

x)

25.

y +

xz

−

2

26.

3y +

x2

−

z

1-2

Skill

s Pr

acti

ceO

rder

of

Op

era

tio

ns

6321

2216

4125

1226

124

1042

5118

3310

1716

7067

1320

6481

125

27

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

1312

/21/

10

5:20

PM



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

14

Gle

ncoe

Alg

ebra

1

Eva

luat

e ea

ch e

xpre

ssio

n.

1. 1

12 2.

83

3. 5

4

4. (

15 -

5)

․

2

5. 9

․ (

3 +

4)

6.

5 +

7 ․

4

7. 4

(3 +

5)

- 5

․ 4

8.

22

÷ 1

1 ․

9 -

32

9.

62

+ 3

․ 7

- 9

10. 3

[10

- (

27 ÷

9)]

11

. 2[5

2 +

(36

÷ 6

)]

12. 1

62 ÷

[6(

7 -

4)2 ]

13.

52 ․ 4

- 5

․ 4

2

−

5(4)

14.

(2 ․

5)2

+ 4

−

32 -

5

15

. 7

+ 32

−

42 · 2

Eva

luat

e ea

ch e

xpre

ssio

n i

f a

= 1

2, b

= 9

, an

d c

= 4

.

16. a

2 +

b -

c2

17

. b2

+ 2

a -

c2

18. 2

c(a

+ b

)

19. 4

a +

2b

- c

2

20. (

a2 ÷

4b)

+ c

21

. c2

· (2b

- a

)

22.

bc2 +

a

−

c

23.

2c3 -

ab

−

4

24. 2

(a

- b)

2

-

5c

25

. b2

- 2c

2 −

a +

c

- b

26. C

AR

REN

TAL

An

n C

arly

le i

s pl

ann

ing

a bu

sin

ess

trip

for

wh

ich

sh

e n

eeds

to

ren

t a

car.

Th

e ca

r re

nta

l co

mpa

ny

char

ges

$36

per

day

plu

s $0

.50

per

mil

e ov

er 1

00 m

iles

. Su

ppos

e M

s. C

arly

le r

ents

th

e ca

r fo

r 5

days

an

d dr

ives

180

mil

es.

a. W

rite

an

exp

ress

ion

for

how

mu

ch i

t w

ill

cost

Ms.

Car

lyle

to

ren

t th

e ca

r.

b.

Eva

luat

e th

e ex

pres

sion

to

dete

rmin

e h

ow m

uch

Ms.

Car

lyle

mu

st p

ay t

he

car

ren

tal

com

pan

y.

27. G

EOM

ETRY

Th

e le

ngt

h o

f a

rect

angl

e is

3n

+ 2

an

d it

s w

idth

is

n -

1. T

he

peri

met

er

of t

he

rect

angl

e is

tw

ice

the

sum

of

its

len

gth

an

d it

s w

idth

.

a. W

rite

an

exp

ress

ion

th

at r

epre

sen

ts t

he

peri

met

er o

f th

e re

ctan

gle.

b.

Fin

d th

e pe

rim

eter

of

the

rect

angl

e w

hen

n =

4 i

nch

es.

1-2

Prac

tice

O

rder

of

Op

era

tio

ns

2063

33

129

48

2162

3

126

137

89

168

50

896

395

7

5(36

) +

0.5

(180

- 1

00)

$220

.00

2[(3

n +

2)

+ (

n -

1)]

34 in

.

1 −

2

-2

121

512

625

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

1412

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-2

Cha

pte

r 1

15

Gle

ncoe

Alg

ebra

1

1. S

CH

OO

LS J

effe

rson

Hig

h S

choo

l h

as

100

less

th

an 5

tim

es a

s m

any

stu

den

ts

as T

aft

Hig

h S

choo

l. W

rite

an

d ev

alu

ate

an e

xpre

ssio

n t

o fi

nd

the

nu

mbe

r of

st

ude

nts

at

Jeff

erso

n H

igh

Sch

ool

if T

aft

Hig

h S

choo

l h

as 3

00 s

tude

nts

.

2. G

EOG

RA

PHY

Gu

adal

upe

Pea

k in

Tex

as

has

an

alt

itu

de t

hat

is

671

feet

mor

e th

an d

oubl

e th

e al

titu

de o

f M

oun

t S

un

flow

er i

n K

ansa

s. W

rite

an

d ev

alu

ate

an e

xpre

ssio

n f

or t

he

alti

tude

of

Gu

adal

upe

Pea

k if

Mou

nt

Su

nfl

ower

has

an

alt

itu

de o

f 40

39 f

eet.

3. T

RA

NSP

OR

TATI

ON

Th

e P

laid

Tax

i C

ab

Com

pan

y ch

arge

s $1

.75

per

pass

enge

r pl

us

$3.4

5 pe

r m

ile

for

trip

s le

ss t

han

10

mil

es. W

rite

an

d ev

alu

ate

an

expr

essi

on t

o fi

nd

the

cost

for

Max

to

take

a P

laid

tax

i 8

mil

es t

o th

e ai

rpor

t.

4. G

EOM

ETRY

Th

e ar

ea o

f a

circ

le i

s re

late

d to

th

e ra

diu

s of

th

e ci

rcle

su

ch

that

th

e pr

odu

ct o

f th

e sq

uar

e of

th

e ra

diu

s an

d a

nu

mbe

r π

giv

es t

he

area

. W

rite

an

d ev

alu

ate

an e

xpre

ssio

n f

or t

he

area

of

a ci

rcu

lar

pizz

a be

low

. A

ppro

xim

ate

π a

s 3.

14.

7 in

.

5.B

IOLO

GY

Lav

ania

is

stu

dyin

g th

e gr

owth

of

a po

pula

tion

of

fru

it f

lies

in

her

la

bora

tory

. Sh

e n

otic

es t

hat

th

e n

um

ber

of f

ruit

fli

es i

n h

er e

xper

imen

t is

fiv

e ti

mes

as

larg

e af

ter

any

six-

day

peri

od.

Sh

e ob

serv

es 2

0 fr

uit

fli

es o

n O

ctob

er 1

. W

rite

an

d ev

alu

ate

an e

xpre

ssio

n t

o pr

edic

t th

e po

pula

tion

of

fru

it f

lies

L

avan

ia w

ill

obse

rve

on O

ctob

er 3

1.

6. C

ON

SUM

ER S

PEN

DIN

G D

uri

ng

a lo

ng

wee

ken

d, D

evon

pai

d a

tota

l of

x d

olla

rs

for

a re

nta

l ca

r so

he

cou

ld v

isit

his

fa

mil

y. H

e re

nte

d th

e ca

r fo

r 4

days

at

a ra

te o

f $3

6 pe

r da

y. T

her

e w

as a

n

addi

tion

al c

har

ge o

f $0

.20

per

mil

e af

ter

the

firs

t 20

0 m

iles

dri

ven

.

a. W

rite

an

alg

ebra

ic e

xpre

ssio

n t

o re

pres

ent

the

amou

nt

Dev

on p

aid

for

addi

tion

al m

ilea

ge o

nly

.

b.

Wri

te a

n a

lgeb

raic

exp

ress

ion

to

repr

esen

t th

e n

um

ber

of m

iles

ove

r 20

0 m

iles

th

at D

evon

dro

ve t

he

ren

ted

car.

c. H

ow m

any

mil

es d

id D

evon

dri

ve

over

all

if h

e pa

id a

tot

al o

f $1

74 f

or

the

car

ren

tal?

1-2

Wor

d Pr

oble

m P

ract

ice

Ord

er

of

Op

era

tio

ns

5t -

10

0; 1

400

stu

den

ts

2n +

671

; 87

49 f

t

$1.7

5 +

$3.

45m

; $2

9.35

πr2 ;

153

.86

in 2

20 ×

55 ;

62,

500

fl ies

x -

(36

× 4

)

350

mi

x -

(36

× 4

)

−

0.20

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

1512

/21/

10

5:20

PM



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

16

Gle

ncoe

Alg

ebra

1

Th

e F

ou

r D

igit

s P

rob

lem

On

e w

ell-

know

n m

ath

emat

ics

prob

lem

is

to w

rite

exp

ress

ion

s fo

r co

nse

cuti

ve n

um

bers

be

gin

nin

g w

ith

1. O

n t

his

pag

e, y

ou w

ill

use

th

e di

gits

1, 2

, 3, a

nd 4

. Eac

h di

git

is u

sed

only

on

ce. Y

ou m

ay u

se a

ddit

ion,

su

btra

ctio

n, m

ult

ipli

cati

on (

not

div

isio

n),

expo

nen

ts, a

nd

pare

nth

eses

in

an

y w

ay y

ou w

ish.

Als

o, y

ou c

an u

se t

wo

digi

ts t

o m

ake

one

num

ber,

such

as

12 o

r 34

.

Exp

ress

eac

h n

um

ber

as

a co

mb

inat

ion

of

the

dig

its

1, 2

, 3, a

nd

4.

1 =

(3

× 1

) -

(4

- 2

) 18

=

35

= 2

(4+

1) +

3

2 =

19 =

3(2

+ 4

) +

1

36 =

3 =

20 =

37 =

4 =

21 =

38 =

5 =

22 =

39 =

6 =

23 =

31

- (

4 ×

2)

40 =

7 =

24 =

41 =

8 =

25 =

42 =

9 =

26 =

43 =

42

+ 1

3

10 =

27 =

44 =

11 =

28 =

45 =

12 =

29 =

46 =

13 =

30

=

47

=

14 =

31 =

48 =

15 =

32 =

49 =

16 =

33 =

50 =

17 =

34 =

Doe

s a

calc

ula

tor

hel

p in

sol

vin

g th

ese

type

s of

pu

zzle

s? G

ive

reas

ons

for

you

r op

inio

n.

1-2

Enri

chm

ent

An

swer

s w

ill v

ary.

Sam

ple

an

swer

s ar

e g

iven

.

(4 -

3)

+ (

2 -

1)

34 +

(2

× 1

)

21 -

(4

- 3

)

4 +

3 +

1 -

2

3(4

- 1)

- 2

(2 +

4)

× (

3 +

1)

(2 +

3)

× (

4 +

1)

An

swer

s w

ill v

ary.

Usi

ng

a c

alcu

lato

r is

a g

oo

d w

ay t

o c

hec

k yo

ur

solu

tio

ns.

4 +

3 +

2 +

1

(4 -

3)

+ (

2 ×

1)

(4 -

2)

+ (

3 -

1)

(4 -

2)

+ (

3 ×

1)

4 +

3 +

2 -

1

4 +

2 +

(3

× 1

)24

+

(3

- 1

)

21 +

3 +

4

2(4 +

1)

- 3

(2 ×

3)

× (

4 +

1)

34 -

(2

+

1)

42 ×

(3

- 1

)

21 +

(3

× 4

)

2 ×

(14

+

3)

43 +

(2

- 1

)

43 +

(2

× 1

)

43 +

(2

+

1)

31 +

42

42 ×

(3

× 1

)

41 +

23

41 +

32

(2 ×

3)

× (

4 -

1)

(4 +

3)

× (

2 +

1)

(4 ×

3) +

(2

- 1

)

(4 ×

3)

× (

2 -

1)

(4 ×

3) +

(2

× 1

)

(4 ×

3) -

(2

- 1

)

2(3

+ 4)

+

1

(4 ×

2)

× (

3 -

1)

3(2

+ 4)

- 1

21 +

(4

- 3

)

32 ×

(4

- 1

)

31 +

2

+ 4

42 -

(3

+

1)

42 -

(3

× 1

)

41 -

(3

- 2

)

43 -

(2

× 1

)

43 -

(2

- 1

)

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

1612

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-2

Cha

pte

r 1

17

Gle

ncoe

Alg

ebra

1

Wh

en e

valu

atin

g al

gebr

aic

expr

essi

ons,

it

is s

omet

imes

hel

pfu

l to

use

th

e st

ore

key

on t

he

calc

ula

tor,

espe

cial

ly t

o ch

eck

solu

tion

s, e

valu

ate

seve

ral

expr

essi

ons

for

the

sam

e va

lues

of

vari

able

s, o

r ev

alu

ate

the

sam

e ex

pres

sion

for

mu

ltip

le v

alu

es o

f th

e va

riab

les.

E

valu

ate

a2 -

4a

+

6

if a

=

8.

Fir

st, o

pen

a n

ew C

alcu

lato

r pa

ge o

n t

he

TI-

Nsp

ire.

Th

en, d

elet

e an

y in

stan

ces

of s

tore

d va

riab

les

by

ente

rin

g C

LE

AR

AZ

.

Sto

re 8

as

the

valu

e fo

r a.

Fin

ally

en

ter

the

expr

essi

on, i

ncl

udi

ng

the

vari

able

s, t

o ev

alu

ate.

Th

e an

swer

is

38.

Exer

cise

s

Eva

luat

e ea

ch e

xpre

ssio

n i

f a

= 4

, b =

6, x

= 8

, an

d y

= 1

2. E

xpre

ss a

nsw

ers

as

inte

gers

or

frac

tion

s.

1. b

x -

ay

÷

b

2. a

[ x

+ (y

÷

a)

2 ]

3. a

3 -

(y

- b

)2 +

x2

4.

b +

a2

−

x2 -

b2

5. 2a

(x -

b)

−

xy

- 9b

6.

b3 -

[3(

a +

b2 )

+

5b

]

−−

y ÷

a(

x -

1)

E

valu

ate

xy -

4y

−

5x i

f x

= 4

an

d y

= 1

2.

En

ter

4 as

th

e va

lue

for

x an

d 12

as

the

valu

e fo

r y.

Eva

luat

e th

e ex

pres

sion

. Th

e T

I-N

spir

e w

ill

disp

lay

the

answ

er

as a

fra

ctio

n.

Th

e an

swer

is

228

−

5 .

1-2

TI-N

spir

e® A

ctiv

ity

Usin

g t

he S

tore

Key

Exam

ple

1

Exam

ple

2

4

0 68

92

8 −

21

22

−

7 11

−

14

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

1712

/21/

10

5:20

PM



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

18

Gle

ncoe

Alg

ebra

1

E

valu

ate

24 �

1 -

8 +

5(9

÷ 3

- 3

). N

ame

the

pro

per

ty u

sed

in

eac

h s

tep

.24

․ 1

- 8

+ 5

(9 ÷

3 -

3)

= 2

4 ․

1 -

8 +

5(3

- 3

) Su

bstitu

tion; 9 ÷

3 =

3

=

24

․

1 -

8 +

5(0

)

Substitu

tion; 3 -

3 =

0

=

24

- 8

+ 5

(0)

M

ultip

licative

Identity

; 24 ․

1 =

24

=

24

- 8

+ 0

Multip

licative

Pro

pert

y o

f Z

ero

; 5(0

) =

0

=

16

+ 0

Substitu

tion; 24 -

8 =

16

=

16

A

dditiv

e I

dentity

; 16 +

0 =

16

Exer

cise

sE

valu

ate

each

exp

ress

ion

. Nam

e th

e p

rop

erty

use

d i

n e

ach

ste

p.

1. 2

[ 1 −

4 + ( 1

−

2 ) 2 ]

2.

15

․

1 -

9 +

2(1

5 ÷

3 -

5)

3. 2

(3 ․

5 ․

1 -

14)

- 4

․ 1 −

4 4.

18

․

1 -

3 ․

2 +

2(6

÷ 3

- 2

)

1-3

Stud

y G

uide

and

Inte

rven

tion

Pro

pert

ies o

f N

um

bers

Iden

tity

an

d E

qu

alit

y Pr

op

erti

es T

he

iden

tity

an

d eq

ual

ity

prop

erti

es i

n t

he

char

t be

low

can

hel

p yo

u s

olve

alg

ebra

ic e

quat

ion

s an

d ev

alu

ate

mat

hem

atic

al e

xpre

ssio

ns.

Ad

dit

ive

Iden

tity

Fo

r a

ny n

um

be

r a,

a +

0 =

a.

Ad

dit

ive

Inve

rse

Fo

r a

ny n

um

be

r a,

a +

(-

a) =

0.

Mu

ltip

licat

ive

Iden

tity

Fo

r a

ny n

um

be

r a,

a .

1 =

a.

Mu

ltip

licat

ive

Pro

per

ty o

f 0

Fo

r a

ny n

um

be

r a,

a .

0 =

0.

Mu

ltip

licat

ive

Inve

rse

Pro

per

tyF

or

eve

ry n

um

be

r a −

b ,

wh

ere

a,

b ≠

0,

the

re is e

xactly

on

e n

um

be

r b

−

a su

ch

th

at

a −

b .

b

−

a = 1.

Refl

exi

ve P

rop

erty

Fo

r a

ny n

um

be

r a,

a =

a.

Sym

met

ric

Pro

per

tyF

or

any n

um

be

rs a

an

d b

, if a

= b

, th

en

b =

a.

Tran

siti

ve P

rop

erty

Fo

r a

ny n

um

be

rs a

, b

, a

nd

c,

if a

= b

an

d b

= c

, th

en

a =

c.

Su

bst

ituti

on

Pro

per

tyIf

a =

b,

the

n a

may b

e r

ep

lace

d b

y b

in

any e

xp

ressio

n.

Exam

ple

= 2

(15

�

1 -

14)

- 4

� 1 −

4 S

ub

st.

= 1

8 �

1 -

3 �

2 +

2(2

- 2

) S

ub

st.

= 2

(15

- 1

4) -

4 �

1 −

4 M

ult

. Id

enti

ty

= 1

8 �

1 -

3 �

2 +

2(0

) S

ub

stitu

tio

n

= 2

(1)

- 4

� 1 −

4 S

ub

stitu

tio

n

= 1

8 -

3 �

2 +

2(0

) M

ult

. Id

enti

ty

= 2

- 4

� 1 −

4 M

ult

. Id

enti

ty

= 1

8 -

6 +

2(0

) S

ub

stitu

tio

n

= 2

- 1

M

ult

. Inv

erse

=

18

- 6

+ 0

M

ult

. Pro

p. Z

ero

= 1

S

ub

stitu

tio

n

= 1

2 +

0

Su

bst

ituti

on

= 1

2 A

dd

. Id

enti

ty

=

2 (

1 −

4 + 1 −

4 )

Su

bst

ituti

on

=

15

�

1 -

9 +

2(5

- 5

) S

ub

stitu

tio

n

=

2 (

1 −

2 )

Su

bst

ituti

on

=

15

�

1 -

9 +

2(0)

S

ub

stitu

tio

n

=

1

Mu

lt. I

nver

se

= 1

5 �

1 -

9 +

0

Mu

lt. P

rop

. Zer

o

=

15

- 9

+ 0

Mu

lt. I

den

tity

=

6 -

0

S

ub

stitu

tio

n

= 6

Su

bst

ituti

on

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

1812

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-3

Cha

pte

r 1

19

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Pro

pert

ies o

f N

um

bers

1-3

Co

mm

uta

tive

an

d A

sso

ciat

ive

Pro

per

ties

Th

e C

omm

uta

tive

an

d A

ssoc

iati

ve

Pro

pert

ies

can

be

use

d to

sim

plif

y ex

pres

sion

s. T

he

Com

mu

tati

ve P

rope

rtie

s st

ate

that

th

e or

der

in w

hic

h y

ou a

dd o

r m

ult

iply

nu

mbe

rs d

oes

not

ch

ange

th

eir

sum

or

prod

uct

. Th

e A

ssoc

iati

ve P

rope

rtie

s st

ate

that

th

e w

ay y

ou g

rou

p th

ree

or m

ore

nu

mbe

rs w

hen

add

ing

or

mu

ltip

lyin

g do

es n

ot c

han

ge t

hei

r su

m o

r pr

odu

ct.

