MathMatters 1: An Integrated Program, Extra Practice Workbook

Extra Practice Workbook Contents Include: 88 worksheets— one for each lesson To The Student: This Extra Practice Work...

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Extra Practice Workbook

Contents Include: 88 worksheets— one for each lesson

To The Student: This Extra Practice Workbook gives you additional problems for the concept exercises in each lesson. The exercises are designed to aid your study of mathematics by reinforcing important mathematical skills needed to succeed in the everyday world. The material is organized by chapter and lesson, with one skills practice worksheet for every lesson in MathMatters 1.

To the Teacher: Answers to each worksheet are found in MathMatters 1 Chapter Resource Masters.

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Except as permitted under the United States Copyright Act, no part of this book may be reproduced in any form, electronic or mechanical, including photocopy, recording, or any information storage or retrieval system, without permission in writing from the publisher. Send all inquiries to: The McGraw-Hill Companies 8787 Orion Place Columbus, OH 43240 ISBN: 0-07-869304-7

MathMatters 1 Extra Practice Workbook

1 2 3 4 5 6 7 8 9 10 XXX 12 11 10 09 08 07 06 05 04

CONTENTS Lesson

1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 4-1 4-2 4-3 4-4 4-5 4-6

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Title

Page

Lesson

Collect and Interpret Data . . . . . . 1 Measures of Central Tendency and Range . . . . . . . . . . . . . . . . . 2 Stem-and-Leaf Plots . . . . . . . . . . . 3 Problem-Solving Skills: Circle Graphs . . . . . . . . . . . . . . . . . . . . 4 Frequency Tables and Pictographs . . . . . . . . . . . . . . . . 5 Bar Graphs and Line Graphs . . . . 6 Scatter Plots and Lines of Best Fit . . . . . . . . . . . . . . . . . . . . . . . 7 Box-and-Whisker Plots . . . . . . . . . 8 Units of Measure . . . . . . . . . . . . . 9 Work with Measurements . . . . . . 10 Perimeters of Polygons . . . . . . . . 11 Area of Parallelograms and Triangles . . . . . . . . . . . . . . . . . 12 Solving Equations and Formulas . . . . . . . . . . . . . . . . . 13 Equivalent Ratios . . . . . . . . . . . . 14 Circumference and Area of a Circle . . . . . . . . . . . . . . . . . . . . 15 Proportions and Scale Drawings . . . . . . . . . . . . . . . . . 16 Area of Irregular Shapes . . . . . . . 17 Add and Subtract Signed Numbers . . . . . . . . . . . . . . . . . 18 Multiply and Divide Signed Numbers . . . . . . . . . . . . . . . . . 19 Order of Operations . . . . . . . . . . 20 Real Number Properties . . . . . . . 21 Variables and Expressions . . . . . 22 Writing Equations From Patterns . . . . . . . . . . . . . . . . . . 23 Exponents and Scientific Notation . . . . . . . . . . . . . . . . . 24 Laws of Exponents . . . . . . . . . . . 25 Squares and Square Roots . . . . . 26 Language of Geometry . . . . . . . . 27 Polygons and Polyhedra . . . . . . . 28 Visualize and Name Solids . . . . . 29 Nets and Surface Area . . . . . . . . 30 Isometric Drawings . . . . . . . . . . . 31 Perspective and Orthogonal Drawings . . . . . . . . . . . . . . . . . 32

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4-7 4-8 4-9 5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8 5-9 6-1 6-2 6-3 6-4 6-5 6-6 6-7 6-8 7-1 7-2 7-3 7-4 7-5 7-6 7-7 7-8 8-1 8-2 8-3 8-4 8-5

iii

Title

Page

Volumes of Prisms and Cylinders . . . . . . . . . . . . . . . . . 33 Volumes of Pyramids and Cones . . . . . . . . . . . . . . . . . . . 34 Surface Area of Prisms and Cylinders . . . . . . . . . . . . . . . . . 35 Introduction to Equations . . . . . . 36 Add or Subtract to Solve Equations . . . . . . . . . . . . . . . . 37 Multiply or Divide to Solve Equations . . . . . . . . . . . . . . . .38 Solve Two-Step Equations . . . . . 39 Combine Like Terms . . . . . . . . . 40 Formulas . . . . . . . . . . . . . . . . . . . 41 Solving Addition and Subtraction Equations . . . . . . . . . . . . . . . . 42 Graph Open Sentences . . . . . . . . 43 Solve Inequalities . . . . . . . . . . . . 44 Percents and Proportions . . . . . . 45 Write Equations for Percents . . . 46 Discount and Sale Price . . . . . . . 47 Tax Rates . . . . . . . . . . . . . . . . . . . 48 Simple Interest . . . . . . . . . . . . . . 49 Commission . . . . . . . . . . . . . . . . 50 Percent of Increase and Decrease . . . . . . . . . . . . . . . . . 51 Simple Interest . . . . . . . . . . . . . . 52 Graphs and Functions . . . . . . . . . 53 Coordinate Plane . . . . . . . . . . . . . 54 Relations and Functions . . . . . . . 55 Linear Graphs . . . . . . . . . . . . . . . 56 Slope of a Line . . . . . . . . . . . . . . 57 Slope-Intercept Form of a Line . . . . . . . . . . . . . . . . . . . . . 58 Distance and the Pythagorean Theorem . . . . . . . . . . . . . . . . . 59 Solutions of Linear and Nonlinear Graphs . . . . . . . . . . . . . . . . . . . 60 Angles and Transversals . . . . . . . 61 Beginning Constructions . . . . . . 62 Diagonals and Angles of Polygons . . . . . . . . . . . . . . . . . 63 Combinations . . . . . . . . . . . . . . . 64 Translations in the Coordinate Plane . . . . . . . . . . . . . . . . . . . . 65

MathMatters 1

Lesson

8-6 8-7 9-1 9-2 9-3 9-4 9-5 9-6 9-7 10-1 10-2

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Lesson

Reflections and Line Symmetry . . . . . . . . . . . . . . . . 66 Rotations and Tessellations . . . . . 67 Monomials and Polynomials . . . 68 Add and Subtract Polynomials . . 69 Multiply Monomials . . . . . . . . . . 70 Multiply a Polynomial by a Monomial . . . . . . . . . . . . . . . . 71 Factor Using Greatest Common Factor (GCF) . . . . . . . . . . . . . . 72 Divide by a Monomial . . . . . . . . 73 Multiplying Monomials and Polynomials . . . . . . . . . . . . . . 74 Probability . . . . . . . . . . . . . . . . . . 75 Experimental Probability . . . . . . 76

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10-3 10-4 10-5 10-6 10-7 11-1 11-2 11-3 11-4 11-5 11-6 11-7

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Page

Sample Spaces and Tree Diagrams . . . . . . . . . . . . . . . . . 77 Counting Principle . . . . . . . . . . . 78 Independent and Dependent Events . . . . . . . . . . . . . . . . . . . 79 Experimental Probability . . . . . . 80 Expected Value and Fair Games . . . . . . . . . . . . . . . . . . . 81 Optical Illusions . . . . . . . . . . . . . 82 Inductive Reasoning . . . . . . . . . . 83 Deductive Reasoning . . . . . . . . . 84 Venn Diagrams . . . . . . . . . . . . . . 85 Logical Reasoning . . . . . . . . . . . 86 A Plan for Problem Solving . . . . 87 Non-Routine Problem Solving . . 88

MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

1-1

COLLECT AND INTERPRET DATA EXERCISES Identify the method used to find the most popular lunch item in the school cafeteria. List advantages and disadvantages of the method. 1. Poll every tenth student who enters the cafeteria to eat lunch.

2. Poll the first 10 students who enter the cafeteria to eat lunch.

3. Poll a randomly chosen sample of 10 students at the school.

4. Poll your friends.

You need to determine teenagers’ favorite sport. Identify the method described, and list its advantages and disadvantages. 5. Poll students in your math class.