E

valu

ate

6 �

2 �

3 �

5

usi

ng

pro

per

ties

of

nu

mb

ers.

Nam

e th

e p

rop

erty

use

d i

n e

ach

ste

p.

6 ․

2 ․

3 ․

5 =

6 ․

3 ․

2 ․

5

Com

muta

tive

Pro

pert

y

=

(6

․

3)(

2 ․

5)

Associa

tive

Pro

pert

y

=

18

․ 1

0 M

ultip

ly.

=

18

0 M

ultip

ly.

Th

e pr

odu

ct i

s 18

0.

E

valu

ate

8.2

+ 2

.5 +

2.5

+ 1

.8 u

sin

g p

rop

erti

es o

f n

um

ber

s. N

ame

the

pro

per

ty u

sed

in

ea

ch s

tep

.8.

2 +

2.5

+ 2

.5 +

1.8

=

8.2

+ 1

.8 +

2.5

+ 2

.5

Com

muta

tive

Pro

p.

=

(8.

2 +

1.8

) +

(2.

5 +

2.5

) As

socia

tive

Pro

p.

=

10

+ 5

A

dd.

=

15

Add.

Th

e su

m i

s 15

.

Exer

cise

sE

valu

ate

each

exp

ress

ion

usi

ng

pro

per

ties

of

nu

mb

ers.

Nam

e th

e p

rop

erty

use

d i

n

each

ste

p.

1. 1

2 +

10

+ 8

+ 5

2.

16

+ 8

+ 2

2 +

12

3.

10

․

7 ․

2.5

4. 4

․ 8

․ 5

․ 3

5.

12

+ 2

0 +

10

+ 5

6.

26

+ 8

+ 4

+ 2

2

7. 3

1 −

2 + 4

+ 2

1 −

2 + 3

8.

3 −

4 ․ 1

2 ․

4 ․

2

9. 3

.5 +

2.4

+ 3

.6 +

4.2

10. 4

1 −

2 + 5

+ 1 −

2 + 3

11

. 0.5

․ 2

.8 ․

4

12. 2

.5 +

2.4

+ 2

.5 +

3.6

13.

4 −

5 ․ 1

8 ․

25

․

2 −

9

14. 3

2 ․

1 −

5 ․ 1 −

2 ․ 1

0

15.

1 −

4 ․ 7

․ 1

6 ․

1 −

7

16. 3

.5 +

8 +

2.5

+ 2

17

. 18

․

8 ․

1 −

2 ․ 1 −

9 18

. 3 −

4 ․ 1

0 ․

16

․

1 −

2

Exam

ple

1Ex

amp

le 2

3558

175

480

4760

1372

13.7

135.

611

8032

4

168

60

Pro

per

ties

will

var

y. S

ee s

tud

ents

’ wo

rk.

Co

mm

uta

tive

Pro

per

ties

Fo

r a

ny n

um

be

rs a

an

d b

, a

+ b

= b

+ a

an

d a

� b

= b

� a

.

Ass

oci

ativ

e P

rop

erti

esF

or

any n

um

be

rs a

, b

, a

nd

c,

(a +

b)

+ c

= a

+ (

b +

c )

an

d (

ab)c

= a

(bc)

.

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

1912

/21/

10

5:20

PM



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

20

Gle

ncoe

Alg

ebra

1

Eva

luat

e ea

ch e

xpre

ssio

n. N

ame

the

pro

per

ty u

sed

in

eac

h s

tep

.

1. 7

(16

÷ 4

2 )

2. 2

[5 -

(15

÷ 3

)]

3. 4

- 3

[7 -

(2

․

3)]

4.

4[8

- (

4 ․

2)]

+ 1

5. 6

+ 9

[10

- 2

(2 +

3)]

6.

2(6

÷ 3

- 1

) ․

1 −

2

7. 1

6 +

8 +

14

+ 1

2

8. 3

6 +

23

+ 1

4 +

7

9. 5

․ 3

․ 4

․ 3

10

. 2 ․

4 ․

5 ․

3

1-3

Skill

s Pr

acti

ceP

rop

ert

ies o

f N

um

bers

=

7(1

6 ÷

16

) S

ub

stit

uti

on

=

2(5

- 5

) S

ub

stit

uti

on

=

7(1

) S

ub

stit

uti

on

=

2(0

) S

ub

stit

uti

on

=

7

Mu

ltip

licat

ive

Iden

tity

=

0

Mu

lt. P

rop

. of

Zer

o

=

4 -

3(7

- 6

) S

ub

stit

uti

on

= 4

(8 -

8)

+ 1

Su

bst

itu

tio

n

= 4

- 3

(1)

Su

bst

itu

tio

n

=

4(0

) +

1

Su

bst

itu

tio

n

= 4

- 3

M

ult

iplic

ativ

e Id

enti

ty

= 0

+ 1

M

ult

. Pro

p. o

f Z

ero

=

1

Su

bst

itu

tio

n

=

1

Ad

dit

ive

Iden

tity

=

6 +

9[1

0 -

2(5

)] S

ub

stit

uti

on

=

2(2

- 1

) �

1 −

2 Su

bst

itu

tio

n

= 6

+ 9

(10

- 1

0)

Su

bst

itu

tio

n

= 2

(1)

�

1 −

2

Su

bst

itu

tio

n

=

6 +

9(0

) S

ub

stit

uti

on

= 6

+ 0

Mu

lt. P

rop

. of

Zer

o

= 2

� 1 −

2

Mu

ltip

licat

ive

Iden

tity

=

6

Ad

dit

ive

Iden

tity

=

1

M

ult

iplic

ativ

e In

vers

e

=

16

+ 1

4 +

8 +

12

C

om

mu

tativ

e (+

) =

36

+ 1

4 +

23

+ 7

C

om

mu

tativ

e (+

)

= (

16 +

14)

+ (

8 +

12)

Ass

oci

ativ

e (+

) =

(36

+ 1

4) +

(23

+ 7

)

A

sso

ciat

ive

(+)

=

30

+ 2

0 o

r 50

S

ub

stit

uti

on

=

50

+ 3

0 o

r 80

Su

bst

ituti

on

=

5 ·

4 · 3

· 3

C

om

mu

tativ

e (×

)

= 2

· 5

· 4 ·

3

Co

mm

uta

tive

(×)

=

(5

· 4)

· (3

· 3) A

sso

ciat

ive

(×)

=

(2

· 5)

· (4

· 3)

Ass

oci

ativ

e (×

)

= 2

0 · 9

or

180

Su

bst

ituti

on

=

10

· 12

or

120

Su

bst

ituti

on

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

2012

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-3

Cha

pte

r 1

21

Gle

ncoe

Alg

ebra

1

Eva

luat

e ea

ch e

xpre

ssio

n. N

ame

the

pro

per

ty u

sed

in

eac

h s

tep

.

1. 2

+ 6

(9 -

32 )

- 2

2.

5(1

4 -

39

÷ 3

) +

4 ․

1 −

4

Eva

luat

e ea

ch e

xpre

ssio

n u

sin

g p

rop

erti

es o

f n

um

ber

s. N

ame

the

pro

per

ty u

sed

in

ea

ch s

tep

.

3. 1

3 +

23

+ 1

2 +

7

4. 6

․ 0

.7 ․

5

5. S

ALE

S A

lth

ea p

aid

$5.0

0 ea

ch f

or t

wo

brac

elet

s an

d la

ter

sold

eac

h f

or $

15.0

0. S

he

paid

$8

.00

each

for

th

ree

brac

elet

s an

d so

ld e

ach

of

them

for

$9.

00.

a.

Wri

te a

n e

xpre

ssio

n t

hat

rep

rese

nts

th

e pr

ofit

Alt

hea

mad

e.

b

. Eva

luat

e th

e ex

pres

sion

. Nam

e th

e pr

oper

ty u

sed

in e

ach

ste

p.

6. S

CH

OO

L SU

PPLI

ES K

rist

en p

urc

has

ed t

wo

bin

ders

th

at c

ost

$1.2

5 ea

ch, t

wo

bin

ders

th

at c

ost

$4.7

5 ea

ch, t

wo

pack

ages

of

pape

r th

at c

ost

$1.5

0 pe

r pa

ckag

e, f

our

blu

e pe

ns

that

cos

t $1

.15

each

, an

d fo

ur

pen

cils

th

at c

ost

$0.3

5 ea

ch.

a.

Wri

te a

n e

xpre

ssio

n t

o re

pres

ent

the

tota

l co

st o

f su

ppli

es b

efor

e ta

x.

b

. Wh

at w

as t

he

tota

l co

st o

f su

ppli

es b

efor

e ta

x?

1-3

Prac

tice

Pro

pert

ies o

f N

um

bers

2(15

-

5)

+

3(

9 -

8)

2(15

− 5

) + 3(

9 -

8)

= 2

(10)

+

3(

1)

=

20

+ 3(

1)

=

20

+ 3

= 2

3

= (

13 +

12

) + (2

3 +

7)

C

om

mu

. Pro

p.

= 2

5 +

30

S

ub

stitu

tio

n=

55

Su

bst

ituti

on

2(1.

25 +

4.7

5 +

1.5

0) +

4(1

.15

+ 0

.35)

= 2

+ 6

(9 -

9)

- 2

S

ub

stitu

tio

n=

2 +

6(0

) -

2

S

ub

stitu

tio

n=

2 +

0 -

2

Mu

lt. P

rop

. of

Zer

o=

2 -

2

Ad

dit

ive

Iden

tity

= 0

S

ub

stitu

tio

n

= 5

(14

- 1

3) +

4 �

1 −

4 S

ub

stitu

tio

n

= 5

(1)

+ 4

� 1 −

4

Su

bst

ituti

on

= 5

+ 4

� 1 −

4 M

ult

iplic

ativ

e Id

enti

ty

= 5

+ 1

M

ult

iplic

ativ

e In

vers

e=

6

Su

bst

ituti

on

$21.

00

= (

6 .

5) .

(0

.7)

Ass

oc.

Pro

p.

= 3

0 .

0.

7 S

ub

stitu

tio

n=

21

Su

bst

ituti

on

Su

bst

ituti

on

S

ub

stitu

tio

n

Mu

ltip

licat

ive

Iden

tity

S

ub

stitu

tio

n

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

2112

/21/

10

5:20

PM



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

1.EX

ERC

ISE

An

nik

a go

es o

n a

wal

k ev

ery

day

in o

rder

to

get

the

exer

cise

her

do

ctor

rec

omm

ends

. If

she

wal

ks a

t a

r

ate

of 3

mil

es p

er h

our

for

1−

3 o

f an

hou

r,

th

en s

he

wil

l h

ave

wal

ked

3 ×

1−

3 m

iles

.

Eva

luat

e th

e ex

pres

sion

an

d n

ame

the

prop

erty

use

d.

2. S

CH

OO

L SU

PPLI

ES A

t a

loca

l sc

hoo

l su

pply

sto

re, a

hig

hli

ghte

r co

sts

$1.2

5, a

ba

llpo

int

pen

cos

ts $

0.80

, an

d a

spir

al

not

eboo

k co

sts

$2.7

5. U

se m

enta

l m

ath

an

d th

e A

ssoc

iati

ve P

rope

rty

of A

ddit

ion

to

fin

d th

e to

tal

cost

if

one

of e

ach

ite

m i

s pu

rch

ased

.

3. M

ENTA

L M

ATH

Th

e tr

ian

gula

r ba

nn

er

has

a b

ase

of 9

cen

tim

eter

s an

d a

hei

ght

of 6

cen

tim

eter

s. U

sin

g th

e fo

rmu

la f

or

area

of

a tr

ian

gle,

th

e ba

nn

er’s

are

a ca

n

b

e ex

pres

sed

as 1 −

2 × 9

×

6. G

abri

elle

f

inds

it

easi

er t

o w

rite

an

d ev

alu

ate

(

1 −

2 × 6

)

× 9

to f

ind

the

area

. Is

G

abri

elle

’s e

xpre

ssio

n e

quiv

alen

t to

th

e ar

ea f

orm

ula

? E

xpla

in.

b

h

4.A

NA

TOM

Y T

he

hu

man

bod

y h

as 6

0 bo

nes

in

th

e ar

ms

and

han

ds, 8

4 bo

nes

in

th

e u

pper

bod

y an

d h

ead,

an

d 62

bon

es

in t

he

legs

an

d fe

et. U

se t

he

Ass

ocia

tive

P

rope

rty

to w

rite

an

d ev

alu

ate

an

expr

essi

on t

hat

rep

rese

nts

th

e to

tal

nu

mbe

r of

bon

es i

n t

he

hu

man

bod

y.

5. T

OLL

RO

AD

S S

ome

toll

hig

hw

ays

asse

ss t

olls

bas

ed o

n w

her

e a

car

ente

red

and

exit

ed. T

he

tabl

e be

low

sh

ows

the

hig

hw

ay t

olls

for

a c

ar e

nte

rin

g an

d ex

itin

g at

a v

arie

ty o

f ex

its.

Ass

um

e th

at

the

toll

for

th

e re

vers

e di

rect

ion

is

the

sam

e.

En

tere

dE

xite

dTo

ll

Exit 5

Exit 8

$0

.50

Exit 8

Exit 1

0$

0.2

5

Exit 1

0E

xit 1

5$

1.0

0

Exit 1

5E

xit 1

8$

0.5

0

Exit 1

8E

xit 2

2$

0.7

5

a.

Ru

nn

ing

an e

rran

d, J

uli

o tr

avel

s fr

om

Exi

t 8

to E

xit

5. W

hat

pro

pert

y w

ould

yo

u u

se t

o de

term

ine

the

toll

?

b

. Gor

don

tra

vels

fro

m h

ome

to w

ork

and

back

eac

h d

ay. H

e li

ves

at E

xit

15 o

n

the

toll

roa

d an

d w

orks

at

Exi

t 22

. W

rite

an

d ev

alu

ate

an e

xpre

ssio

n t

o fi

nd

his

dai

ly t

oll

cost

. Wh

at p

rope

rty

or p

rope

rtie

s di

d yo

u u

se?

Wor

d Pr

oble

m P

ract

ice

Pro

pert

ies o

f N

um

bers

1-3

Cha

pte

r 1

22

Gle

ncoe

Alg

ebra

1

1

mi;

Mu

ltip

licat

ive

Inve

rse

Sym

met

ric

Pro

per

ty o

f E

qu

alit

y

t =

2 ×

($0

.50

+ $0

.75)

;

t =

$2.

50;

Su

bst

ituti

on

Sam

ple

an

swer

: (6

0 +

84

) + 62

=84

+

(6

0 +

62

) =

206

$4.8

0

Y

es;

the

Co

mm

uta

tive

an

d

Ass

oci

ativ

e P

rop

erti

es o

f M

ult

iplic

atio

n a

llow

it t

o b

e re

wri

tten

.

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

2212

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-3

Cha

pte

r 1

23

Gle

ncoe

Alg

ebra

1

Pro

pert

ies o

f O

pera

tio

ns

Let

’s m

ake

up

a n

ew o

per

atio

n a

nd

den

ote

it b

y �

, so

that

a �

b

mea

ns

ba.

2 �

3 =

32

= 9

(1 �

2)

�

3 =

21

�

3 =

32

= 9

1. W

hat

nu

mbe

r is

rep

rese

nte

d by

2 �

3?

2. W

hat

nu

mbe

r is

rep

rese

nte

d by

3 �

2?

3. D

oes

the

oper

atio

n �

app

ear

to b

e co

mm

uta

tive

?

4. W

hat

nu

mbe

r is

rep

rese

nte

d by

(2

�

1)

�

3?

5. W

hat

nu

mbe

r is

rep

rese

nte

d by

2 �

(1

�

3)?

6. D

oes

the

oper

atio

n �

app

ear

to b

e as

soci

ativ

e?

Let

’s m

ake

up

an

oth

er o

per

atio

n a

nd

den

ote

it b

y ⊕

, so

that

a ⊕

b =

(a

+ 1

)(b

+ 1

).

3 ⊕

2 =

(3

+ 1

)(2

+ 1

) =

4 ․

3 =

12

(1 ⊕

2)

⊕ 3

= (

2 ․

3)

⊕ 3

= 6

⊕ 3

= 7

․ 4

= 2

8

7. W

hat

nu

mbe

r is

rep

rese

nte

d by

2 ⊕

3?

8. W

hat

nu

mbe

r is

rep

rese

nte

d by

3 ⊕

2?

9. D

oes

the

oper

atio

n ⊕

app

ear

to b

e co

mm

uta

tive

?

10. W

hat

nu

mbe

r is

rep

rese

nte

d by

(2

⊕ 3

) ⊕

4?

11. W

hat

nu

mbe

r is

rep

rese

nte

d by

2 ⊕

(3

⊕ 4

)?

12. D

oes

the

oper

atio

n ⊕

app

ear

to b

e as

soci

ativ

e?

13. W

hat

nu

mbe

r is

rep

rese

nte

d by

1 �

(3

⊕ 2

)?

14. W

hat

nu

mbe

r is

rep

rese

nte

d by

(1

� 3)

⊕ (

1 �

2)

?

15. D

oes

the

oper

atio

n �

ap

pear

to

be d

istr

ibu

tive

ove

r th

e op

erat

ion

⊕?

16. L

et’s

exp

lore

th

ese

oper

atio

ns

a li

ttle

fu

rth

er. W

hat

nu

mbe

r is

rep

rese

nte

d by

3

� (4

⊕ 2

)?

17. W

hat

nu

mbe

r is

rep

rese

nte

d by

(3

� 4)

⊕ (

3 �

2)

?

18. I

s th

e op

erat

ion

� ac

tual

ly d

istr

ibu

tive

ove

r th

e op

erat

ion

⊕?

1-3

Enri

chm

ent

32 =

9

23 =

8

no

3 9

no

12 12

yes

65 63

no

12

12

yes

3375

585

no

013_

023_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

2312

/21/

10

5:20

PM



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

24

Gle

ncoe

Alg

ebra

1

Eval

uat

e Ex

pre

ssio

ns

Th

e D

istr

ibu

tive

Pro

pert

y ca

n b

e u

sed

to h

elp

eval

uat

e ex

pres

sion

s.

Dis

trib

uti

ve P

rop

erty

Fo

r a

ny n

um

be

rs a

, b

, a

nd

c,

a(b

+ c

) =

ab

+ a

c a

nd

(b

+ c

)a =

ba

+ c

a a

nd

a(b

- c

) =

ab

- a

c a

nd

(b

- c

)a =

ba

- c

a.

U

se t

he

Dis

trib

uti

ve P

rop

erty

to

rew

rite

6(8

+ 10

). T

hen

eva

luat

e.

6(8

+ 1

0) =

6 ․

8 +

6 ․

10

Dis

trib

utive

Pro

pert

y

=

48

+ 6

0 M

ultip

ly.

=

108

A

dd.

U

se t

he

Dis

trib

uti

ve P

rop

erty

to

rew

rite

-2(

3x2

+ 5

x +

1).

T

hen

sim

pli

fy.