6. Poll the basketball team.

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Glencoe/McGraw-Hill

1

MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

1-2

MEASURES OF CENTRAL TENDENCY AND RANGE EXERCISES Rita’s test scores in math so far for this grading period are shown. 91

82

77

98

66

85

82

1. Find the mean.

2. Find the median.

3. Find any modes.

4. Find the range.

5. Which measure of central tendency best describes Rita’s test scores?

6. If Rita takes an eighth test and earns a grade equal to the mean, which measure of central tendency would not change? Which measure of central tendency best represents each data set? 7. middle value of hourly wage of employees at a convenience store 8. number of people with green eyes among your classmates 9. favorite subject among your friends 10. average number of hours spent each week at a health club by members The table shows the daily sales at an ice cream store one week last summer. 11. Find the mean. ________________________________ 12. Find the median. ______________________________ 13. Find any modes. _______________________________

Day Monday Tuesday Wednesday Thursday Friday Saturday

Sales $1562 $1895 $1704 $1650 $1895 $2368

14. Find the range. ________________________________ 15. Which measure of central tendency best describes the average daily sales? Explain.

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MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

1-3

STEM-AND-LEAF PLOTS EXERCISES This stem-and-leaf plot shows the number of minutes students exercised one school day.

1 2 5 9 2 0 4 5 8 3 1 3 6 7 9 4 2 5 5 8 5 3 5 8 6 0 3|1 represents 31 minutes

1. How many students are represented in this stem-and-leaf plot? 2. How many students exercised more than 40 minutes? 3. How many students exercised fewer than 30 minutes? 4. How many students exercised 55 minutes? 5. Find the mean of this data. 6. Find the median of this data. 7. Find the mode of this data. 8. Find the range of this data. For Exercises 9–16, use the data at the right that represents the number of hours Nina worked each week since she started her new job.

46 32 16 24 40 45 40 36 29 24 25 38 40 42 50 40 35 45 46 36 35 28 25 38

9. Create a stem-and-leaf plot of the data.

10. How many weeks are represented? 11. What is the greatest number of hours? 12. What is the least number of hours? 13. Identify any outliers. 14. Identify the clusters. 15. Identify the gaps. ©

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MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

1-4

CIRCLE GRAPHS MUSIC For Exercises 1 and 2, use the circle graph below that shows data about music sales in 2001.

INVESTMENTS For Exercises 3–6, use the table below that shows how Mr. Broussard has invested his money.

Music Sales, 2001

Investments

5% Others

2.4% Singles

Savings Account

3.4% Full-Length Cassettes

89.2% Full-Length CDs

$60,000

Money Market Account

$100,000

Mutual Funds

$140,000

Stocks

$500,000

Bonds

$200,000

1. What angle corresponds to the sector labeled “Others” in the circle graph? Explain how you found your answer.

2. Use the circle graph to describe music sales in 2001.

3. Explain how a circle graph could help you visualize the data in the table.

4. Determine the percent of Mr. Broussard’s total investments that each type of investment represents.

5. Draw a circle graph to represent the data.

6. Use the circle graph you made in Exercise 5 to describe Mr. Broussard’s investments.

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MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

1-5

FREQUENCY TABLES AND PICTOGRAPHS The prices in dollars of exercise equipment sold at a sporting goods store are shown. 325 450 175 500 350 425 200 350 475 150 175 180 210 350 400 500 250 375 460 250

EXERCISES 1. Make a frequency table of the data on your own paper. 2. What price is charged most often for exercise equipment? 3. What is the average price paid for exercise equipment at this store? 4. How many pieces of exercise equipment are sold for between $300 and $600? 5. How many pieces of exercise equipment are sold for less than $200? Use the pictograph for Exercises 6–11.

Number of CDs Sold

6. On which day were the most CDs purchased?

Fri Thurs

7. On which day were the fewest CDs purchased?

Weds Tues

8. About how many more CDs were purchased on Thursday than on Tuesday?

Mon

Key:

= 10 CDs

9. About how many fewer CDs were purchased on Monday than on Friday?

10. About how many total CDs were purchased on all five days? 11. If 75 CDs were sold on Saturday, how many symbols would you use to add Saturday to the graph?

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MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

1-6

BAR GRAPHS AND LINE GRAPHS EXERCISES Use the bar graph for Exercises 1–5. 1. Which day of the week did the most people visit the website? Approximately how many visits were there?

Visitors to Website 100 80

Number

2. Which day of the week did the fewest number of people visit the website? Approximately how many visits were there?

60 40 20

3. Which days had over 50 visits? 0

S

M

T W Day

T

F

S

4. About how many times more visits were there to the website on Saturday than on Tuesday? 5. Estimate on which day the number of visits was about one-half the number of visits on Sunday. Use the line graph for Exercises 6–8.