-2(

3x2

+ 5

x +

1)

= -

2(3x

2 ) +

(-

2)(5

x) +

(-

2)(1

) D

istr

ibutive

Pro

pert

y

= -

6x2

+ (

-10

x) +

(-

2)

Multip

ly.

= -

6x2

- 1

0x -

2

Sim

plif

y.

Exer

cise

sU

se t

he

Dis

trib

uti

ve P

rop

erty

to

rew

rite

eac

h e

xpre

ssio

n. T

hen

eva

luat

e.

1. 2

0(31

) 2.

12

� 4

1 −

2 3.

5(3

11)

4. 5

(4x

- 9

)

5. 3

(8 -

2x)

6.

12

(6 -

1 −

2 x )

7. 1

2 (2

+ 1 −

2 x )

8. 1 −

4 (12

- 4

t)

9. 3

(2x

- y

)

10. 2

(3x

+ 2

y -

z)

11. (

x -

2)y

12

. 2(3

a -

2b

+ c

)

13.

1 −

4 (16x

- 1

2y +

4z)

14

. (2

- 3

x +

x2 )

3 15

. -2(

2x2

+ 3

x +

1)

1-4

Stud

y G

uide

and

Inte

rven

tion

Th

e D

istr

ibu

tive P

rop

ert

y

Exam

ple

1

Exam

ple

2

20x -

45

24 -

6x

72 -

6x

24 +

6x

3 -

t6x

- 3

y

6

x +

4y -

2z

xy -

2y

6a -

4b

+ 2

c

4

x -

3y +

z

6 -

9x +

3x

2 -

4x2

- 6

x -

2

620

5415

55

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

2412

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-4

Cha

pte

r 1

25

Gle

ncoe

Alg

ebra

1

Sim

plif

y Ex

pre

ssio

ns

A t

erm

is

a n

um

ber,

a va

riab

le, o

r a

prod

uct

or

quot

ien

t of

n

um

bers

an

d va

riab

les.

Lik

e te

rms

are

term

s th

at c

onta

in t

he

sam

e va

riab

les,

wit

h

corr

espo

ndi

ng

vari

able

s h

avin

g th

e sa

me

pow

ers.

Th

e D

istr

ibu

tive

Pro

pert

y an

d pr

oper

ties

of

equ

alit

ies

can

be

use

d to

sim

plif

y ex

pres

sion

s. A

n e

xpre

ssio

n i

s in

sim

ple

st f

orm

if

it i

s re

plac

ed b

y an

eq

uiv

alen

t ex

pres

sion

wit

h n

o li

ke t

erm

s or

par

enth

eses

.

Sim

pli

fy 4

(a2

+ 3

ab)

- a

b.

4(a2

+ 3

ab)

- a

b =

4(a

2 +

3ab

) -

1ab

M

ultip

licative

Identity

=

4a2

+ 1

2ab

- 1

ab

Dis

trib

utive

Pro

pert

y

=

4a2

+ (

12 -

1)a

b D

istr

ibutive

Pro

pert

y

=

4a2

+ 1

1ab

Substitu

tion

Exer

cise

sS

imp

lify

eac

h e

xpre

ssio

n. I

f n

ot p

ossi

ble

, wri

te s

imp

lifi

ed.

1. 1

2a -

a

2. 3

x +

6x

3.

3x

- 1

4. 2

0a +

12a

- 8

5.

3x2

+ 2

x2 6.

-6x

+ 3

x2 +

10x

2

7. 2

p +

1 −

2 q

8. 1

0xy

- 4

(xy

+ x

y)

9. 2

1a +

18a

+ 3

1b -

3b

10. 4

x +

1 −

4 (16x

- 2

0y)

11. 2

- 1

- 6

x +

x2

12. 4

x2 +

3x2

+ 2

x

Wri

te a

n a

lgeb

raic

exp

ress

ion

for

eac

h v

erb

al e

xpre

ssio

n. T

hen

sim

pli

fy,

ind

icat

ing

the

pro

per

ties

use

d.

13. s

ix t

imes

th

e di

ffer

ence

of

2a a

nd

b, i

ncr

ease

d by

4b

14. t

wo

tim

es t

he

sum

of

x sq

uar

ed a

nd

y sq

uar

ed, i

ncr

ease

d by

th

ree

tim

es t

he

sum

of

x sq

uar

ed a

nd

y sq

uar

ed

1-4

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Th

e D

istr

ibu

tive P

rop

ert

y

Exam

ple

1

1a

9x

sim

plifi

ed

3

2a -

85x

2 -

6x +

13x

2

8

x -

5y

1 -

6x +

x

2 7

x2

+ 2

x

s

imp

lifi e

d

2xy

39a

+ 2

8b

2(x

2 +

y

2 ) +

3(

x2

+ y

2 )

2x2

+ 2y

2 +

3x

2 +

3y

2 D

istr

ibu

tive

Pro

per

ty5x

2 +

5y

2 S

ub

stitu

tio

n

= 6

(2a -

b) +

4b

=

12a

- 6

b +

4b

D

istr

ibu

tive

Pro

per

ty=

12a

- 2

b

Su

bst

ituti

on

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

2512

/21/

10

5:20

PM



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

26

Gle

ncoe

Alg

ebra

1

Use

th

e D

istr

ibu

tive

Pro

per

ty t

o re

wri

te e

ach

exp

ress

ion

. Th

en e

valu

ate.

1. 4

(3 +

5)

2.

2(6

+ 1

0)

3. 5

(7 -

4)

4.

(6

- 2

)8

5. 5

․ 8

9

6. 9

․ 9

9

7. 1

5 ․

104

8.

15 (

2 1 −

3 )

Use

th

e D

istr

ibu

tive

Pro

per

ty t

o re

wri

te e

ach

exp

ress

ion

. Th

en e

valu

ate.

9. (

a +

7)2

10

. 7(h

- 1

0)

11. 3

(m +

n)

12

. 2(x

- y

+ 1

)

Sim

pli

fy e

ach

exp

ress

ion

. If

not

pos

sib

le, w

rite

sim

pli

fied

.

13. 2

x +

8x

14

. 17g

+ g

15. 2

x2 +

6x2

16

. 7a2

- 2

a2

17. 3

y2 -

2y

18

. 2(n

+ 2

n)

19. 4

(2b

- b

)

20. 3

q2 +

q -

q2

Wri

te a

n a

lgeb

raic

exp

ress

ion

for

eac

h v

erb

al e

xpre

ssio

n. T

hen

sim

pli

fy,

ind

icat

ing

the

pro

per

ties

use

d.

21. T

he

prod

uct

of

9 an

d t

squ

ared

, in

crea

sed

by t

he

sum

of

the

squ

are

of t

an

d 2

22. 3

tim

es t

he

sum

of

r an

d d

squ

ared

min

us

2 ti

mes

th

e su

m o

f r

and

d s

quar

ed

Skill

s Pr

acti

ceTh

e D

istr

ibu

tive P

rop

ert

y

1-4

4 .

3 +

4 .

5; 3

22

.

6 +

2 .

10;

32

5 .

7 -

5 .

4; 1

56

.

8 -

2 .

8; 3

2

9t

2 +

(t2

+ 2

) =

(9t

2 +

t2 )

+ 2

A

sso

ciat

ive

(+)

=

10

t2 +

2

S

ub

stitu

tio

n

7 .

h -

7 .

10;

7h -

70

5(90

- 1

); 4

459(

100-

1)

; 89

1

15(1

00

+ 4

); 1

560

15 (2

+ 1 −

3 ) ; 3

5

10x

18g

8x2

5a2

sim

plifi

ed

6n

4b2q

2 +

q

3 .

m +

3 .

n;

3m +

3n

2

. x -

2 .

y +

2 .

1; 2

x -

2y +

2

a .

2 +

7 .

2; 2

a +

14

3(r

+ d

2 ) -

2(r

+ d

2 ) =

3r

+ 3

d2

- 2

r -

2d

2 D

istr

ibu

tive

= (3

d2

- 2

d2 )

+ (

3r -

2r)

A

sso

ciat

ive

= d

2 +

r

S

ub

stitu

tio

n

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

2612

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-4

Cha

pte

r 1

27

Gle

ncoe

Alg

ebra

1

Use

th

e D

istr

ibu

tive

Pro

per

ty t

o re

wri

te e

ach

exp

ress

ion

. Th

en e

valu

ate.

1. 9

(7 +

8)

2. 7

(6 -

4)

3. (

4 +

6)1

1

4. 9

․ 4

99

5. 7

․ 1

10

6. 1

6 (4

1 −

4 )

Use

th

e D

istr

ibu

tive

pro

per

ty t

o re

wri

te e

ach

exp

ress

ion

. Th

en s

imp

lify

.

7. (

9 -

p)3

8.

(5y

- 3

)7

9. 1

5 ( f

+ 1 −

3 )

10. 1

6(3b

- 0

.25)

11

. m(n

+ 4

) 12

. (c

- 4

)d

Sim

pli

fy e

ach

exp

ress

ion

. If

not

pos

sib

le, w

rite

sim

pli

fied

.

13. w

+ 1

4w -

6w

14

. 3(5

+ 6

h)

15

. 12b

2 +

9b2

16. 2

5t3

- 1

7t3

17

. 3a2

+ 6

a +

2b2

18. 4

(6p

+ 2

q -

2p)

Wri

te a

n a

lgeb

raic

exp

ress

ion

for

eac

h v

erb

al e

xpre

ssio

n. T

hen

sim

pli

fy,

ind

icat

ing

the

pro

per

ties

use

d.

19. 4

tim

es t

he

diff

eren

ce o

f f

squ

ared

an

d g,

in

crea

sed

by t

he

sum

of

f sq

uar

ed a

nd

2g

20. 3

tim

es t

he

sum

of

x an

d y

squ

ared

plu

s 5

tim

es t

he

diff

eren

ce o

f 2x

an

d y

21. D

ININ

G O

UT

Th

e R

oss

fam

ily

rece

ntl

y di

ned

at

an I

tali

an r

esta

ura

nt.

Eac

h o

f th

e fo

ur

fam

ily

mem

bers

ord

ered

a p

asta

dis

h t

hat

cos

t $1

1.50

, a d

rin

k th

at c

ost

$1.5

0, a

nd

dess

ert

that

cos

t $2

.75.

a.

Wri

te a

n e

xpre

ssio

n t

hat

cou

ld b

e u

sed

to c

alcu

late

th

e co

st o

f th

e R

oss’

din

ner

bef

ore

addi

ng

tax

and

a ti

p.

b

. Wh

at w

as t

he

cost

of

din

ing

out

for

the

Ros

s fa

mil

y?

1-4

Prac

tice

Th

e D

istr

ibu

tive P

rop

ert

y

9

(50

0 -

1)

; 44

91

7(1

00

+ 10

);

770

16 (

4 +

1 −

4 ) ;

68

9

� 3

- p

� 3

; 27

- 3

p

5y �

7 -

3 �

7;

35y -

21

15

�

f +

15

�

1 −

3 ;

15f

+ 5

1

6 �

3b

- 1

6 �

0.2

5;

m �

n +

m �

4;

c �

d -

4 �

d;

48

b -

4

mn

+ 4

m

cd

- 4

d

9w15

+ 1

8h21

b2

8t3

s

imp

lifi e

d

16p

+ 8

q

4(11

.5 +

1.5

+ 2

.75)

$63.

00

= 4

(f 2

- g

) + (f

2 +

2g

) =

4f 2

- 4g

+

f 2

+ 2g

D

istr

ibu

tive

Pro

per

ty=

5f 2

- 2g

S

ub

stitu

tio

n

= 3

(x +

y2 )

+

5(

2x -

y)

= 3

x +

3y

2 +

10

x -

5y

D

istr

ibu

tive

Pro

per

ty=

3y

2 -

5y +

13

x

Su

bst

ituti

on

9

� 7

+ 9

� 8

; 13

5 7

�

6

- 7

� 4

; 14

4

� 1

1 +

6 �

11;

110

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

2712

/21/

10

5:20

PM



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

28

Gle

ncoe

Alg

ebra

1

1.O

PER

A M

r. D

elon

g’s

dram

a cl

ass

is

plan

nin

g a

fiel

d tr

ip t

o se

e M

ozar

t’s

fam

ous

oper

a D

on G

iova

nn

i. T

icke

ts c

ost

$39

each

, an

d th

ere

are

23 s

tude

nts

an

d 2

teac

her

s go

ing

on t

he

fiel

d tr

ip. W

rite

an

d ev

alu

ate

an e

xpre

ssio

n t

o fi

nd

the

grou

p’s

tota

l ti

cket

cos

t.

2. S

ALA

RY I

n a

rec

ent

year

, th

e m

edia

n

sala

ry f

or a

n e

ngi

nee

r in

th

e U

nit

ed

Sta

tes

was

$55

,000

an

d th

e m

edia

n

sala

ry f

or a

com

pute

r pr

ogra

mm

er w

as

$52,

000.

Wri

te a

nd

eval

uat

e an

ex

pres

sion

to

esti

mat

e th

e to

tal

cost

for

a

busi

nes

s to

em

ploy

an

en

gin

eer

and

a pr

ogra

mm

er f

or 5

yea

rs.

3. C

OST

UM

ES I

sabe

lla’

s ba

llet

cla

ss i

s pe

rfor

min

g a

spri

ng

reci

tal

for

wh

ich

th

ey n

eed

butt

erfl

y co

stu

mes

. Eac

h

b

utt

erfl

y co

stu

me

is m

ade

from

3 3 −

5 yar

ds

o

f fa

bric

. Use

th

e D

istr

ibu

tive

Pro

pert

y to

fin

d th

e n

um

ber

of y

ards

of

fabr

ic

nee

ded

for

5 co

stu

mes

. (H

int:

A m

ixed

n

um

ber

can

be

wri

tten

as

the

sum

of

an

inte

ger

and

a fr

acti

on.)

4. F

ENC

ES D

emon

stra

te t

he

Dis

trib

uti

ve

Pro

pert

y by

wri

tin

g tw

o eq

uiv

alen

t ex

pres

sion

s to

rep

rese

nt

the

peri

met

er o

f th

e fe

nce

d do

g pe

n b

elow

.

5. M

ENTA

L M

ATH

Du

rin

g a

mat

h f

acts

sp

eed

con

test

, Jam

al c

alcu

late

d th

e fo

llow

ing

expr

essi

on f

aste

r th

an a

nyo

ne

else

in

his

cla

ss.

19

7 ×

4

Wh

en c

lass

mat

es a

sked

him

how

he

was

ab

le t

o an

swer

so

quic

kly,

he

told

th

em

he

use

d th

e D

istr

ibu

tive

Pro

pert

y to

th

ink

of t

he

prob

lem

dif

fere

ntl

y. W

rite

an

d ev

alu

ate

an e

xpre

ssio

n u

sin

g th

e D

istr

ibu

tive

Pro

pert

y th

at w

ould

hel

p Ja

mal

per

form

th

e ca

lcu

lati

on q

uic

kly.

6. IN

VES

TMEN

TS L

etis

ha

and

Noe

l ea

ch

open

ed a

ch

ecki

ng

acco

un

t, a

sav

ings

ac

cou

nt,

an

d a

coll

ege

fun

d. T

he

char

t be

low

sh

ows

the

amou

nts

th

at t

hey

de

posi

ted

into

eac

h a

ccou

nt.

Ch

ecki

ng

Sav

ing

sC

olle

ge

Let

ish

a$

12

5$

75

$5

0

No

el$

25

0$

50

$5

0

a. I

f N

oel

use

d on

ly $

50 b

ills

wh

en h

e de

posi

ted

the

mon

ey t

o op

en h

is

acco

un

ts, h

ow m

any

$50

bill

s di

d h

e de

posi

t?

b.

If a

ll a

ccou

nts

ear

n 1

.5%

in

tere

st p

er

year

an

d n

o fu

rth

er d

epos

its

are

mad

e, h

ow m

uch

in

tere

st w

ill

Let

ish

a h

ave

earn

ed o

ne

year

aft

er h

er

acco

un

ts w

ere

open

ed?

m

nDo

g Pe

n

Wor

d Pr

oble

m P

ract

ice

Th

e D

istr

ibu

tive P

rop

ert

y

1-4 $3

9(23

+ 2

) =

$97

5

5 (3

3 −

5 ) =

5 (3

+ 3 −

5 ) =

5(3

) +

5 ( 3

−

5 )

= 1

5 +

3 =

18

2n +

2m

an

d 2

(n +

m)

4(20

0 -

3)

= 8

00

- 1

2 =

788

7 $5

0 b

ills

$3.7

5

5(55

,00

0 +

52,

00

0)=

$53

5,0

00

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

2812

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-4

Cha

pte

r 1

29

Gle

ncoe

Alg

ebra

1

Th

e M

aya

Th

e M

aya

wer

e a

Nat

ive

Am

eric

an p

eopl

e w

ho

live

d fr

om a

bou

t 15

00 B

.C. t

o ab

out

1500

A.D

. in

th

e re

gion

th

at t

oday

en

com

pass

es

mu

ch o

f C

entr

al A

mer

ica

and

sou

ther

n M

exic

o. T

hei

r m

any

acco

mpl

ish

men

ts i

ncl

ude

exc

epti

onal

arc

hit

ectu

re, p

otte

ry,

pain

tin

g, a

nd

scu

lptu

re, a

s w

ell

as s

ign

ific

ant

adva

nce

s in

th

e fi

elds

of

astr

onom

y an

d m

ath

emat

ics.

T

he

May

a de

velo

ped

a sy

stem

of

nu

mer

atio

n t

hat

was

bas

ed o

n

the

nu

mbe

r tw

enty

. Th

e ba

sic

sym

bols

of

this

sys

tem

are

sh

own

in

th

e ta

ble

at t

he

righ

t. T

he

plac

es i

n a

May

an n

um

eral

are

wri

tten

ve

rtic

ally

—th

e bo

ttom

pla

ce r

epre

sen

ts o

nes

, th

e pl

ace

abov

e re

pres

ents

tw

enti

es, t

he

plac

e ab

ove

that

rep

rese

nts

20

× 2

0, o

r fo

ur

hu

nd

red

s, a

nd

so o

n. F

or i

nst

ance

, th

is i

s h

ow t

o w

rite

th

e n

um

ber

997

in M

ayan

nu

mer

als.

←

2

×

40

0

=

800

←

9

×

20

=

18

0

←

17

×

1

=

17

99

7

Eva

luat

e ea

ch e

xpre

ssio

n w

hen

v =

•

__

__

_, w

=

• •

• _

__

__

__

__

__

__

__, x

= •

• •

•, y

= �

, an

d

z =

•

•_

__

__

__

__

_. T

hen

wri

te t

he

answ

er i

n M

ayan

nu

mer

als.

Exe

rcis

e 5

is d

one

for

you

.

1. z −

w

2. v

+ w

+ z

−

x

3. x

v

4. v

xy

5. w

x -

z

6. v

z +

xy

7. w

(v +

x +

z)

8.

vw

z

9. z

(wx

- x

)

Tel

l w

het

her

eac

h s

tate

men

t is

tru

e or

fa

lse.

10.

• •

•_

__

__

__

__

_ +

•

__

__

_ =

•

__

__

_ +

•

• •

__

__

__

__

__

11.

• •

•_

__

__

__

__

_

•_

__

__ =

•

__

__

_

• •

•_

__

__

__

__

_

12.