Daily High Temperature

7. Between which two consecutive days was the difference in the high temperatures the greatest? What was the approximate difference in the temperatures?

80 Temperature (°F)

6. On which day was the high temperature the greatest? Approximately what was the temperature?

60

40

20

0

1

2

3

4

5

6

7

8. Between which two consecutive days Day was the difference in the high temperatures the least? What was the approximate difference in the temperatures?

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MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

1-7

SCATTER PLOTS AND LINES OF BEST FIT EXERCISES

Average Number of Points Scored Per Game

The scatter plot shows the average number of points scored by basketball team members who responded to a survey. 1. How many players responded to the survey? 2. How many points did the players with 7 years of experience score?

Number of Points

32

3. What is the range of the average number of points scored per game?

24

16

8

0

1

2

3 4 5 6 Years Played

7

4. Is there a positive or negative correlation between the number of years a player has played and the average number of points scored per game? 5. Which data point lies farthest from the line of best fit? What could account for this piece of data? Use the data table to answer Exercises 6–9. 6. Make a scatter plot and a line of best fit on your own paper. Make the horizontal axis number of customers and the vertical axis hourly sales in dollars. 7. What intervals did you choose for each axis? 8. What effect does changing the intervals have on the scatter plot? 9. Is there a positive or negative correlation between the number of customers per hour and the hourly sales?

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Number of Customers per Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Hourly Sales (dollars) 6 9 6 15 28 22 18 33 25 48 44 52 60 61

MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

1-8

BOX-AND-WHISKER PLOTS EXERCISES Use the box-and-whisker plot to answer Exercises 1–5. Cost of Items on Menu

1

2

3

4

5

6

7

8

9

10

1. What are the greatest and least prices?

2. What is the range of the prices?

3. What is the median price?

4. What is the range of the middle 50%?

5. In which interval are the prices most closely clustered? (What is the typical price range of an item?) Use the data below for Exercises 6–9. Tomas Kirk

Hits During League Tournament Games 2 3 4 3 2 5 4 1 3 6 5 1 1 4 2 3

4 1

6. Make a box-and-whisker plot showing both sets of data on the same number line using a different color for Tomas and Kirk.

1

2

3

4

5

6

7

8

9 10

7. Does the plot for Tomas or Kirk have the greatest median? What does this mean?

8. Does Tomas or Kirk have the least range in the middle 50%? What does this mean?

9. Identify any outliers.

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MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

2-1

UNITS OF MEASURE EXERCISES Which unit of measure gives a more precise measurement? 1. meter, kilometer ___________________

2. pound, gram ________________________

3. centimeter, inch ___________________

4. cup, pint ___________________________

5. kiloliter, liter ______________________

6. foot, yard ___________________________

7. quart, gallon ______________________

8. meter, centimeter ___________________

Name the tool or tools that would best measure each object. 9. human arm _______________________ 10. length of a basketball court ___________ 11. weight of a newborn baby___________ 12. flour _______________________________ 13. outside temperature _______________ 14. height of a house ____________________ Choose the appropriate unit to estimate the measure. 15. mass of a dog: ounce, pound, or milligram______________________________________ 16. length of a car: centimeter, mile, or foot ________________________________________ 17. pitcher of lemonade: liter, milliliter, or kiloliter __________________________________ 18. width of an envelope: yard, meter, or inch ______________________________________ Choose the best estimate for each measure. 19. length of a pen: 15 cm, 15 ft, or 15 m ___________________________________________ 20. height of a door: 8 in., 8 ft, or 8 m ______________________________________________ 21. paint in a can: 1 gal, 1 mL, or 1 oz______________________________________________ 22. An interior designer is preparing to order carpet for a client’s living room. She has to estimate the amount of carpeting needed to complete the job. How accurate must her estimate be? Does her estimate have to be precise?

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9

MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

2-2

WORK WITH MEASUREMENTS EXERCISES Complete. 1. 32 fl oz __________ c

2. 18 in. ____________ ft

3. 5 L ____________ mL

4. 6 yd _____________ ft

5. 3 T ______________ lb

6. 90 in. _____ ft ____in.