• •

•_

__

__

__

__

__

__

__ =

•

• •

__

__

__

__

__

__

__

__

__

__

13. (

• •

• +

__

__

_)

+ _

__

__

__

__

_ =

• •

• +

(_

__

__ +

__

__

__

__

__)

14. H

ow a

re E

xerc

ises

10

and

11 a

like

? H

ow a

re t

hey

dif

fere

nt?

• •

__

__

__

__

__

__

__

_

• •

• •

__

__

_

• •

0

10

1

11

2

12

3

13

4

14

5

15

6

16

7

17

8

18

9

19

�

• • •

• •

•

• •

• •

__

__

_

•_

__

__

• •

__

__

_

• •

•_

__

__

• •

• •

__

__

_

__

__

__

__

__

•_

__

__

__

__

_

• •

__

__

__

__

__

• •

•_

__

__

__

__

_

• •

• •

__

__

__

__

__

__

__

_

• •

• •

__

__

__

__

__

__

__

__

__

__

__

__

_

•_

__

__

__

__

__

__

__

• •

__

__

__

__

__

__

__

_

• •

• _

__

__

__

__

__

__

__

Enri

chm

ent

1-4 •

• •

t

rue

fals

e

fals

e

tru

e

B

oth

invo

lve

chan

gin

g t

he

ord

er o

f th

e sy

mb

ols

. Exe

rcis

e 10

invo

lves

ch

ang

ing

th

e o

rder

of

the

add

end

s in

an

ad

dit

ion

pro

ble

m. E

xerc

ise

11

invo

lves

ch

ang

ing

th

e o

rder

of

the

dig

its

in a

nu

mer

al.

• •

• •

__

__

_•

• •

• •

�

• •

•

• •

__

__

__

__

__

• •

• •

__

__

__

__

__

__

__

_

•_

__

__

__

__

__

__

__

• •

•

• •

• •

•_

__

__

__

__

__

__

__

• •

�

•_

__

__

__

__

__

__

__

• •

•

�

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

2912

/21/

10

5:20

PM



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

30

Gle

ncoe

Alg

ebra

1

Solv

e Eq

uat

ion

s A

mat

hem

atic

al s

ente

nce

wit

h o

ne

or m

ore

vari

able

s is

cal

led

an

open

sen

ten

ce. O

pen

sen

ten

ces

are

solv

ed b

y fi

ndi

ng

repl

acem

ents

for

th

e va

riab

les

that

re

sult

in

tru

e se

nte

nce

s. T

he

set

of n

um

bers

fro

m w

hic

h r

epla

cem

ents

for

a v

aria

ble

may

be

chos

en i

s ca

lled

th

e re

pla

cem

ent

set.

Th

e se

t of

all

rep

lace

men

ts f

or t

he

vari

able

th

at

resu

lt i

n t

rue

stat

emen

ts i

s ca

lled

th

e so

luti

on s

et f

or t

he

vari

able

. A s

ente

nce

th

at

con

tain

s an

equ

al s

ign

, =, i

s ca

lled

an

eq

uat

ion

.

F

ind

th

e so

luti

on

set

of 3

a +

12

= 3

9 if

th

e re

pla

cem

ent

set

is {

6, 7

, 8, 9

, 10}

.

Rep

lace

a i

n 3

a +

12

= 3

9 w

ith

eac

h

valu

e in

th

e re

plac

emen

t se

t.3(

6) +

12

� 3

9 →

30

≠ 3

9 fa

lse

3(7)

+ 1

2 �

39

→ 3

3 ≠

39

fals

e

3(8)

+ 1

2 �

39

→ 3

6 ≠

39

fals

e

3(9)

+ 1

2 �

39

→ 3

9 =

39

true

3(10

) +

12

� 3

9 →

42

≠ 3

9 fa

lse

Sin

ce a

= 9

mak

es t

he

equ

atio

n

3a +

12

= 3

9 tr

ue,

th

e so

luti

on i

s 9.

Th

e so

luti

on s

et i

s {9

}.

S

olve

2(3

+ 1

) −

3(7

- 4

) =

b.

2(3

+ 1)

−

3(7

- 4)

=

b

Ori

gin

al equation

2(

4)

−

3(3)

= b

Add in t

he n

um

era

tor;

subtr

act

in t

he d

enom

inato

r.

8 −

9 = b

S

implif

y.

Th

e so

luti

on i

s 8 −

9 .

Exer

cise

sF

ind

th

e so

luti

on o

f ea

ch e

qu

atio

n i

f th

e re

pla

cem

ent

sets

are

x =

{

1 −

4 , 1 −

2 , 1,

2, 3

}

an

d y

= {

2, 4

, 6, 8

}.

1. x

+ 1 −

2 = 5 −

2 2.

x +

8 =

11

3.

y -

2 =

6

4. x

2 -

1 =

8

5. y

2 -

2 =

34

6.

x2

+ 5

= 5

1 −

16

7. 2

(x +

3)

= 7

8.

(y

+ 1

)2 =

9

9. y

2 +

y =

20

Sol

ve e

ach

eq

uat

ion

.

10. a

= 2

3 -

1

11. n

= 6

2 -

42

12

. w =

62

․

32

13.

1 −

4 + 5 −

8 = k

14

. 18

- 3

−

2 +

3

= p

15

. t =

15

- 6

−

27 -

24

16. 1

8.4

- 3

.2 =

m

17. k

= 9

.8 +

5.7

18

. c =

3 1 −

2 + 2

1 −

4

Stud

y G

uide

and

Inte

rven

tion

Eq

uati

on

s

1-5

Exam

ple

1Ex

amp

le 2

{2}

{3}

{8}

{3}

{6} {2}

{4}

720

324

33

15.2

15.5

5 3 −

4

7 −

8 { 1 −

2 }

{ 1 −

4 }

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

3012

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-5

Cha

pte

r 1

31

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Eq

uati

on

s

1-5

Solv

e Eq

uat

ion

s w

ith

Tw

o V

aria

ble

s S

ome

equ

atio

ns

con

tain

tw

o va

riab

les.

It

is

ofte

n u

sefu

l to

mak

e a

tabl

e of

val

ues

in

wh

ich

you

can

use

su

bsti

tuti

on t

o fi

nd

the

corr

espo

ndi

ng

valu

es o

f th

e se

con

d va

riab

le.

MU

SIC

DO

WN

LOA

DS

Em

ily

bel

ongs

to

an I

nte

rnet

mu

sic

serv

ice

that

ch

arge

s $5

.99

per

mon

th a

nd

$0.

89 p

er s

ong.

Wri

te a

nd

sol

ve a

n e

qu

atio

n t

o fi

nd

th

e to

tal

amou

nt

Em

ily

spen

ds

if s

he

dow

nlo

ads

10 s

ongs

th

is m

onth

.

Th

e co

st o

f th

e m

usi

c se

rvic

e is

a f

lat

rate

. Th

e va

riab

le i

s th

e n

um

ber

of s

ongs

sh

e do

wn

load

s. T

he

tota

l co

st i

s th

e pr

ice

of t

he

serv

ice

plu

s $0

.89

tim

es t

he

nu

mbe

r of

son

gs.

C =

0.8

9n +

5.9

9

To

fin

d th

e to

tal

cost

for

th

e m

onth

, su

bsti

tute

10

for

n i

n t

he

equ

atio

n.

C =

0.8

9n +

5.9

9

Ori

gin

al equation

=

0.8

9(10

) +

5.9

9

Substitu

te 1

0 for

n.

=

8.9

0 +

5.9

9 M

ultip

ly.

=

14.

89

Add.

Em

ily

spen

t $1

4.89

on

mu

sic

dow

nlo

ads

in o

ne

mon

th.

Exer

cise

s 1

. AU

TO R

EPA

IR A

mec

han

ic r

epai

rs M

r. E

stes

’ car

. Th

e am

oun

t fo

r pa

rts

is $

48.0

0 an

d th

e ra

te f

or t

he

mec

han

ic i

s $4

0.00

per

hou

r. W

rite

an

d so

lve

an e

quat

ion

to

fin

d th

e to

tal

cost

of

repa

irs

to M

r. E

stes

’ car

if

the

mec

han

ic w

orks

for

1.5

hou

rs.

2. S

HIP

PIN

G F

EES

Mr.

Moo

re p

urc

has

es a

n i

nfl

atab

le k

ayak

wei

ghin

g 30

pou

nds

fro

m a

n

onli

ne

com

pan

y. T

he

stan

dard

rat

e to

sh

ip h

is p

urc

has

e is

$2.

99 p

lus

$0.8

5 pe

r po

un

d.

Wri

te a

nd

solv

e an

equ

atio

n t

o fi

nd

the

tota

l am

oun

t M

r. M

oore

wil

l pa

y to

hav

e th

e ka

yak

ship

ped

to h

is h

ome.

3. S

OU

ND

Th

e sp

eed

of s

oun

d is

108

8 fe

et p

er s

econ

d at

sea

lev

el a

t 32

° F

. Wri

te a

nd

solv

e an

equ

atio

n t

o fi

nd

the

dist

ance

sou

nd

trav

els

in 8

sec

onds

un

der

thes

e co

ndi

tion

s.

4. V

OLL

EYB

ALL

You

r to

wn

dec

ides

to

buil

d a

voll

eyba

ll c

ourt

. If

the

cou

rt i

s ap

prox

imat

ely

40 b

y 70

fee

t an

d it

s su

rfac

e is

of

san

d, o

ne

foot

dee

p, t

he

cou

rt w

ill

requ

ire

abou

t 16

6 to

ns

of s

and.

A l

ocal

san

d pi

t se

lls

san

d fo

r $1

1.00

per

ton

wit

h a

de

live

ry c

har

ge o

f $3

.00

per

ton

. Wri

te a

nd

solv

e an

equ

atio

n t

o fi

nd

the

tota

l co

st o

f th

e sa

nd

for

this

cou

rt.

Exam

ple

C =

48

+ 4

0x; $

108.

00

C =

2.9

9 +

0.8

5x; $2

8.49

d =

108

8x; 8

704

ft

C =

14x

; $23

24.0

0

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

3112

/21/

10

5:20

PM



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

32

Gle

ncoe

Alg

ebra

1

Fin

d t

he

solu

tion

of

each

eq

uat

ion

if

the

rep

lace

men

t se

ts a

re A

= {

4, 5

, 6, 7

, 8}

and

B =

{9,

10,

11,

12,

13}

.

1. 5

a -

9 =

26

2.

4a

- 8

= 1

6

3. 7

a +

21

= 5

6

4. 3

b +

15

= 4

8

5. 4

b -

12

= 2

8

6. 36

−

b -

3 =

0

Fin

d t

he

solu

tion

of

each

eq

uat

ion

usi

ng

the

give

n r

epla

cem

ent

set.

7.

1 −

2 + x

= 5 −

4 ; {

1 −

2 , 3 −

4 , 1,

5 −

4 }

8. x

+ 2 −

3 = 13

−

9 ; { 5

−

9 , 2 −

3 , 7 −

9 }

9.

1 −

4 (x +

2)

= 5 −

6 ; {

2 −

3 , 3 −

4 , 5 −

4 , 4 −

3 }

10. 0

.8(x

+ 5

) =

5.2

; {1.

2, 1

.3, 1

.4, 1

.5}

Sol

ve e

ach

eq

uat

ion

.

11. 1

0.4

- 6

.8 =

x

12. y

= 2

0.1

- 1

1.9

13.

46 -

15

−

3 +

28

=

a

14. c

=

6 +

18

−

31 -

25

15.

2(4)

+ 4

−

3(3

- 1)

=

b

16.

6(7

- 2

) −

3(8)

+ 6 =

n

17. S

HO

PPIN

G O

NLI

NE

Jen

nif

er i

s pu

rch

asin

g C

Ds

and

a n

ew C

D p

laye

r fr

om a

n o

nli

ne

stor

e. S

he

pays

$10

for

eac

h C

D, a

s w

ell

as $

50 f

or t

he

CD

pla

yer.

Wri

te a

nd

solv

e an

eq

uat

ion

to

fin

d th

e to

tal

amou

nt

Jen

nif

er s

pen

t if

sh

e bu

ys 4

CD

s an

d a

CD

pla

yer

from

th

e st

ore.

18. T

RA

VEL

An

air

plan

e ca

n t

rave

l at

a s

peed

of

550

mil

es p

er h

our.

Wri

te a

nd

solv

e an

eq

uat

ion

to

fin

d th

e ti

me

it w

ill

take

to

fly

from

Lon

don

to

Mon

trea

l, a

dist

ance

of

appr

oxim

atel

y 33

00 m

iles

.

Skill

s Pr

acti

ceE

qu

ati

on

s

1-5

76

511

1012

1.5

3.6

8.2

14

21

7 −

9

4 −

3

3 −

4

50 +

10

(4)

= t;

t =

$

90

330

0 −

550

= t;

t =

6

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

3212

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-5

Cha

pte

r 1

33

Gle

ncoe

Alg

ebra

1

Fin

d t

he

solu

tion

of

each

eq

uat

ion

if

the

rep

lace

men

t se

ts a

re a

= {0

, 1 −

2 , 1,

3 −

2 , 2 }

and

b =

{3,

3.5

, 4, 4

.5, 5

}.

1. a

+ 1 −

2 = 1

2.

4b

- 8

= 6

3.

6a

+ 1

8 =

27

4. 7

b -

8 =

16.

5

5. 1

20 -

28a

= 7

8

6. 28

−

b +

9 =

16

Sol

ve e

ach

eq

uat

ion

.

7. x

= 1

8.3

- 4

.8

8. w

= 2

0.2

- 8

.95

9.

37

- 9

−

18 -

11

= d

10.

97 -

25

−

41 -

23

= k

11

. y =

4(22

- 4)

−

3(6)

+

6

12

. 5(

2 2 ) +

4(

3)

−

4( 2 3

-

4)

=

p

13. T

EAC

HIN

G A

tea

cher

has

15

wee

ks i

n w

hic

h t

o te

ach

six

ch

apte

rs. W

rite

an

d th

en s

olve

an

equ

atio

n t

hat

rep

rese

nts

th

e n

um

ber

of l

esso

ns

the

teac

her

mu

st t

each

per

wee

k if

th

ere

is a

n a

vera

ge o

f 8.

5 le

sson

s pe

r ch

apte

r.

14. C

ELL

PHO

NES

Gab

riel

pay

s $4

0 a

mon

th f

or b

asic

cel

l ph

one

serv

ice.

In

add

itio

n,

Gab

riel

can

sen

d te

xt m

essa

ges

for

$0.2

0 ea

ch. W

rite

an

d so

lve

an e

quat

ion

to

fin

d th

e to

tal

amou

nt

Gab

riel

spe

nt

this

mon

th i

f h

e se

nds

40

text

mes

sage

s.

1-5

Prac

tice

Eq

uati

on

s

3.5

3.5

4

3 −

2 1 −

2

3 −

2

n =

6(8.

5)

−

15

; 3.

4 13.5

11.2

54

23

4

c =

40

+ 0

.20(

40);

$48

.00

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

3312

/21/

10

5:20

PM



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

34

Gle

ncoe

Alg

ebra

1

1.TI

ME

Th

ere

are

6 ti

me

zon

es i

n t

he

Un

ited

Sta

tes.

Th

e ea

ster

n p

art

of t

he

U.S

., in

clu

din

g N

ew Y

ork

Cit

y, i

s in

th

e E

aste

rn T

ime

Zon

e. T

he

cen

tral

par

t of

th

e U

.S.,

incl

udi

ng

Dal

las,

is

in t

he

Cen

tral

Tim

e Z

one,

wh

ich

is

one

hou

r be

hin

d E

aste

rn T

ime.

San

Die

go i

s in

th

e P

acif

ic T

ime

Zon

e, w

hic

h i

s 3

hou

rs

beh

ind

Eas

tern

Tim

e. W

rite

an

d so

lve

an

equ

atio

n t

o de

term

ine

wh

at t

ime

it i

s in

C

alif

orn

ia i

f it

is

noo

n i

n N

ew Y

ork.

2. F

OO

D P

art

of t

he

Nu

trit

ion

Fac

ts l

abel

fr

om a

box

of

mac

aron

i an

d ch

eese

is

show

n b

elow

.

Nu

trit

ion

Fac

tsS

erv

ing

Siz

e 1

cu

p (

22

8g

)

Se

rvin

gs P

er

Co

nta

ine

r 2

Am

ount P

er

Serv

ing

Cal

ori

es 2

50

Ca

lorie

s f

rom

Fa

t 1

10

To

tal F

at 1

2g

Sa

tura

ted

Fa

t 3

g

Tran

s F

at

3g

Ch

ole

ster

ol 3

0m

g

% D

aily

Val

ue

*

18 %

15 %

10 %

W

rite

an

d so

lve

an e

quat

ion

to

dete

rmin

e h

ow m

any

serv

ings

of

this

ite

m A

lisa

can

ea

t ea

ch d

ay i

f sh

e w

ants

to

con

sum

e ex

actl

y 45

gra

ms

of c

hol

este

rol.

3. C

RA

FTS

You

nee

d 30

yar

ds o

f ya

rn t

o cr

och

et a

sm

all

scar

f. C

her

yl b

ough

t a

100-

yard

bal

l of

yar

n a

nd

has

alr

eady

u

sed

10 y

ards

. Wri

te a

nd

solv

e an

eq

uat

ion

to

fin

d h

ow m

any

scar

ves

she

can

cro

chet

if

she

plan

s on

usi

ng

up

the

enti

re b

all.

4.PO

OLS

Th

ere

are

appr

oxim

atel

y 20

2 ga

llon

s pe

r cu

bic

yard

of

wat

er. W

rite

an

d so

lve

an e

quat

ion

for

th

e n

um

ber

of

gall

ons

of w

ater

th

at f

ill

a po

ol w

ith

a

volu

me

of 1

161

cubi

c fe

et. (

Hin

t: T

her

e ar

e 27

cu

bic

feet

per

cu

bic

yard

.)

5. V

EHIC

LES

Rec

entl

y de

velo

ped

hyb

rid

cars

con

tain

bot

h a

n e

lect

ric

and

a ga

soli

ne

engi

ne.

Hyb

rid

car

batt

erie

s st

ore

extr

a en

ergy

, su

ch a

s th

e en

ergy

pr

odu

ced

by b

raki

ng.

Sin

ce t

he

car

can

u

se t

his

sto

red

ener

gy t

o po

wer

th

e ca

r, th

e h

ybri

d u

ses

less

gas

olin

e pe

r m

ile

than

car

s po

wer

ed o

nly

by

gaso

lin

e.

Su

ppos

e a

new

hyb

rid

car

is r

ated

to

driv

e 45

mil

es p

er g

allo

n o

f ga

soli

ne.

a. I

t co

sts

$40

to f

ill

the

gaso

lin

e ta

nk

wit

h g

as t

hat

cos

ts $

3.00

per

gal

lon

. W

rite

an

d so

lve

an e

quat

ion

to

fin

d th

e di

stan

ce t

he

hyb

rid

car

can

go

usi

ng

one

tan

k of

gas

.

b. W

rite

an

d so

lve

an e

quat

ion

to

fin

d th

e co

st o

f ga

soli

ne

per

mil

e fo

r th

is h

ybri

d ca

r. R

oun

d to

th

e n

eare

st c

ent.