7. 72 in. ___________ yd

8. 0.6 m __________ cm

9. 7 g ____________ mg

10. 80 m __________ km

11. 9 qt _____ gal____ qt

12. 2 gal ____________ qt

13. 2400 L __________ kL

14. 4.2 km __________ m

15. 40 ft _____ yd_____ft

16. 1.8 m _________ mm

17. 5 yd ____________ in.

18. 6 qt ____________ pt

Complete. Write each answer in simplest form. 19.

22.

8 lb 4 oz 3 lb15 oz

4 lb 5 oz 8 oz

25. 3 yd 2 ft 2

20.

23.

6 ft 2 in. 3 ft 6 in.

21.

2 c 4 fl oz 6

26. 5 ft 6 in. 4

24.

8 yd 3 yd 2 ft

7 lb 6 oz 3

27. 8 gal 2 qt 8

28. 8 cm 6 mm _______________ mm

29. 60 g • 8 _______________________ kg

30. 3.5 kg 200 g ________________ kg

31. 8 • 25 mm ____________________ cm

32. 2.4 L 6 ____________________ mL

33. 2 m 100 mm _______________ cm

34. 400 mg 5 ____________________ g

35. 60 mL • 6 ______________________ L

36. 1 km 60 cm _________________ m

37. 1 kL 5 _______________________ L

38. Rita bought 168 inches of string for a kite at $0.25/ft. How much did she pay for the string, to the nearest cent? 39. Nic is making a cake and the recipe calls for 2 cups of milk. He has 1 quart of milk. Does he have enough milk to make the cake? If so, will he have any left over? How much? ©

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MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

2-3

LINEAR MEASURE AND PERIMETER EXERCISES Find the perimeter of each figure with its given dimensions. 1.

2.

2.6 ft

2.6 ft

3. 6.8 m

2.6 ft

6.8 m

10.5 in.

4 in.

6 in.

7 in. 2 in.

2.6 ft

4.

5.

6.

9.8 cm 4.5 cm

12.5 ft

4.8 ft

3.5 in.

6.8 m

3.5 cm

4.5 m 4m

4 cm

11 cm 15 ft

4.5 cm

5m

10 m

3.5 m 2.5 m 3.5 cm

3m 12.5 m

9.8 cm

7. square: 15 mm 9. triangle: 12 cm, 15 cm, 18 cm

8. rectangle: 4 in., 6 in. 10. rectangle: 5.7 cm, 6.5 cm

11. square: 5.8 cm

12. triangle: 4.5 in., 5.6 in., 3.8 in.

13. rectangle: 4.5 ft, 3.75 ft

14. square: 2.25 in.

Estimate the perimeter of the following objects. 15. square picture: 6.5 in.

16. window: 5.8 ft by 8.4 ft

17. patio: 3.8 m by 4.9 m

18. door: 8.5 ft by 4.8 ft

19. A builder needs to order trim to put around a window. The dimensions of the window are 4 ft by 8 ft. How many feet of trim should he order?

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MathMatters 1

Name _________________________________________________________

Date ____________________________

2-4

EXTRA PRACTICE

AREA OF PARALLELOGRAMS AND TRIANGLES EXERCISES Find the area of each figure, given the dimensions. 1. rectangle: 1 ft by 31 ft 4 2 2. parallelogram: b 15 m, h 6 m 3. square: 15 yd sides 4. triangle: h 3.5 in., b 5.2 in. 5. rectangle: 4.6 cm by 8.3 cm 6. square: 1.8 m sides 7. triangle: h 25 mi, b 16 mi 8. parallelogram: b 8.2 ft,h 2.5ft 9. square: 3.5 yd sides 10. rectangle: 3.8 ft by 4.9 ft Find the area of each figure. 11.

12.

18 yd

13. 6m

18 yd 11.4 in.

6m

8.6 in.

14.

15.

16.

45 cm 3.8 in. 20 cm 15 in.