1-5

Wor

d Pr

oble

m P

ract

ice

Eq

uati

on

s

12 -

c =

3;

9:0

0 A

M

c =

45

−

30 ;

1.5

serv

ing

s

100

- 1

0 =

30s

;

g

= g

al in

po

ol

g

= 11

61

−

27

× 2

02;

8686

gal

40

−

3.0

0 (45

) =

m;

600

mi

3.0

0 −

45

= c

; ≈

7¢ p

er m

i

3 sc

arve

s

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

3412

/21/

10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-5

Cha

pte

r 1

35

Gle

ncoe

Alg

ebra

1

So

luti

on

Sets

Con

side

r th

e fo

llow

ing

open

sen

ten

ce.

It i

s th

e n

ame

of a

mon

th b

etw

een

Mar

ch a

nd

July

.

You

kn

ow t

hat

a r

epla

cem

ent

for

the

vari

able

It

mu

st b

e fo

un

d in

ord

er t

o de

term

ine

if t

he

sen

ten

ce i

s tr

ue

or f

alse

. If

It i

s re

plac

ed b

y ei

ther

Apr

il, M

ay, o

r Ju

ne,

th

e se

nte

nce

is

tru

e.T

he

set

{Apr

il, M

ay, J

un

e} i

s ca

lled

th

e so

luti

on s

et o

f th

e op

en s

ente

nce

giv

en a

bove

. Th

is

set

incl

ude

s al

l re

plac

emen

ts f

or t

he

vari

able

th

at m

ake

the

sen

ten

ce t

rue.

Wri

te t

he

solu

tion

set

for

eac

h o

pen

sen

ten

ce.

1. I

t is

th

e n

ame

of a

sta

te b

egin

nin

g w

ith

th

e le

tter

A.

2. I

t is

a p

rim

ary

colo

r.

3. I

ts c

apit

al i

s H

arri

sbu

rg.

4. I

t is

a N

ew E

ngl

and

stat

e.

5. x

+ 4

= 1

0

6. I

t is

th

e n

ame

of a

mon

th t

hat

con

tain

s th

e le

tter

r.

7. S

he

was

th

e w

ife

of a

U.S

. Pre

side

nt

wh

o se

rved

in

th

e ye

ars

2000

-20

10.

8. I

t is

an

eve

n n

um

ber

betw

een

1 a

nd

13.

9. 3

1 =

72

- k

10. I

t is

th

e sq

uar

e of

2, 3

, or

4.

Wri

te a

n o

pen

sen

ten

ce f

or e

ach

sol

uti

on s

et.

11. {

A, E

, I, O

, U}

12. {

1, 3

, 5, 7

, 9}

13. {

Jun

e, J

uly

, Au

gust

}

14. {

Atl

anti

c, P

acif

ic, I

ndi

an, A

rcti

c}

Enri

chm

ent

1-5

{

Ala

bam

a, A

lask

a, A

rizo

na,

Ark

ansa

s}

{

red

, yel

low

, blu

e}

{Pen

nsy

lvan

ia}

{Mai

ne,

New

Ham

psh

ire,

{6}

{

Jan

, Feb

, Mar

, Ap

r, S

ept,

Oct

, No

v, D

ec}

{

Hill

ary

Clin

ton

, Lau

ra B

ush

, Mic

hel

le O

bam

a}

{2, 4

, 6, 8

, 10,

12}

{41}

{4, 9

, 16}

It is

a v

ow

el.

It is

an

od

d n

um

ber

bet

wee

n 0

an

d 1

0.

It is

a s

um

mer

mo

nth

.

It is

an

oce

an.

V

erm

on

t, M

assa

chu

sett

s, R

ho

de

Isla

nd

, Co

nn

ecti

cut}

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

3512

/21/

10

5:20

PM



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

A s

prea

dshe

et is

a t

ool f

or w

orki

ng w

ith

and

anal

yzin

g nu

mer

ical

dat

a. T

he d

ata

is e

nte

red

into

a

tabl

e in

wh

ich

eac

h r

ow i

s n

um

bere

d an

d ea

ch c

olu

mn

is

labe

led

by a

lett

er. Y

ou c

an u

se a

sp

read

shee

t to

find

sol

utio

ns o

f ope

n se

nten

ces.

Exer

cise

s

Use

a s

pre

adsh

eet

to f

ind

th

e so

luti

on o

f ea

ch e

qu

atio

n u

sin

g th

e gi

ven

re

pla

cem

ent

set.

1. x

+

7.

5 =

18

.3; {

8.8,

9.8

, 10.

8, 1

1.8}

2.

6(x

+ 2

) =

18;

{0,

1, 2

, 3, 4

, 5}

3. 4

x +

1

= 17

; {0,

1, 2

, 3, 4

, 5}

4. 4

.9 -

x =

2.

2; {

2.6,

2.7

, 2.8

, 2.9

, 3.0

}

5. 2

.6x

= 16

.9; {

6.1,

6.3

, 6.5

, 6.7

, 6.9

} 6.

12x

- 8

=

22

; {2.

1, 2

.2, 2

.3, 2

.4, 2

.5, 2

.6}

U

se a

sp

read

shee

t to

fin

d t

he

solu

tion

for

4(

x -

3)

=

32

if

the

rep

lace

men

t se

t is

{7,

8, 9

, 10,

11,

12}

.

You

can

sol

ve t

he

open

sen

ten

ce b

y re

plac

ing

x w

ith

eac

h v

alu

e in

th

e re

plac

emen

t se

t.

Ste

p 1

U

se t

he

firs

t co

lum

n o

f th

e sp

read

shee

t fo

r th

e re

plac

emen

t se

t. E

nte

r th

e n

um

bers

usi

ng

the

form

ula

bar

. Cli

ck o

n a

cel

l of

th

e sp

read

shee

t,

type

th

e n

um

ber

and

pres

s E

NT

ER

.

Ste

p 2

T

he

seco

nd

colu

mn

con

tain

s th

e fo

rmu

la f

or

the

left

sid

e of

th

e op

en s

ente

nce

. To

ente

r a

form

ula

, en

ter

an e

qual

s si

gn f

ollo

wed

by

the

form

ula

. Use

th

e n

ame

of t

he

cell

con

tain

ing

each

rep

lace

men

t va

lue

to e

valu

ate

the

form

ula

for

th

at v

alu

e. F

or e

xam

ple,

in

cel

l B

2, t

he

form

ula

con

tain

s A

2 in

pla

ce o

f x.

Th

e so

luti

on i

s th

e va

lue

of x

for

wh

ich

th

e fo

rmu

la i

n

colu

mn

B r

etu

rns

32. T

he

solu

tion

is

11.

A

1 4 5 6 7 8 2 3

B

C

4(x

- 3)

=

4*(A

2-3)

=

4*(A

3-3)

=

4*(A

4-3)

=

4*(A

5-3)

=

4*(A

6-3)

=

4*(A

7-3)

x 7 8 9 10

11

12

Sh

eet

1 S

hee

t 2

Sh

eet

3

A

1 4 5 6 7 8 2 3

B

C

4(x

- 3)

x

7 8 9 10

11

12

16

20

24

28

32

36

Sh

eet

1 S

hee

t 2

Sh

eet

3

1-5

Spre

adsh

eet

Act

ivit

yS

olv

ing

Op

en

Sen

ten

ces

Exam

ple

Cha

pte

r 1

36

Gle

ncoe

Alg

ebra

1

{1

0.8}

{1

}

{4

}

{2.7

}

{6

.5}

{2

.5}

024_

041_

ALG

1_A

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M_C

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6049

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10

5:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-6

Cha

pte

r 1

37

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

Rela

tio

ns

1-6

Rep

rese

nt

a R

elat

ion

A r

elat

ion

is

a se

t of

ord

ered

pai

rs. A

rel

atio

n c

an b

e re

pres

ente

d by

a s

et o

f or

dere

d pa

irs,

a t

able

, a g

raph

, or

a m

app

ing.

A m

appi

ng

illu

stra

tes

how

eac

h e

lem

ent

of t

he

dom

ain

is

pair

ed w

ith

an

ele

men

t in

th

e ra

nge

. Th

e se

t of

fir

st

nu

mbe

rs o

f th

e or

dere

d pa

irs

is t

he

dom

ain

. Th

e se

t of

sec

ond

nu

mbe

rs o

f th

e or

dere

d pa

irs

is t

he

ran

ge o

f th

e re

lati

on.

a.

Exp

ress

th

e re

lati

on {

(1, 1

), (

0, 2

), (

3, -

2)}

as a

tab

le, a

gra

ph

, an

d

a m

app

ing.

x

y

11

02

3-

2

x

y O

X

Y

1 0 3

1 2-

2

b. D

eter

min

e th

e d

omai

n a

nd

th

e ra

nge

of

the

rela

tion

.

Th

e do

mai

n f

or t

his

rel

atio

n i

s {0

, 1, 3

}. T

he

ran

ge f

or t

his

rel

atio

n i

s {-

2, 1

, 2}.

Exer

cise

s 1A

. Exp

ress

th

e re

lati

on {

(-2,

-

1), (3,

3)

, (4,

3)

} as

a ta

ble,

a

grap

h, an

d a

map

pin

g.

1B. D

eter

min

e th

e do

mai

n a

nd

the

ran

ge o

f th

e re

lati

on.

Exam

ple

x

y

O

XY

-2 3 4

-1 3

xy

-2

-1

33

43

do

mai

n {-

2, 3

, 4};

ra

ng

e {-

1, 3

}

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

3712

/21/

10

5:20

PM



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

38

Gle

ncoe

Alg

ebra

1

Gra

ph

s o

f a

Rel

atio

n T

he

valu

e of

th

e va

riab

le i

n a

rel

atio

n t

hat

is

subj

ect

to c

hoi

ce i

s ca

lled

th

e in

dep

end

ent

vari

able

. Th

e va

riab

le w

ith

a v

alu

e th

at i

s de

pen

den

t on

th

e va

lue

of t

he

inde

pen

den

t va

riab

le i

s ca

lled

th

e d

epen

den

t va

riab

le. T

hes

e re

lati

ons

can

be

grap

hed

wit

hou

t a

scal

e on

eit

her

axi

s, a

nd

inte

rpre

ted

by a

nal

yzin

g th

e sh

ape.

T

he

grap

h b

elow

re

pre

sen

ts t

he

hei

ght

of a

foo

tbal

l af

ter

it i

s k

ick

ed d

own

fiel

d. I

den

tify

th

e in

dep

end

ent

and

th

e d

epen

den

t va

riab

le f

or t

he

rela

tion

. Th

en d

escr

ibe

wh

at h

app

ens

in t

he

grap

h.

Th

e in

depe

nde

nt

vari

able

is

tim

e, a

nd

the

depe

nde

nt

vari

able

is

hei

ght.

Th

e fo

otba

ll

star

ts o

n t

he

grou

nd

wh

en i

t is

kic

ked.

It

gain

s al

titu

de u

nti

l it

rea

ches

a m

axim

um

h

eigh

t, t

hen

it

lose

s al

titu

de u

nti

l it

fal

ls t

o th

e gr

oun

d.

Tim

e

Hei

gh

t

T

he

grap

h b

elow

re

pre

sen

ts t

he

pri

ce o

f st

ock

ove

r ti

me.

Id

enti

fy t

he

ind

epen

den

t an

d

dep

end

ent

vari

able

for

th

e re

lati

on.

Th

en d

escr

ibe

wh

at h

app

ens

in t

he

grap

h.

Th

e in

depe

nde

nt

vari

able

is

tim

e an

d th

e de

pen

den

t va

riab

le i

s pr

ice.

Th

e pr

ice

incr

ease

s st

eadi

ly, t

hen

it

fall

s, t

hen

in

crea

ses,

th

en f

alls

aga

in.

Tim

e

Pric

e

Exer

cise

sId

enti

fy t

he

ind

epen

den

t an

d d

epen

den

t va

riab

les

for

each

rel

atio

n. T

hen

des

crib

e w

hat

is

hap

pen

ing

in e

ach

gra

ph

.

1. T

he

grap

h r

epre

sen

ts t

he

spee

d of

a c

ar a

s it

tra

vels

to

the

groc

ery

st

ore.

2. T

he

grap

h r

epre

sen

ts t

he

bala

nce

of

a sa

vin

gs a

ccou

nt

over

tim

e.

3. T

he

grap

h r

epre

sen

ts t

he

hei

ght

of a

bas

ebal

l af

ter

it i

s h

it.

Tim

e

Hei

gh

t

Tim

e

Acc

ou

nt

Bal

ance

(do

llars

)

Tim

e

Spee

d

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Rela

tio

ns

1-6

Exam

ple

1Ex

amp

le 2

I

nd

: ti

me;

dep

: sp

eed

. Th

e ca

r st

arts

fro

m a

sta

nd

still

, ac

cele

rate

s, t

hen

tra

vels

at

a co

nst

ant

spee

d f

or

a w

hile

.Th

en it

slo

ws

do

wn

an

d s

top

s.

I

nd

: ti

me;

dep

: b

alan

ce. T

he

acco

un

t b

alan

ce h

as a

n

init

ial v

alu

e th

en it

incr

ease

s as

dep

osi

ts a

re m

ade.

It

then

sta

ys t

he

sam

e fo

r a

wh

ile, a

gai

n in

crea

ses,

an

d

last

ly g

oes

to

0 a

s w

ith

dra

wal

s ar

e m

ade.

I

nd

: ti

me;

dep

: h

eig

ht.

Th

e b

all i

s h

it a

cer

tain

hei

gh

t ab

ove

th

e g

rou

nd

. Th

e h

eig

ht

of

the

bal

l in

crea

ses

un

til

it r

each

es it

s m

axim

um

val

ue,

th

en t

he

hei

gh

t d

ecre

ases

u

nti

l th

e b

all h

its

the

gro

un

d.

024_

041_

ALG

1_A

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M_C

01_C

R_6

6049

8.in

dd

3812

/21/

10

5:21

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-6

Cha

pte

r 1

39

Gle

ncoe

Alg

ebra

1

Skill

s Pr

acti

ceR

ela

tio

ns

1-6

Exp

ress

eac

h r

elat

ion

as

a ta

ble

, a g

rap

h, a

nd

a m

app

ing.

Th

en d

eter

min

e th

e d

omai

n a

nd

ran

ge.

1. {

(-1,

-1)

, (1,

1),

(2, 1

), (3

, 2)}

x

y

O

X

Y

-1 1 2

-1 1 2 3

2. {

(0, 4

), (-

4, -

4), (

-2,

3),

(4, 0

)}

3. {

(3, -

2), (

1, 0

), (-

2, 4

), (3

, 1)}

x

y

O

XY

-2 0 4 1

3 1-

2

Iden

tify

th

e in

dep

end

ent

and

dep

end

ent

vari

able

s fo

r ea

ch r

elat

ion

.

4. T

he

mor

e h

ours

Mar

ibel

wor

ks a

t h

er jo

b, t

he

larg

er h

er p

aych

eck

beco

mes

.

5. I

ncr

easi

ng

the

pric

e of

an

ite

m d

ecre

ases

th

e am

oun

t of

peo

ple

wil

lin

g to

bu

y it

.

x

y

O

xy

0

4

-4

-4

-2

3

4

0

xy

3

-2

1

0

-2

4

3

1

xy

-1

-1

1

1

2

1

3

2 D

= {

-1,

1, 2

, 3};

R =

{-

1, 1

, 2}

D =

{-

4, -

2, 0

, 4};

R =

{-

4, 0

, 3, 4

}

XY

0-

4-

2 4

4-

4 3 0

D =

{-

2, 1

, 3};

R =

{-

2, 0

, 1, 4

}

ind

epen

den

t: h

ou

rs w

ork

ed, d

epen

den

t: s

ize

of

pay

chec

k

ind

epen

den

t: p

rice

of

an it

em,

dep

end

ent:

nu

mb

er o

f p

eop

le w

illin

g t

o b

uy it

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

3912

/21/

10

5:21

PM



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

40

Gle

ncoe

Alg

ebra

1

1-6

Prac

tice

R

ela

tio

ns

1. E

xpre

ss {

(4, 3

), (-

1, 4

), (3

, -2)

, (-

2, 1

)} a

s a

tabl

e, a

gra

ph, a

nd

a m

appi

ng.

Th

en

dete

rmin

e th

e do

mai

n a

nd

ran

ge.

X

Y

43

-1

43

-2

-2

1

x

y

O

Des

crib

e w

hat

is

hap

pen

ing

in e

ach

gra

ph

.

2. T

he

grap

h b

elow

rep

rese

nts

th

e h

eigh

t of

a

3.

T

he

grap

h b

elow

rep

rese

nts

a

tsu

nam

i as

it

trav

els

acro

ss a

n o

cean

.

st

ude

nt

taki

ng

an e

xam

.

Exp

ress

th

e re

lati

on s

how

n i

n e

ach

tab

le, m

app

ing,

or

grap

h a

s a

set

of o

rder

ed

pai

rs.

4.

XY

09

-8

3

2-

6

14

5.

X

Y 5-

5 3 7

9-

6 4 8

6.

x

y

O

7. B

ASE

BA

LL T

he

grap

h s

how

s th

e n

um

ber

of h

ome

run

s h

it b

y A

ndr

uw

Jon

es o

f th

e A

tlan

ta B

rave

s.

Exp

ress

th

e re

lati

on a

s a

set

of o

rder

ed p

airs

. T

hen

des

crib

e th

e do

mai

n a

nd

ran

ge.

Tim

e

Nu

mb

er o

fQ

ues

tio

ns

An

swer

ed

Tim

e

Hei

gh

t

2432 283640444852

’02

’03

’04

’05

’06

’07

0

An

dru

w J

on

es’

Ho

me R

un

s

Home Runs

Yea

r

XY 3 4

-2 1

4-

1 3-

2

D =

{-

2, -

1, 3

, 4};

R =

{-

2, 1

, 3, 4

}

{

(0, 9

), (-

8, 3

),

{(9,

5),

(9, 3

), (-

6, -

5),

{(-

3, -

1), (

-2,

-2)

,(2

, -6)

, (1,

4)}

(4, 3

), (8

, -5)

, (8,

7)}

(-

1, -

3), (

1, 1

), (2

, 1)}

T

he

lon

ger

it t

rave

ls, t

he

hig

her

T

he

stu

den

t re

pea

ted

ly a

nsw

ers

the

tsu

nam

i bec

om

es.

q

ues

tio

ns

and

th

en p

ause

s.

{

('02,

35)

, ('03

, 36)

, ('04

, 29)

, ('05

, 51)

, ('0

6, 4

1), (

'07

, 26)

};

D =

{'

02, '

03, '

04, '

05, '

06, '

07};

R

=

{2

6, 2

9, 3

5, 3

6, 4

1, 5

1}

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

4012

/21/

10

5:21

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-6

Cha

pte

r 1

41

Gle

ncoe

Alg

ebra

1

1.H

EALT

H T

he

Am

eric

an H

eart

A

ssoc

iati

on r

ecom

men

ds t

hat

you

r ta

rget

hea

rt r

ate

duri

ng

exer

cise

sh

ould

be

betw

een

50%

an

d 75

% o

f yo

ur

max

imu

m h

eart

rat

e. U

se t

he

data

in

th

e ta

ble

belo

w t

o gr

aph

th

e ap

prox

imat

e m

axim

um

hea

rt r

ates

for

pe

ople

of

give

n a

ges.

So

urce

: Am

eric

an H

eart

Ass

ocia

tion

Ag

e

Maxim

um

Heart

Rate

200

2535

40

y

x30

Heart Rate

180

190

170

160

200

2. N

ATU

RE

Map

le s

yru

p is

mad

e by

co

llec

tin

g sa

p fr

om s

uga

r m

aple

tre

es

and

boil

ing

it d

own

to

rem

ove

exce

ss

wat

er. T

he

grap

h s

how

s th

e n

um

ber

of

gall

ons

of t

ree

sap

requ

ired

to

mak

e di

ffer

ent

quan

titi

es o

f m

aple

syr

up.

E

xpre

ss t

he

rela

tion

as

a se

t of

ord

ered

pa

irs.

Gal

lon

s o

f Sy

rup

10

24

5

y

x3

78

96

Gallons of Sap16

0

200

120 80240

280

320

Map

le S

ap

to

Syru

p

So

urce

: Ve

rmon

t M

aple

Sug

ar M

aker

s’ A

ssoc

iatio

n

3.B

AK

ING

Ide

nti

fy t

he

grap

h t

hat

bes

t re

pres

ents

th

e re

lati

onsh

ip b

etw

een

th

e n

um

ber

of c

ooki

es a

nd

the

equ

ival

ent

nu

mbe

r of

doz

ens.

Nu

mb

er o

f d

oze

ns

Number of cookies

y

x

Gra

ph

A

Nu

mb

er o

f d

oze

ns

Number of cookies

y

x

Gra

ph

B

Nu

mb

er o

f d

oze

ns

Number of cookies

y

x

Gra

ph

C

4. D

ATA

CO

LLEC

TIO

N M

arga

ret

coll

ecte

d da

ta t

o de

term

ine

the

nu

mbe

r of

boo

ks

her

sch

oolm

ates

wer

e br

ingi

ng

hom

e ea

ch e

ven

ing.

Sh

e re

cord

ed h

er d

ata

as a

se

t of

ord

ered

pai

rs. S

he

let

x be

th

e n

um

ber

of t

extb

ooks

bro

ugh

t h

ome

afte

r sc

hoo

l, an

d y

be t

he

nu

mbe

r of

stu

den

ts

wit

h x

tex

tboo

ks. T

he

rela

tion

is

show

n

in t

he

map

pin

g.

a. E

xpre

ss t

he

rela

tion

as

a se

t of

or

dere

d pa

irs.

b.

Wh

at i

s th

e do

mai

n o

f th

e re

lati

on?

c. W

hat

is

the

ran

ge o

f th

e re

lati

on?

xy 8 11 12 23 28

0 1 2 3 4 5

Ag

e (y

ears

)2

02

53

03

54

0

Max

imu

m H

eart

Rat

e(b

eats

per

min

ute

)2

00

19

519

018

518

0

1-6

Wor

d Pr

oble

m P

ract

ice

Rela

tio

ns

{(0,

12)

, (1,

8),

(2, 2

3), (

3, 2

8),

(4, 1

1), (

5, 1

1)}

{0, 1

, 2, 3

, 4, 5

}

{8, 1

1, 1

2, 2

3, 2

8}

{(2,

80)

, (3,

120

), (6

, 240

), (8

, 320

)}

Gra

ph

B

024_

041_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

4112

/21/

10

5:21

PM



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass




NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

42

Gle

ncoe

Alg

ebra

1

Even

an

d O

dd

Fu

ncti

on

sW

e kn

ow t

hat

nu

mbe

rs c

an b

e ei

ther

eve

n o

r od

d. I

t is

als

o tr

ue

that

fu

nct

ion

s ca

n b

e de

fin

ed a

s ev

en o

r od

d. F

or a

fu

nct

ion

to

be e

ven

mea

ns

that

it

is s

ymm

etri

c ab

out

the

y-ax

is. T

hat

is,

if

you

fol

d th

e gr

aph

alo

ng

the

y-ax

is, t

he

two

hal

ves

of t

he

grap

h m

atch

ex

actl

y. F

or a

fu

nct

ion

to

be o

dd m

ean

s th

at t

he

fun

ctio

n i

s sy

mm

etri

c ab

out

the

orig

in.

Th

is m

ean

s if

you

rot

ate

the

grap

h u

sin

g th

e or

igin

as

the

cen

ter,

it w

ill

mat

ch i

ts o

rigi

nal

po

siti

on b

efor

e co

mpl

etin

g a

full

tu

rn.

Th

e fu

nct

ion

y =

x2

is a

n e

ven

fu

nct

ion

. T

he

fun

ctio

n y

=

x5

is a

n o

dd f

un

ctio

n. I

f yo

u

rota

te t

he

grap

h 1

80º t

he

grap

h w

ill

lie

on i

tsel

f.

y

xO

1. T

he

tabl

e be

low

sh

ows

the

orde

red

pair

s of

an

eve

n f

un

ctio

n. C

ompl

ete

the

tabl

e. P

lot

the

poin

ts a

nd

sket

ch t

he

grap

h.

2. T

he

tabl

e be

low

sh

ows

the

orde

red

pair

s of

an

odd

fu

nct

ion

. Com

plet

e th

e ta

ble.

Plo

t th

e po

ints

an

d sk

etch

th

e gr

aph

.

y

xO

y

xO

24

68

1012

-4

-6

-8

-10

-12

-2

456 3 2 1

-1

-2

-3

-4

-5

-6 y

xO

24

68

10-

4-

6-

8-

10-

2

810 6 4 2

-2

-4

-6

-8

-10

Enri

chm

ent

x-

12

-5

-1

15

12

y

6

3

11

36

x-

10

-4

-2

24

10

y

8

4

2-

2-

4-

8

1-6

042_

054_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

4212

/21/

10

5:21

PM

Lesson X-1


NA

ME

DAT

E

P

ER

IOD

Lesson 1-7

Cha

pte

r 1

43

Gle

ncoe

Alg

ebra

1

Iden

tify

Fu

nct

ion

s R

elat

ion

s in

wh

ich

eac

h e

lem

ent

of t

he

dom

ain

is

pair

ed w

ith

ex

actl

y on

e el

emen

t of

th

e ra

nge

are

cal

led

fun

ctio

ns.

D

eter

min

e w

het

her

th

e re

lati

on {

(6, -

3),

(4, 1

), (

7, -

2), (

-3,

1)}

is

a fu

nct

ion

. Exp

lain

.

Sin

ce e

ach

ele

men

t of

th

e do

mai

n i

s pa

ired

wit

h e

xact

ly o

ne

elem

ent

of

the

ran

ge, t

his

rel

atio

n i

s a

fun

ctio

n.

D

eter

min

e w

het

her

3x

- y

= 6

is

a f

un

ctio

n.

Sin

ce t

he

equ

atio

n i

s in

th

e fo

rm

Ax

+ B

y =

C, t

he

grap

h o

f th

e eq

uat

ion

wil

l be

a l

ine,

as

show

n

at t

he

righ

t.

If y

ou d

raw

a v

erti

cal

lin

e th

rou

gh e

ach

val

ue

of x

, th

e ve

rtic

al l

ine

pass

es t

hro

ugh

just

on

e po

int

of t

he

grap

h. T

hu

s, t

he

lin

e re

pres

ents

a f

un

ctio

n.

Exer

cise

sD

eter

min

e w

het

her

eac

h r

elat

ion

is

a fu

nct

ion

.

1.

2.

3.

4.

5.

6.

7. {

(4, 2

), (2

, 3),

(6, 1

)}

8. {

(-3,

-3)

, (-

3, 4

), (-

2, 4

)}

9. {

(-1,

0),

(1, 0

)}

10. -

2x +

4y

= 0

11

. x2

+ y

2 =

8

12. x

= -

4

x

y

Ox

y

Ox

y O

XY 4 5 6 7

-1 0 1 2

x

y

Ox

y

O

x

y

O

1-7

Stud

y G

uide

and

Inte

rven

tion

Fu

ncti

on

s

Exam

ple

1Ex

amp

le 2

y

es

yes

n

o

n

o

no

y

es

y

es

no

y

es

y

es

no

n

o

042_

054_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

4312

/21/

10

5:21

PM


An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass




NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

44

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Fu

ncti

on

s

1-7

Fin

d F

un

ctio

n V

alu

es E

quat

ions

tha

t ar

e fu

ncti

ons

can

be w

ritt

en i

n a

form

cal

led

fun

ctio

n n

otat

ion

. For

exa

mpl

e, y

= 2

x -

1 ca

n be

wri

tten

as

f(x)

= 2

x -

1. I

n th

e fu

ncti

on,

x re

pres

ents

the

ele

men

ts o

f th

e do

mai

n, a

nd f

(x)

repr

esen

ts t

he e

lem

ents

of

the

rang

e.

Sup

pose

you

wan

t to

fin

d th

e va

lue

in t

he r

ange

tha

t co

rres

pond

s to

the

ele

men

t 2

in t

he

dom

ain.

Thi

s is

wri

tten

f(2

) an

d is

rea

d “f

of

2.”

The

val

ue o

f f(

2) i

s fo

und

by s

ubst

itut

ing

2 fo

r x

in t

he e

quat

ion.

If

f(x

) =

3x

- 4

, fin

d e

ach

val

ue.

a. f

(3)

f(3)

= 3

(3)

- 4

R

epla

ce x

with 3

.

=

9 -

4

Multip

ly.

=

5

Sim

plif

y.

b.

f(-

2) f(

-2)

= 3

(-2)

- 4

R

epla

ce x

with -

2.

=

-6

- 4

M

ultip

ly.

=

-10

S

implif

y.

Exer

cise

sIf

f(x

) =

2x

- 4

an

d g

(x)

= x

2 -

4x,

fin

d e

ach

val

ue.

1. f

(4)

2. g

(2)

3. f

(-5)

4. g

(-3)

5.

f(0

) 6.

g(0

)

7. f

(3)

- 1

8.

f ( 1 −

4 ) 9.

g ( 1 −

4 )

10. f

(a2 )

11

. f(k

+ 1

) 12

. g(2

n)

13. f

(3x)

14

. f(2

) +

3

15. g

(-4)

Exam

ple

4

-

4 -

14

2

1 -

4 0

1

-

3 1 −

2 -

15

−

16

2

a2

- 4

2

k -

2

4n

2 -

8n

6

x -

4

3

32

042_

054_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

4412

/21/

10

5:21

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-7

Cha

pte

r 1

45

Gle

ncoe

Alg

ebra

1

1-7

Skill

s Pr

acti

ceFu

ncti

on

s

Det

erm

ine

wh

eth

er e

ach

rel

atio

n i

s a

fun

ctio

n.

1.

2.

3.

4.

xy

4

-

5

-1

-10

0

-

9

1

-

7

9

1

5.

x

y

2

7

5

-3

3

5

-4

-2

5

2

6.

x

y

3

7

-1

1

1

0

3

5

7

3

7. {

(2, 5

), (4

, -2)

, (3,

3),

(5, 4

), (-

2, 5

)}

8. {

(6, -

1), (

-4,

2),

(5, 2

), (4

, 6),

(6, 5

)}

9.

y =

2x

- 5

10

. y

= 1

1

11.

12

.

13.

If f

(x)

= 3

x +

2 a

nd

g(x

) =

x2

- x

, fin

d e

ach

val

ue.

14. f

(4)

15

. f(

8)

16. f

(-2)

17

. g(2

)

18. g

(-3)

19

. g(-

6)

20. f

(2)

+ 1

21

. f(1

) -

1

22. g

(2)

- 2

23

. g(-

1) +

4

24. f

(x +

1)

25

. g(3

b)

x

y

Ox

y

Ox

y

O

XY

4 6 7

2-

1 3 5

XY 4 1

-2

5 2 0-

3

XY 4 1

-3

-5

-6

-2 1 3

yes

yes

no

yes

no

no

yes

no

yes

yes

yes

no

no

1426

-4

2

1242

94

06

3x +

59b

2 -

3b

042_

054_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

4512

/21/

10

5:21

PM


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass




NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

46

Gle

ncoe

Alg

ebra

1

1-7

Prac

tice

Fu

ncti

on

s

Det

erm

ine

wh

eth

er e

ach

rel

atio

n i

s a

fun

ctio

n.

1.

2.

X

Y

1

-5

-4

3

7

6

1

-2

3.

4. {

(1, 4

), (2

, -2)

, (3,

-6)

, (-

6, 3

), (-

3, 6

)}

5. {

(6, -

4), (

2, -

4), (

-4,

2),

(4, 6

), (2

, 6)}

6. x

= -

2 7.

y =

2

If f

(x)

= 2

x -

6 a

nd

g(x

) =

x -

2x2 ,

fin

d e

ach

val

ue.

8. f

(2)

9.

f (-

1 −

2 )

10

. g(

-1)

11. g

(-

1 −

3 ) 12

. f(7

) -

9

13. g

(-3)

+ 1

3

14. f

(h +

9)

15

. g(3

y)

16. 2

[g(b

) +

1]

17. W

AG

ES M

arti

n e

arn

s $7

.50

per

hou

r pr

oofr

eadi

ng

ads

at a

loc

al n

ewsp

aper

. His

wee

kly

wag

e w

can

be

desc

ribe

d by

th

e eq

uat

ion

w =

7.5

h, w

her

e h

is

the

nu

mbe

r of

hou

rs

wor

ked.

a. W

rite

th

e eq

uat

ion

in

fu

nct

ion

not

atio

n.

b.

Fin

d f(

15),

f(20

), an

d f(

25).

18. E

LEC

TRIC

ITY

Th

e ta

ble

show

s th

e re

lati

onsh

ip b

etw

een

res

ista

nce

R a

nd

curr

ent

I in

a c

ircu

it.

Res

ista

nce

(o

hm

s)12

08

04

86

4

Cu

rren

t (a

mp

eres

)0

.10

.15

0.2

52

3

a. I

s th

e re

lati

onsh

ip a

fu

nct

ion

? E

xpla

in.

b.

If t

he

rela

tion

can

be

repr

esen

ted

by t

he

equ

atio

n I

R =

12,

rew

rite

th

e eq

uat

ion

in

fu

nct

ion

not

atio

n s

o th

at t

he

resi

stan

ce R

is

a fu

nct

ion

of

the

curr

ent

I.

c. W

hat

is

the

resi

stan

ce i

n a

cir

cuit

wh

en t

he

curr

ent

is 0

.5 a

mpe

re?

x

y

O

XY 0 3

-2

-3

-2 1 5

yes

no

yes

y

es

n

on

oye

s

2h +

12

3y -

18y

22b

- 4

b2

+ 2

f(h

) =

7.5

h

112.

50, 1

50, 1

87.5

0

Yes;

fo

r ea

ch v

alu

e in

th

e d

om

ain

, th

ere

is o

nly

on

e va

lue

in t

he

ran

ge.

24 o

hm

s

-2

-7

-3

f(I)

= 12

−

I

-

5 −

9 -

1 -

8

042_

054_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

4612

/21/

10

5:21

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-7

Cha

pte

r 1

47

Gle

ncoe

Alg

ebra

1

1.TR

AN

SPO

RTA

TIO

N T

he

cost

of

ridi

ng

in a

cab

is

$3.0

0 pl

us

$0.7

5 pe

r m

ile.

Th

e eq

uat

ion

th

at r

epre

sen

ts t

his

rel

atio

n i

s y

= 0.

75x

+ 3,

wh

ere

x is

th

e n

um

ber

of

mil

es t

rave

led

and

y is

th

e co

st o

f th

e tr

ip. L

ook

at t

he

grap

h o

f th

e eq

uat

ion

an

d de

term

ine

wh

eth

er t

he

rela

tion

is

a fu

nct

ion

.

Dis

tan

ce (

mile

s)2

10

43

y

x5

67

89

10

Cost ($)

68 4 21016 14 12

2. T

EXT

MES

SAG

ING

Man

y ce

ll p

hon

es

hav

e a

text

mes

sagi

ng

opti

on i

n a

ddit

ion

to

reg

ula

r ce

ll p

hon

e se

rvic

e. T

he

fun

ctio

n f

or t

he

mon

thly

cos

t of

tex

t m

essa

gin

g se

rvic

e fr

om N

olin

e W

irel

ess

Com

pan

y is

f(x

) =

0.

10x

+ 2,

wh

ere

x is

th

e n

um

ber

of t

ext

mes

sage

s th

at a

re

sen

t. F

ind

f(10

) an

d f(

30),

the

cost

of

10

text

mes

sage

s in

a m

onth

an

d th

e co

st o

f 30

tex

t m

essa

ges

in a

mon

th.

3.G

EOM

ETRY

Th

e ar

ea f

or a

ny

squ

are

is

give

n b

y th

e fu

nct

ion

y =

x2 ,

wh

ere

x is

th

e le

ngt

h o

f a

side

of

the

squ

are

and

y is

th

e ar

ea o

f th

e sq

uar

e. W

rite

th

e eq

uat

ion

in

fu

nct

ion

not

atio

n a

nd

fin

d th

e ar

ea o

f a

squ

are

wit

h a

sid

e le

ngt

h o

f 3.

5 in

ches

.

4.TR

AV

EL T

he

cost

for

car

s en

teri

ng

Pre

side

nt

Geo

rge

Bu

sh T

urn

pike

at

Bel

tlin

e ro

ad i

s gi

ven

by

the

rela

tion

x

= 0.

75, w

her

e x

is t

he

doll

ar a

mou

nt

for

entr

ance

to

the

toll

roa

d an

d y

is t

he

nu

mbe

r of

pas

sen

gers

. Det

erm

ine

if t

his

re

lati

on i

s a

fun

ctio

n. E

xpla

in.

5. C

ON

SUM

ER C

HO

ICES

Ais

ha

just

re

ceiv

ed a

$40

pay

chec

k fr

om h

er n

ew

job.

Sh

e sp

ends

som

e of

it

buyi

ng

mu

sic

onli

ne

and

save

s th

e re

st i

n a

ban

k ac

cou

nt.

Her

sav

ings

is

give

n b

y f(

x) =

40 –

1.2

5x, w

her

e x

is t

he

nu

mbe

r of

so

ngs

sh

e do

wn

load

s at

$1.

25 p

er s

ong.

a. G

raph

th

e fu

nct

ion

.

Son

gs

Purc

has

ed10

50

2015

x25

3035

40

Savings ($)

1520 10 52540 35 30

f (x)

b.

Fin

d f(

3), f

(18)

, an

d f(

36).

Wh

at d

o th

ese

valu

es r

epre

sen

t?

c. H

ow m

any

son

gs c

an A

ish

a bu

y if

sh

e w

ants

to

save

$30

?

1-7

Wor

d Pr

oble

m P

ract

ice

Fu

ncti

on

s

yes

f(10

) = $

3; f

(30)

= $

5

Th

is r

elat

ion

is n

ot

a fu

nct

ion

. T

he

gra

ph

wo

uld

be

a ve

rtic

al li

ne,

w

hic

h w

ou

ld n

ot

pas

s th

e ve

rtic

al

line

test

.

f(3)

= 3

6.25

; bu

ys 3

so

ng

s,

save

s $3

6.25

f(18

) =

17.

50;

buys

18

son

gs,

sa

ves

$17.