10 ft

8.2 ft

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MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

2-5

SOLVING EQUATIONS AND FORMULAS EXERCISES Solve each equation or formula for the variable specified. 1. d rt, for r ______

2. 6w y 2z, for w ____________

3. mx 4y 3c, for x _____________

4. 9s 5g 4u, for s ______________

5. ab 3c 2d, for b _____________

6. 2p kx q, for x ____________

2 7. m a a c, for m _________

2 8. h g d, for h _____________

2 9. y v s, for y _____________

3 10. a q k, for a _____________

3

3

rx 9 5

5

4

3b 4 2

11. h, for x ____________

12. c, for b ____________

13. 2w y 7w 2, for w ___________

14. 3 y 5 5, for ___________

Write an equation and solve for the variable specified. 15. Three times a number s plus 4 times a number y is 1 more than 6 times the number s. Solve for s.

16. Five times a number k minus 9 is two thirds of a number j. Solve for j.

ELECTRICITY For Exercises 17 and 18, use the following information. The formula for Ohm’s Law is E IR, where E represents voltage measured in volts, I represents current measured in amperes, and R represents resistance measured in ohms. 17. Solve the formula for R. 18. Suppose a current of 0.25 ampere flows through a resistor connected to a 12-volt battery. What is the resistance in the circuit?

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MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

2-6

EQUIVALENT RATIOS EXERCISES Write each ratio two other ways. 1. 8 to 9

2. 14 : 5

3. 3 4

4. 4 5

5. 6 to 19

6. 15 : 7

7. 6 to 1

8. 5 : 9

9. 7 8

Write each ratio as a fraction in lowest terms. 10. 6 cm : 3 cm

11. 8 h to 5 h

12. 2.5 m to 10 m

13. 8 ft to 3 yd

14. 4 m to 4 cm

15. $1.50 : $0.75

Are the ratios equivalent? Write yes or no. 16. 3 to 5, 9 to 15

17. 16 : 6, 8 : 2

25 18. 5, 7 3 0

19. 12 : 32, 6 : 24

20. 6 to 9, 8 12

21. 21 to 14, 12 to 8

Find the ratio of width to length in each rectangle. Express the ratio as a fraction in lowest terms. 22.

23.

60 cm

24.

9 cm 40 mm

2m 70 cm

1m

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MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

2-7

CIRCUMFERENCE AND AREA OF A CIRCLE EXERCISES Find the area. If necessary, round the answer to the nearest tenth. 1.

2 2

3. 2 4.

m

4.

. in

36 ft

5. 8m

6. 2.5 yd

15 i

n.

Find the circumference of the circles in Exercises 1–6. 7. Exercise 1

8. Exercise 2

9. Exercise 3

10. Exercise 4

11. Exercise 5

12. Exercise 6

Find the area of a circle with the given dimensions. 13. d 10 cm

14. r 1.4 in.

15. r 31 ft 2

Find the circumference of the circles described in Exercises 13–15. 16. Exercise 13

17. Exercise 14

18. Exercise 15

Complete the chart. Radius 19.

Area

14 in. 15 cm

22.

©

Circumference

6 ft

20. 21.

Diameter

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2m

15

MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

2-8

PROPORTIONS AND SCALE DRAWINGS EXERCISES Tell whether each statement is a proportion. Write yes or no. ? 12 1. 4 7 2 1 ?

4. 6 : 9 8 : 9

? 2. 3 4 9 12

? 3. 8 3 25 15

5. 18 : 12 12 : 8

6. 16 : 32 12 : 28

Use mental math to solve each proportion. 7. 2 6 5 ?

8. 8 4 ? 3

9. 3 ? 4 20

10. ? : 10 3 : 15

11. 5 : 2 25 : ?

12. 14 : ? 28 : 18

13. ? 6 16 24 8 1 2 7 16. ? 4

14. 6 : 14 ? : 42

15. 8 : ? 16 : 27

1 2 6 0 17. 7 ?

18. 14 : 9 42 : ?

Find the actual or drawing length. 19. Scale, 1 cm : 4 m

20. Scale, 1 in. : 3 ft

21. Scale, 1 in. : 5 mi

Drawing length, 12 cm

Drawing length,

Drawing length, 3 in.