50f(

36)

= -

5; s

amp

le a

nsw

er:

if s

he

wan

ts t

o b

uy 3

6 so

ng

s,

she

nee

ds

$5 e

xtra 8

son

gs

f

(x)

= x

2 f(

3.5)

= (3

.5)2

=

12

.25

in2

042_

054_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

4712

/21/

10

5:21

PM


An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass




NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

48

Gle

ncoe

Alg

ebra

1

Co

mp

osit

e F

un

cti

on

s

Th

ree

thin

gs a

re n

eede

d to

hav

e a

fun

ctio

n—

a se

t ca

lled

th

e do

mai

n,

a se

t ca

lled

th

e ra

nge

, an

d a

rule

th

at m

atch

es e

ach

ele

men

t in

th

e do

mai

n w

ith

on

ly o

ne

elem

ent

in t

he

ran

ge. H

ere

is a

n e

xam

ple.

Ru

le: f

(x)

= 2

x +

1

3

-5

f(x)

5

x 21

-3

f(

x) =

2x

+ 1

f(

1) =

2(1

) +

1 =

2 +

1 =

3

f(

2) =

2(2

) +

1 =

4 +

1 =

5

f(

-3)

=

2(

-3)

+ 1

= -

6 +

1 =

-5

Su

ppos

e w

e h

ave

thre

e se

ts A

, B, a

nd

C a

nd

two

fun

ctio

ns

desc

ribe

d as

sh

own

bel

ow.

Ru

le: f

(x)

= 2

x +

1

Ru

le: g

(y)

= 3

y -

4

AB

C

f(x) 3

5

x 1

g[f(x

)]

g(

y) =

3y

- 4

g(3)

= 3

(3)

- 4

= 5

Let

’s f

ind

a ru

le t

hat

wil

l m

atch

ele

men

ts o

f se

t A

wit

h e

lem

ents

of

set

C w

ith

out

fin

din

g an

y el

emen

ts i

n s

et B

. In

oth

er w

ords

, let

’s f

ind

a ru

le f

or t

he

com

pos

ite

fun

ctio

n g

[f(x

)].

Sin

ce f

(x)

= 2

x +

1, g

[f(x

)] =

g(2

x +

1).

Sin

ce g

(y)

= 3

y -

4, g

(2x

+ 1

) =

3(2

x +

1)

- 4

, or

6x -

1.

Th

eref

ore,

g[f

(x)]

= 6

x -

1.

Fin

d a

ru

le f

or t

he

com

pos

ite

fun

ctio

n g

[f(x

)].

1. f

(x)

= 3

x an

d g(

y) =

2y

+ 1

2.

f(x

) =

x2

+ 1

an

d g(

y) =

4y

3. f

(x)

= -

2x a

nd

g(y)

= y

2 -

3y

4. f

(x)

=

1 −

x -

3 a

nd

g(y)

= y

-1

5. I

s it

alw

ays

the

case

th

at g

[f(x

)] =

f[g

(x)]

? Ju

stif

y yo

ur

answ

er.

Enri

chm

ent

1-7

g

[f(x

)] =

6x +

1

g

[f(x

)] =

4x

2 +

4

g

[f(x

)] =

4x

2 +

6x

g

[f(x

)] =

x -

3

N

o. F

or

exam

ple

, in

Exe

rcis

e 1,

f[g

(x)]

= f

(2x +

1)

= 3

(2x +

1)

+ 6

x +

3, n

ot

6x +

1.

042_

054_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

4812

/21/

10

5:21

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-8

Cha

pte

r 1

49

Gle

ncoe

Alg

ebra

1

1-8

Stud

y G

uide

and

Inte

rven

tion

Inte

rpre

tin

g G

rap

hs o

f Fu

ncti

on

s

Inte

rpre

t In

terc

epts

an

d S

ymm

etry

Th

e in

terc

epts

of

a gr

aph

are

poi

nts

wh

ere

the

grap

h i

nte

rsec

ts a

n a

xis.

Th

e y-

coor

din

ate

of t

he

poin

t at

wh

ich

th

e gr

aph

in

ters

ects

th

e y-

axis

is

call

ed a

y-

inte

rcep

t. S

imil

arly

, th

e x-

coor

din

ate

of t

he

poin

t at

wh

ich

a g

raph

in

ters

ects

th

e x-

axis

is

call

ed a

n x

-in

terc

ept.

A

gra

ph p

osse

sses

lin

e sy

mm

etry

in

a l

ine

if e

ach

hal

f of

th

e gr

aph

on

eit

her

sid

e of

th

e li

ne

mat

ches

exa

ctly

.

AR

CH

ITEC

TUR

E T

he

grap

h s

how

s a

fun

ctio

n t

hat

ap

pro

xim

ates

th

e sh

ape

of t

he

Gat

eway

Arc

h, w

her

e x

is t

he

dis

tan

ce f

rom

th

e ce

nte

r p

oin

t in

fee

t an

d y

is

the

hei

ght

in f

eet.

Id

enti

fy t

he

fun

ctio

n a

s li

nea

r or

n

onli

nea

r. T

hen

est

imat

e an

d i

nte

rpre

t th

e in

terc

epts

, an

d d

escr

ibe

and

in

terp

ret

any

sym

met

ry.

Lin

ear

or N

onli

nea

r: S

ince

th

e gr

aph

is

a cu

rve

and

not

a

lin

e, t

he

grap

h i

s n

onli

nea

r.y-

Inte

rcep

t: T

he

grap

h i

nte

rsec

ts t

he

y-ax

is a

t ab

out

(0, 6

30),

so t

he

y-in

terc

ept

of t

he

grap

h i

s ab

out

630.

Th

is m

ean

s th

at

the

hei

ght

of t

he

arch

is

630

feet

at

the

cen

ter

poin

t.x-

Inte

rcep

t(s)

: T

he

grap

h i

nte

rsec

ts t

he

x-ax

is a

t ab

out

(-32

0, 0

) an

d (3

20, 0

). S

o th

e x-

inte

rcep

ts a

re a

bou

t -

320

and

320.

Th

is m

ean

s th

at t

he

obje

ct t

ouch

es t

he

grou

nd

to t

he

left

an

d ri

ght

of t

he

cen

ter

poin

t.S

ymm

etry

: T

he

righ

t h

alf

of t

he

grap

h i

s th

e m

irro

r im

age

of t

he

left

hal

f in

th

e y-

axis

. In

th

e co

nte

xt o

f th

e si

tuat

ion

, th

e sy

mm

etry

of

the

grap

h t

ells

you

th

at t

he

arch

is

sym

met

ric.

T

he

hei

ght

of t

he

arch

at

any

dist

ance

to

the

righ

t of

th

e ce

nte

r is

th

e sa

me

as i

ts h

eigh

t th

at s

ame

dist

ance

to

the

left

.

Iden

tify

th

e fu

nct

ion

gra

ph

ed a

s li

nea

r or

non

lin

ear.

Th

en e

stim

ate

and

in

terp

ret

the

inte

rcep

ts o

f th

e gr

aph

an

d a

ny

sym

met

ry.

1.

Righ

t Wha

le P

opul

atio

n

Population80 0

160

240

Gene

ratio

ns S

ince

200

74

812

y

x

2.

St

ock

Pric

e

Price Variation (points)

-22 0 Ti

me

Sinc

e O

peni

ng B

ell (

h)

24

6

y

x

3.

y

x

Ave

rage

Gas

olin

ePr

ice

Price ($ per gallon)

23 1 0456

Year

s Si

nce

1987

1510

525

2030

L

inea

r; t

he

y-i

nte

rcep

t is

250

, so

th

ere

wer

e 25

0 ri

gh

t w

hal

es in

19

87;

x-in

terc

ept

is 1

0, s

o t

her

e w

ill b

e n

o r

igh

t w

hal

es a

fter

10

gen

erat

ion

s; n

o li

ne

sym

met

ry.

N

on

linea

r; y

-in

terc

ept

is 0

, so

th

eres

n

o c

han

ge

in t

he

sto

ck v

alu

e at

th

e o

pen

ing

bel

l; x-

inte

rcep

ts a

re 0

an

d

abo

ut

5.3,

so

th

ere

is n

o c

han

ge

in

the

valu

e af

ter

0 h

ou

rs a

nd

ab

ou

t 5.

3 h

ou

rs a

fter

op

enin

g;

no

lin

e sy

mm

etry

.

No

nlin

ear;

y-in

terc

ept

abo

ut

1,

so t

he

aver

age

pri

ce o

f g

as

was

ab

ou

t $1

per

gal

lon

in

1987

; no

x-in

terc

epts

, so

th

ere

is n

o t

ime

wh

en g

as w

as f

ree;

n

o li

ne

sym

met

ry.

Exam

ple

O

y

x

y -in

terc

ept

x -in

terc

ept

Gate

way

Arc

h

Height (ft)

0Di

stan

ce (f

t)80

-80

-24

024

0

160

240 80320

400

480

560y

x

042_

054_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

4912

/21/

10

5:21

PM


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass




NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

50

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Inte

rpre

tin

g G

rap

hs o

f Fu

ncti

on

s

1-8

Inte

rpre

t Ex

trem

a an

d E

nd

Beh

avio

r In

terp

reti

ng

a gr

aph

als

o in

volv

es

esti

mat

ing

and

inte

rpre

tin

g w

her

e th

e fu

nct

ion

is

incr

easi

ng,

dec

reas

ing,

pos

itiv

e, o

r n

egat

ive,

an

d w

her

e th

e fu

nct

ion

has

an

y ex

trem

e va

lues

, eit

her

hig

h o

r lo

w.

Exam

ple

HEA

LTH

Th

e ou

tbre

ak o

f th

e H

1N1

viru

s ca

n b

e m

odel

ed b

y th

e fu

nct

ion

gra

ph

ed a

t th

e ri

ght.

Est

imat

e an

d i

nte

rpre

t w

her

e th

e fu

nct

ion

is

pos

itiv

e, n

egat

ive,

in

crea

sin

g, a

nd

d

ecre

asin

g, t

he

x-co

ord

inat

es o

f an

y re

lati

ve e

xtre

ma,

an

d

the

end

beh

avio

r of

th

e gr

aph

.

Pos

itiv

e: f

or x

bet

wee

n 0

an

d 42

N

egat

ive:

no

part

s of

dom

ain

Th

is m

ean

s th

at t

he

nu

mbe

r of

rep

orte

d ca

ses

was

alw

ays

posi

tive

. Th

is i

s re

ason

able

bec

ause

a n

egat

ive

nu

mbe

r of

cas

es

can

not

exi

st i

n t

he

con

text

of

the

situ

atio

n.

Incr

easi

ng:

for

x b

etw

een

0 a

nd

42

Dec

reas

ing:

no

part

s of

dom

ain

Th

e n

um

ber

of r

epor

ted

case

s in

crea

sed

each

day

fro

m t

he

firs

t da

y of

th

e ou

tbre

ak.

Rel

ativ

e M

axim

um

: at

abo

ut

x =

42

Rel

ativ

e M

inim

um

: at

x =

0T

he e

xtre

ma

of t

he g

raph

ind

icat

e th

at t

he n

umbe

r of

rep

orte

d ca

ses

peak

ed a

t ab

out

day

42.

En

d B

ehav

ior:

As

x in

crea

ses,

y a

ppea

rs t

o ap

proa

ch 1

1,00

0. A

s x

decr

ease

s, y

dec

reas

es.

Th

e en

d be

hav

ior

of t

he

grap

h i

ndi

cate

s a

max

imu

m n

um

ber

of r

epor

ted

case

s of

11,

000.

Est

imat

e an

d i

nte

rpre

t w

her

e th

e fu

nct

ion

is

pos

itiv

e, n

egat

ive,

in

crea

sin

g, a

nd

d

ecre

asin

g, t

he

x-co

ord

inat

e of

an

y re

lati

ve e

xtre

ma,

an

d t

he

end

beh

avio

r of

th

e gr

aph

.

1.

Righ

t Wha

le P

opul

atio

n

Population

80 0

160

240

Gene

ratio

ns S

ince

200

74

812

y

x

2.

Stoc

k Pr

ice

Price Variation (points)

-22 0 Ti

me

Sinc

e O

peni

ng B

ell (

h)

24

6

y

x

3.

y

x

Ave

rage

Gas

olin

ePr

ice

Price ($ per gallon)

23 1 0456

Year

s Si

nce

1987

1510

525

2030

y

x

Wor

ldw

ide

H1N

1

Reported Cases

4000 0

8000

12,0

00

Day

s Si

nce

Out

brea

k21

147

3528

42

Th

e p

op

ula

tio

n is

ab

ove

0 fo

r th

e fi

rst

10 g

ener

atio

ns,

an

d t

hen

bel

ow

0. A

neg

ativ

e p

op

ula

tio

n is

no

t re

aso

nab

le. T

he

po

pu

lati

on

is

go

ing

do

wn

fo

r th

e en

tire

ti

me.

Th

ere

are

no

ext

rem

a.

As

the

tim

e in

crea

ses,

th

e p

op

ula

tio

n w

ill c

on

tin

ue

to

dro

p.

Th

e st

ock

wen

t d

own

in v

alu

e fo

r th

e fi

rst

3.2

ho

urs

, an

d t

hen

ro

se

un

til t

he

end

of

the

day

. Th

e st

ock

va

lue

dec

reas

es in

val

ue

for

the

fi rs

t 3.

2 h

ou

rs, a

nd

th

en g

oes

up

in

val

ue

for

the

rem

ain

der

of

the

day

. Th

e st

ock

had

a r

elat

ive

low

va

lue

afte

r 3.

2 h

ou

rs a

nd

th

en a

re

lativ

e h

igh

val

ue

at t

he

end

of

the

day

. As

the

day

go

es o

n, t

he

sto

ck in

crea

ses

in v

alu

e.

Th

e av

erag

e g

aso

line

pri

ce is

alw

ays

po

siti

ve. I

t in

crea

ses

for

the

fi rs

t fe

w

year

s, d

ecre

ases

un

til

abo

ut

the

11th

yea

r, th

en

incr

ease

s. T

he

rela

tive

m

inim

a ar

e at

1 a

nd

ab

ou

t 11

. Th

e av

erag

e p

rice

ap

pea

rs t

o in

crea

se a

s ti

me

pas

ses.

042_

054_

ALG

1_A

_CR

M_C

01_C

R_6

6049

8.in

dd

5012

/21/

10

5:21

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 1-8

Cha

pte

r 1

51

Gle

ncoe

Alg

ebra

1

Skill

s Pr

acti

ceIn

terp

reti

ng

Gra

ph

s o

f Fu

ncti

on

s

1-8

Iden

tify

th

e fu

nct

ion

gra

ph

ed a

s li

nea

r or

non

lin

ear.

Th

en e

stim

ate

and

in

terp

ret

the

inte

rcep

ts o

f th

e gr

aph

, an

y sy

mm

etry

, wh

ere

the

fun

ctio

n i

s p

osit

ive,

n

egat

ive,

in

crea

sin

g, a

nd

dec

reas

ing,

th

e x-

coor

din

ate

of a

ny

rela

tive

ext

rem

a,

and

th

e en

d b

ehav

ior

of t

he

grap

h.

1.

Dav

id’s

Sav

ings

for

Car

Savings ($) 1400

1200 0

1600

1800

2000

2200

Wee

ks2

46

810

y

x

3.

y

x

Hei

ght o

f Gol

f Bal

l

Height (ft)

40 080120

160

Dist

ance

from

Tee

(yd)

4080

120

160

2.

y

x

Baki

ng S

uppl

ies

Flour (c)

4 08121620

Batc

hes

of C

ooki

es4

812

4.

Sola

r Re

flect

or

Height (ft)

Wid

th (f

t)

y

xO16 8

−8

−16

−8

−16

816

focu

s

linea

r; y

-in

terc

ept

= 1

400;

no

x-i

nte

rcep

t; n

o li

ne

sym

met

ry;

po

siti

ve a

nd

incr

easi

ng

fo

r x >

0;

min

imu

m is

$14

00

at t

ime

0;

savi

ng

s w

ill c

on

tin

ue

to in

crea

se;

see

stu

den

ts’ w

ork

fo

r in

terp

reta

tio

ns.

linea

r; y

-inte

rcep

t =

20;

x-in

terc

ept

= 1

0; n

o li

ne

sym

met

ry;

po

sitiv

e an

d

dec

reas

ing

fo

r x >

0; m

axim

um

is

20 c

up

s at

tim

e 0;

am

ou

nt

of

fl ou

r w

ill d

ecre

ase

un

til it

is g

on

e; s

ee

stu

den

ts’ w

ork

fo

r in

terp

reta

tion

s.

nonl

inea

r; y

-inte

rcep

t ≈

0;

x-in

terc

epts

≈ 0

and

120

; lin

e sy

mm

etry

x ≈

60;

hei

ght

was

al

way

s po

sitiv

e an

d in

crea

sed

until

it

was

60

yard

s fr

om t

he te

e an

d

decr

ease

d 60

to 1

20 y

ards

fro

m t

he

tee;

see

stu

dent

s’ w

ork

for

inte

rpre

tatio

ns.

no

nlin

ear;

y-i

nte

rcep

t =

-6.

25;

x-i

nte

rcep

ts =

-12

.5 a

nd

12.

5;

line

sym

met

ry a

bo

ut

the

y-a

xis;

p

osi

tive

fo

r x <

12.

5 an

d x

> 1

2.5;

th

e m

inim

um

is -

6.25

at

0;

see

stu

den

ts’ w

ork

fo

r in

terp

reta

tio

ns.

042_

054_

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M_C

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10

5:21

PM


An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass




NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

52

Gle

ncoe

Alg

ebra

1

Prac

tice

Inte

rpre

tin

g G

rap

hs o

f Fu

ncti

on

s

1-8

Iden

tify

th

e fu

nct

ion

gra

ph

ed a

s li

nea

r or

non

lin

ear.

Th

en e

stim

ate

and

in

terp

ret

the

inte

rcep

ts o

f th

e gr

aph

, an

y sy

mm

etry

, wh

ere

the

fun

ctio

n i

s p

osit

ive,

n

egat

ive,

in

crea

sin

g, a

nd

dec

reas

ing,

th

e x-

coor

din

ate

of a

ny

rela

tive

ext

rem

a,

and

th

e en

d b

ehav

ior

of t

he

grap

h.

1.

y

x

Who

lesa

le T

-Shi

rt O

rder

Total Cost ($)

200 0

400

600

800

1000

Shirt

s (d

ozen

s)2

46

810

3.

y

x

Hei

ght o

f Div

er

Height Above Water (m)

2 04681012

Tim

e (s

)0.

51

1.5

22.

5

2.

y

x

Wat

er L

evel

Water Level (cm)

28 032364044

Tim

e (s

econ

ds)

4080

120

160

200

240

4.

y

x

Boys

’ Ave

rage

Hei

ght

Height (in.)

24 04872

Age

(yr)

48

1216

20

Lin

ear;

y-i

nte

rcep

t is

50,

so

th

e se

t u

p c

ost

is

$50;

no

x-i

nte

rcep

t, so

at

no

tim

e is

th

e co

st $

0;

no

lin

e sy

mm

etry

; p

osi

tive

an

d in

crea

sin

g f

or

x

> 0

, so

th

e co

st is

alw

ays

po

siti

ve w

ill in

crea

se

as m

ore

sh

irts

are

ord

ered

.