Actual length,

Actual length, 12 ft

Actual length,

22. Scale, 1 cm : 9 km

23. Scale, 1 cm : 8 m

24. Scale, 1 in. : 20 mi

Drawing length,

Drawing length, 15 cm

Drawing length,

Actual length, 27 km

Actual length,

Actual length, 50 mi

25. Riley makes a model of a building. He used the scale 1 in. : 5 ft. The height of the model is 15 in. Find the height of the actual building. 26. Cristia uses 3 cups of butter to make 9 dozen cookies. How many dozen cookies could she make with 1 cup of butter? 27. Andrea got 4 hits during a softball tournament. Her ratio of hits to times at bat is 2 : 5. How many times did Andrea bat?

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2-9

EXTRA PRACTICE

AREA OF IRREGULAR SHAPES EXERCISES Find the area of each figure. 1.

2.

9 ft 3 ft 6 ft 3 ft

4 in.

4.5 m

2 in.

9m

3.5 in.

5.

9.8 cm 4.5 cm

3.5 m 2.5 m

3.5 cm

5.5 m

4 cm 4.5 cm

6.

9m

3m 11 cm

3m

6 in.

7 in.

3 ft

6 ft

4.

3.

10.5 in.

12.5 m

13 yd

3.5 cm

6 yd

9.8 cm

6 yd

7.

8.

12 in.

9.

20 cm

3.8 in.

25 cm

15 in. 12.5 in.

20 cm 25 cm

3.4 in. 6.8 in.

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3-1

ADD AND SUBTRACT SIGNED NUMBERS EXERCISES Add or subtract. Use a number line or the rules for adding integers. 1. 6 6

2. 15 24

3. 6 8

4. 7 (5)

1 3 5. 4 8

6. 20 13

7. 8 (9)

8. 12 6

9. 8 (17)

10. 5.2 4.5

11. 8 (8)

2 5 12. 3 6

13. 50 (24)

14. 0.7 (20.4)

15. 18 15

16. 6 6

17. 15 24

18. 6 8

19. 14.5 (12.8)

2 20. 2 3

3 2 21. 7 3

Simplify. 22. 14 (16) 19

23. 3.6 4.8 6.1

24. 1 3 5 2 4 6

25. 28 35 (36)

26. 8 7 9 (15)

27. 13 (10) 5 (4)

Without subtracting, tell whether the answer will be positive or negative. 28. 1.8 (2.1)

29. 12 16

30. 15 (5)

31. 18 24

Use , , or to complete each sentence. 32. 9 4 34. 6 (9)

56

33. 5 (4)

5 (10)

35. |14| |10|

6 15 |9| |15|

36. WEATHER The high temperature on Monday was 8°C and the low was 2°C. What was the difference in temperatures on Monday? 37. FINANCE On Friday morning, Hana had $235 in her checking account. Friday afternoon she wrote checks for $42, $10, and $35. What was her balance?

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3-2

MULTIPLY AND DIVIDE SIGNED NUMBERS EXERCISES Multiply or divide. 1. 14 2 28 4. 7 7. 6 • (7) 81 10. 9 13. 5 • (2) • 3

2. 5 • (9)

3. 7 • 7

5. 5 • (6)

6. 32 (4)

8. 12 • (4)

9. 54 (6)

11. 3 • (8)

12. 15 • (3)

14. 75 (5)

15. 8 • (6) • (3)

Use , , or to complete each sentence. 16. 3 • (7) 18. 36 4 20. 8 • (2)

17. 20 4

3 • 7 18 2 4 • 4

19. 15 (3) 21. 32 8

20 (4) 12 (4) 24 (6)

22. INVESTING A stock lost $4 a day for 6 days. What was the net change in value of the stock after those 6 days? 23. SPORTS A team lost a total of 12 yards on 2 plays. What was the average loss per play? 24. WEATHER A total of 6 inches of rain fell in 3 hours. What was the average rain fall per hour? Write the multiplication sentence that describes each word phrase. Then find the product or quotient. 25. six times negative three 26. negative fifteen divided by five 27. negative seven times negative six 28. five times negative eight 29. negative four times nine