No

nlin

ear;

y-in

terc

ept

is a

bo

ut

43, s

o w

ater

leve

l w

as a

bo

ut

43 c

m w

hen

tim

e st

arte

d; n

o

x-in

terc

ept,

so t

he

wat

er le

vel d

id n

ot

reac

h 0

; no

lin

e sy

mm

etry

; wat

er le

vel w

as a

lway

s p

osi

tive

and

dec

reas

ed t

he

entir

e tim

e; g

rap

h a

pp

ears

to

le

vel o

ff o

r b

egin

to

incr

ease

as

x in

crea

ses.

No

nlin

ear;

y-i

nte

rcep

t is

24,

so

th

e av

erag

e b

oy

is 2

4 in

ches

at

bir

th;

no

x-i

nte

rcep

t; n

o li

ne

sym

met

ry;

alw

ays

po

siti

ve, s

o h

eig

hts

are

al

way

s p

osi

tive

; ap

pea

rs t

o b

e a

max

imu

m o

f ab

ou

t 72

at

abo

ut

19, t

his

mea

ns

that

an

av

erag

e b

oy r

each

es h

is m

axim

um

hei

gh

t o

f 72

in

ches

at

age

19.

No

nlin

ear;

y-i

nte

rcep

t is

10,

so

div

er s

tart

ed a

t 10

m;

x-i

nte

rcep

t o

f ab

ou

t 1.

8, s

o d

iver

en

tere

d

the

wat

er a

fter

ab

ou

t 1.

8 se

c.;

no

lin

e sy

mm

etry

; h

eig

ht

was

po

siti

ve f

or

x <

1.8

an

d n

egat

ive

for

x >

1.8

, so

div

er w

as a

bov

e th

e w

ater

un

til 1

.8

sec.

; th

e h

eig

ht

incr

ease

d u

nti

l max

. of

10.5

at

0.3

sec.

, th

en it

dec

reas

ed;

div

er w

ou

ld c

on

tin

ue

to g

o d

ow

n f

or

som

e ti

me,

th

en w

ou

ld c

om

e u

p.

042_

054_

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1_A

_CR

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NA

ME

DAT

E

P

ER

IOD

Lesson 1-8

Cha

pte

r 1

53

Gle

ncoe

Alg

ebra

1

1-8

Wor

d Pr

oble

m P

ract

ice

Inte

rpre

tin

g G

rap

hs o

f Fu

ncti

on

s

1.H

EALT

H T

he g

raph

sho

ws

the

Cal

orie

s y

burn

ed b

y a

130-

poun

d pe

rson

sw

imm

ing

free

styl

e la

ps a

s a

func

tion

of t

ime

x.

Iden

tify

the

func

tion

as

line

ar o

r no

nlin

ear.

T

hen

esti

mat

e an

d in

terp

ret

the

inte

rcep

ts.

y

x

Calo

ries

Bur

ned

Swim

min

g

Calories (kC)

800

1200 400 0

1600

2000

2400

2800

Tim

e (h

)3

21

57

46

8

2. T

ECH

NO

LOG

Y T

he

grap

h b

elow

sh

ows

the

resu

lts

of a

pol

l th

at a

sks

Am

eric

ans

wh

eth

er t

hey

use

d th

e In

tern

et

yest

erda

y. E

stim

ate

and

inte

rpre

t w

her

e th

e fu

nct

ion

is

posi

tive

, neg

ativ

e,

incr

easi

ng,

an

d de

crea

sin

g, t

he

x-co

ordi

nat

es o

f an

y re

lati

ve e

xtre

ma,

an

d th

e en

d be

hav

ior

of t

he

grap

h.

y

x

Did

you

use

the

Inte

rnet

yes

terd

ay?

Yes Responses(percent of polled)

60 070

Mon

ths

Sinc

e Ja

nuar

y 20

0512

2436

4860

3.G

EOM

ETRY

Th

e gr

aph

sh

ows

the

area

yin

squ

are

cen

tim

eter

s of

a r

ecta

ngl

e w

ith

pe

rim

eter

20

cen

tim

eter

s an

d w

idth

xce

nti

met

ers.

Des

crib

e an

d in

terp

ret

any

sym

met

ry i

n t

he

grap

h.

Are

a (c

m2 )

Area (cm2)

Wid

th (c

m)

10

-102030 0

24

68

10

y

x

4. E

DU

CATI

ON

Ide

ntify

the

func

tion

gra

phed

as

line

ar o

r no

nlin

ear.

The

n es

tim

ate

and

inte

rpre

t th

e in

terc

epts

of t

he g

raph

, any

sy

mm

etry

, whe

re t

he fu

ncti

on is

pos

itiv

e,

nega

tive

, inc

reas

ing,

and

dec

reas

ing,

the

x-

coor

dina

te o

f any

rel

ativ

e ex

trem

a, a

nd

the

end

beha

vior

of t

he g

raph

.

U.S.

Edu

catio

n Sp

endi

ng

Spending (billions of $)

200 0

400

600

800

1000

Year

s Si

nce

1949

3020

1050

7040

60

y

x

Lin

ear;

th

e x-

an

d y

-in

terc

epts

are

0. T

his

m

ean

s th

at n

o C

alo

ries

are

bu

rned

wh

en n

o

tim

e is

sp

ent

swim

min

g.

Th

e g

rap

h is

sym

met

ric

in t

he

line

x =

5. I

n

the

con

text

of

the

situ

atio

n, t

he

sym

met

ry

mea

ns

that

th

e ar

ea is

th

e sa

me

wh

en w

idth

is

a n

um

ber

less

th

an o

r g

reat

er t

han

5.

No

nlin

ear;

y-i

nte

rcep

t is

ab

ou

t 10

, so

sp

end

ing

was

ab

ou

t $1

0 b

illio

n in

194

9; n

o

x-in

terc

ept;

fu

nct

ion

is p

osi

tive

fo

r al

l val

ues

o

f x, s

o e

du

cati

on

sp

end

ing

has

nev

er b

een

$0

; fu

nct

ion

is in

crea

sin

g f

or

all v

alu

es o

f x,

wit

h n

o r

elat

ive

max

ima

or

min

ima;

as

x-in

crea

ses,

y-i

ncr

ease

s, s

o t

he

up

war

d

tren

d in

sp

end

ing

is e

xpec

ted

to

co

nti

nu

e.

Th

e fu

nct

ion

is p

osi

tive

an

d in

crea

sin

g f

or

x >

0, s

o In

tern

et u

se is

incr

easi

ng

am

on

g

tho

se p

olle

d. T

her

e ar

e n

o e

xtre

ma.

As

x

incr

ease

s, y

incr

ease

s, s

o In

tern

et u

se is

ex

pec

ted

to

co

nti

nu

e to

incr

ease

. Ho

wev

er

sin

ce t

he

dat

a ar

e p

erce

nts

, 10

0 is

th

e m

axim

um

it c

ou

ld e

ver

reac

h.

042_

054_

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_CR

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ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF 2nd




NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 1

54

Gle

ncoe

Alg

ebra

1

1-8

Enri

chm

ent

Sym

metr

y i

n G

rap

hs o

f Fu

ncti

on

sYo

u h

ave

seen

th

at t

he

grap

hs

of s

ome

fun

ctio

ns

hav

e li

ne

sym

met

ry. F

un

ctio

ns

that

hav

e li

ne

sym

met

ry i

n t

he

y-ax

is a

re c

alle

d ev

en f

un

ctio

ns.

Th

e gr

aph

of

a fu

nct

ion

can

als

o h

ave

poin

t sy

mm

etry

. Rec

all

that

a f

igu

re h

as p

oin

t sy

mm

etry

if

it c

an b

e ro

tate

d le

ss t

han

36

0° a

bou

t th

e po

int

so t

hat

th

e im

age

mat

ches

th

e or

igin

al f

igu

re. F

un

ctio

ns

that

are

sy

mm

etri

c ab

out

the

orig

in a

re c

alle

d od

d f

un

ctio

ns.

Eve

n F

un

ctio

ns

Od

d F

un

ctio

ns

Nei

ther

Eve

n n

or

Od

d

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

Th

e gr

aph

of

a fu

nct

ion

can

not

be

sym

met

ric

abou

t th

e x-

axis

bec

ause

th

e gr

aph

wou

ld f

ail

the

Ver

tica

l L

ine

Tes

t.

Exer

cise

sId

enti

fy t

he

fun

ctio

n g

rap

hed

as

even

, od

d, o

r n

eith

er.

1.

y

xO

2.

y

x

3.

y

xO

4.

y

xO

od

dev

en

even

n

eith

er

5.

y

xO

6.

y

xO

7.

y

xO

8.

y

xO

even

od

dn

eith

erev

en

042_

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A15_A26_ALG1_A_CRM_C01_AN_660498.indd A26A15_A26_ALG1_A_CRM_C01_AN_660498.indd A26 12/30/10 8:04 AM12/30/10 8:04 AM

Chapter 1 Assessment Answer KeyQuiz 1 (Lessons 1-1 and 1-2) Quiz 3 (Lesson 1-5 and 1-6) Mid-Chapter TestPage 57 Page 58 Page 59

Quiz 4 (Lessons 1-7 and 1-8)

Page 58

Quiz 2 (Lessons 1-3 and 1-4)

Page 57

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

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raw

-Hill

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mp

anie

s, In

c.

PDF Pass


1.

2.

3.

4.

5.

1.

2.

3.

4.

5.

84 + 6

Multiplicative Property of Zero; 0

Substitiution

7(100-2); 686

B

two plus the product of 5 and p

1

8

B

= 7 · 7 · 2 · 5 Commutative (×)

= (7 · 7) · (2 · 5) Associative (×)

= 49 · 10 = 490 Substitution

1.

2.

3.

4.

11

X Y

56843

3-4

21

D = {–4, 1, 2, 3}R = {3, 4, 5, 6, 8}

B

t = 1000 _

40 ; t = 25 min

1.

2.

3.

4.

Nonlinear; see students’ work.

A

30

function

8.

9.

10.

11.

12.

13.

14.

15.

1.

2.

3.

4.

5.

6.

7.

18 times p

G

C

F

D

x squared minus 5

Sample answer: Mult. Iden. and Mult. Inv.

6(10) + 6(2); 72

13b + 2b2

= 6.4 + 1.6 + 2.7 + 5.3 Commutative (+)

= (6.4 + 1.6) + (2.7 + 5.3)Associative (+)

= 8 + 8 Substitution

= 16 Substitution

D

D

J

= 4

_ 3 � 3 � 7 � 10 Commutative (×)

= ( 4

_ 3 � 3) �

(7 � 10) Associative (×)

= 4 � 70 Substitution

= 280 Substitution

$2375


Chapter 1 Assessment Answer KeyVocabulary Test Form 1Page 60 Page 61 Page 62

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Sample answer: The solution set of an open sentence is the set of elements from the replacement set that make an open sentence true.

coefficient

function

domain

like terms

continuous function

power

open sentence

variable

the behavior of the values of a function at the positive and negative extremes in its domain

range

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

C

D

G

F

B

H

C

H

J

A

B

J

B

H

B

F

15.

16.

17.

18.

19.

G 20.

C

J

B

B: 12x + 6


Chapter 1 Assessment Answer KeyForm 2A Form 2BPage 63 Page 64 Page 65 Page 66

An

swer

s

Co

pyr

ight

© G

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oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

G

C

D

G

A

H

C

F

B

G

B

J

G

B

15.

16.

17.

18.

19.

20.

C

G

D

H

A

B: 212

H

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

C

G

A

G

D

F

C

G

D

G

C

F

C

G

15.

16.

17.

18.

19.

20.

D

H

A

H

C

F

B: 8a2


Chapter 1 Assessment Answer KeyForm 2CPage 67 Page 68

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pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF 2nd


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

4(5 · 1 ÷ 20)

= 4(5 ÷ 20) (Mult. Identity)

= 4 ( 1 _ 4 ) (Substitution)

= 1 (Mult. Inverse)

n2 + 34

60

Substitution; 10

Additive Identity; 5

18

5(2x)

128

3(14) - 3(5); 27

9w + 14w 2

17y + 7

6

5

7

4 times n cubed plus 6

(5.0, 4.20), (6.0, 5.05), (7.0, 5.90), (8.0, 6.75)

time; temperature

(8, 87); at 8 A.M. the temperature is 87°.

B: a.

b.

c.

- (1 � 9) + 8 + 7

198 � 7

1 + (9 - 8) + 7

As the weight of the letter increases, the cost increases.

16.

17.

18.

19.

Weight (oz)

Rat

e ($

)

0

1

2

3

4

5

6

7

5.0 6.0 7.0 8.0

20.

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Chapter 1 Assessment Answer KeyForm 2DPage 69 Page 70

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23x + 8

11w 2 + 7z 2

10(5) + 3(5); 65

Refl exive Property; 3

Multiplicative

Inverse; 1

_ 11

20

36

6(6 · 1 ÷ 36) = 6(6 ÷ 36) (Mult. Identity)

= 6 (

1 _ 6 )

(Substitution)

= 1 (Mult. Inverse)

5 times a number cubed plus 9

1 _ 3 n + 27

4n 2

6

8

40

260

16.

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Weight (oz)

Rat

e ($

)

0

1

2

3

4

5

6

1.0 2.0 3.0 4.0 5.0

(2.0, 1.80), (3.0, 2.75), (4.0,

3.70), and (5.0, 4.65)

game; score

Sample answer:

Between the fi rst and

third game Robert

becomes comfortable

with the lane. Robert is

tired for the fourth game.

As the weight of the letter increases, the rate increases.

B: 2[(5 - 1) ÷ 4 +

1]


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2 _ 3 (3 ÷ 2) + (9 - 9) (Subst.)

= 2 _ 3 ( 3 _ 2 ) + 0 (Subst.)

= 1 + 0 (Mult. Inverse)

= 1 (Add. Identity)

42 + 2nsix times a numbersquared divided by 5

45

200

88

(2)(x) + (2)(3y)

- (2)(2z);

2x + 6y - 4z

3 + 30a + 33an

simplifi ed

105

100

Multi. Iden.; 1

Substitution; 9

5

_ 4

1

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B:

year; number of newspapers soldThe number of

newspapers sold was

decreasing during the

years 2006–2010.

Dis

tan

ce

Time

The population of Ohio

was about 4 million in

1900.

function

t = 50 + 4(8); t = 82

The population of Ohio will approach about 13 million.

-6r 2 - 4r + 2

10

Sample answer:

The puppy goes a

distance on the trail, stays

there for a while, goes

ahead some more, stays

there for a while, then

goes back to the

beginning of the trail. The

function is continuous.


Chapter 1 Assessment Answer Key Page 73, Extended-Response Test

Scoring Rubric

Score General Description Specifi c Criteria

4 Superior

A correct solution that

is supported by well-

developed, accurate

explanations

• Shows thorough understanding of the concepts of translating between verbal and algebraic expressions, open sentence equations, algebraic properties, and graphs of functions.

• Uses appropriate strategies to solve problems.

• Computations are correct.

• Written explanations are exemplary.

• Graphs are accurate and appropriate.

• Goes beyond requirements of some or all problems.

3 Satisfactory

A generally correct solution,

but may contain minor fl aws

in reasoning or computation

• Shows an understanding of most of the concepts of translating between verbal and algebraic expressions, open sentence equations, algebraic properties, and graphs of functions.

• Uses appropriate strategies to solve problems.

• Computations are mostly correct.

• Written explanations are effective.

• Graphs are mostly accurate and appropriate.

• Satisfi es all requirements of problems.

2 Nearly Satisfactory

A partially correct

interpretation and/or

solution to the problem

• Shows an understanding of most of the concepts of

translating between verbal and algebraic expressions, open sentence equations, algebraic properties, and graphs of functions.

• May not use appropriate strategies to solve problems.

• Computations are mostly correct.

• Written explanations are satisfactory.

• Graphs are mostly accurate.

• Satisfi es the requirements of most of the problems.

1 Nearly Unsatisfactory

A correct solution with no

supporting evidence or

explanation

• Final computation is correct.

• No written explanations or work shown to substantiate the

fi nal computation.

• Graphs may be accurate but lack detail or explanation.

• Satisfi es minimal requirements of some of the problems.

0 Unsatisfactory

An incorrect solution

indicating no mathematical

understanding of the

concept or task, or no

solution is given

• Shows little or no understanding of most of the concepts

of translating between verbal and algebraic expressions, open sentence equations, algebraic properties, and graphs of functions.

• Does not use appropriate strategies to solve problems.

• Computations are incorrect.

• Written explanations are unsatisfactory.

• Graphs are inaccurate or inappropriate.

• Does not satisfy requirements of problems.

• No answer may be given.

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Chapter 1 Assessment Answer Key Page 73, Extended-Response Test

Sample Answers

In addition to the scoring rubric found on page A33, the following sample answers may be used as guidance in evaluating extended response assessment items.

1a. Sample answer: 2x + 1; two times x plus 1

1b. Sample answer: the quotient of x

minus 1 and 2; x - 1 _____ 2

2. The student should explain that a replacement set is a set of possible values for the variable in an open sentence. The solution set is the set of values for the variable in an open sentence that makes the open sentence true.

3a. The student should write an equation that represents the Additive Identity Property, the Multiplicative Identity Property, the Multiplicative Property of Zero, or the Multiplicative Inverse Property. The student should also name the property that is illustrated. Sample answer: 1 + 0 = 1; Additive Identity Property

3b. Since 23 is the sum of 20 and 3, the Distributive Property allows the product of 7 and 23 to be found by calculating the sum of the products of 7 and 20, and 7 and 3.

3c. The student should explain that the Commutative and Associative Properties allow the terms in the expression 18 + 33 + 82 + 67 to be moved and regrouped so that sums of consecutive terms are multiples of 10. Thus, after the first step of addition the remaining sums are easier to accomplish.

18 + 33 + 82 + 67= 18 + 82 + 33 + 67 Commutative (+)= (18 + 82) + (33 + 67) Associative (+)= 100 + 100 Substitution = 200 Substitution

4. Sample answer: The distance a boy is from his home as a function of time. Label the vertical axis as distance and

the horizontal axis as time. The boy rides his bike to the post office to drop off a letter. He rides to his high school which is a bit closer to his house. He jogs twice around the track, then rides his bike straight home.

5a. Sample answer: {(-1, -3), (0, -1), (1, 4), (2, 5)}

5b. Sample answer:

x y

-1 -1

0 -3

0 -1

1 4

2 5

5c. The student should identify in their relation where they used the same domain element with two or more different range elements.

6. Nonlinear; y-intercept about 2.9, so about 2.9% of polled accessed the Internet away from home several times a day in March 2004. No x-intercept, so no time when no one accessed the Internet away from home several times a day; no symmetry; positive for x > 0; increasing between x = 0 and x ≈ 15 and between about x ≈ 38 and x ≈ 72, it is slightly decreasing between x ≈ 15 and x ≈ 38, away from home Internet use increased from March 2004 for about 15 months to about 4%, decreased slightly until March 2007 when it began to increase; appears to continue to increase.

X Y

-1012

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Chapter 1 Assessment Answer KeyStandardized Test Practice

Page 74 Page 75

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33a.

1000 computers were affected when time started.

33b.

The number of affected computers is expected to continue to increase.

Time

Dis

tan

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Sample answer:

x =

18

11y +

3

11n

8

4

22

11

four times m squared plus two

2x - 6

5.04

12

136

1 _ 6

{2}


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