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3-3

ORDER OF OPERATIONS EXERCISES Simplify. Use the order of operations. 1. 4 8 2

2. 28 6 • 3

3. 2 • 10 4

4. 19 6 3

5. 2 1 3 10 5 5

6. 4 • 3 2 • 5

7. 18 3 2 • 6

8. 4 22 • 5

9. (16 9) 4 • 3 11. 1(3 7) • 5 4 2 13. 9 3 • 3 23

10. 0.5 • 0.2 0.3 • 0.4 12. 8 • (4 2) 8

17. 2 • 16 (15 3) 5

14. (25 42) • 3 2 16. (4 3)2 • 1 7 18. 48 2 • 3 9

19. (16 32) (2 3)2

20. 2.5 0.5 0.6 • 5

15. 36 (4 5) • (4 • 2)

Write a numerical expression for each of the following. 21. the sum of three and seven, divided by two 22. three squared, times the difference of fifteen and six, times seven 23. the difference of eight and five, multiplied by two cubed plus four

Write true or false for each. For any that are false, insert parentheses to make them true. 24. 10 4 • 2 12 25. 6 • 4 22 48 26. 18 3 3 • 2 18

27. 1.4 • 0 4 0.2 20

28. Raul earned $30 on Monday and twice as much on Tuesday. On Wednesday, he spent one-half of the money he earned on Monday and Tuesday. How much money did he have left?

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3-4

REAL NUMBER PROPERTIES EXERCISES To which sets of numbers do the following belong? 1. 18 2. 5 3. 14.235 4. 5 3 5. 8.123286 . . . 6. 1 7. 1 2 Complete. Name the property you used. 8. 14 • 21 9.

•

14

(15 12) (3 • 15) (3 • 12)

10. (3 • 7) • 5 3 • (

•

11. 1.75 2.6

1.75

5)

12. 2(15 6) (2 • 15) (2 •

)

Simplify using mental math. Name the properties you used. 13. 16 8 6 12 14. 15 • 3 • 2 15. 40 • 201 16. 0.3 14 0.7 State whether the following sets are closed under the given operation. 17. integers, multiplication 18. whole numbers, subtraction 19. rational numbers, addition

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20. irrational numbers, division

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3-5

VARIABLES AND EXPRESSIONS EXERCISES Write a variable expression. Let n represent “a number.” 1. three times a number

2. six more than a number

3. a number divided by four

4. a number increased by eight

5. nine less than a number

6. twenty decreased by a number

7. the product of twelve and a number 8. seven less than ten times a number Evaluate each expression. Let x 12, y 2, and z 3. 10. 16 z

9. x 2 11. 6y

12. 8 z

13. y 14

14. x y

15. 3x 5

16. 2z 4

17. x y

18. x z 2x 20. 3 22. x 4y

19. 3z 3 21. 2z • 3y 23. 4z y

24. 2x 3z 15 26. x z

25. x y z Write an expression to describe each situation. 27. n notebooks decreased by two

28. p pieces of pizza shared equally by four friends 29. six more than two times t tapes 30. two less than three times c cents Trevor has b baseball cards. He buys eight more. 31. Write an expression to describe the situation. 32. Evaluate the expression if b 25.

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3-6

WRITING EQUATIONS FROM PATTERNS EXERCISES 1. Give the next two items for the pattern. Then find the 21st figure in the pattern.

Find the next three terms in each sequence 2. 5, 2, 3, 0, 1, 2, 1, 4, …

3. 0, 1, 3, 6, 10, 15, …

4. 0, 1, 8, 27, …

5. 3, 2, 4, 3, 5, 4, …

6. a 1, a 4, a 9, …

7. 3d 1, 4d 2, 5d 3, …

Write an equation in function notation for each relation. 8.

9.

y

10.

y O

y

x

x

O

O

x

BIOLOGY Use the following information. Male fireflies flash in various patterns to signal location and perhaps to ward off predators. Different species of fireflies have different flash characteristics, such as the intensity of the flash, its rate, and its shape. The table below shows the rate at which a male firefly is flashing. Time (seconds)

1

2

3

4

5

Number of Flashes

2

4

6

8

10

11. Write an equation in function notation for the relation.

12. How many times will the firefly flash in 20 seconds?

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3-7

EXPONENTS AND SCIENTIFIC NOTATION EXERCISES Write in exponential form. 1. 8 • 8 • 8

2. 3 • 3 • 3 • 3 • 3 • 3 • 3

1 3. • 2 • 2 2•2

4. 12 • 12 • 12 • 12 • 12

Write in standard form. 5. 23

6. 52

7. 43

8. 91

9. 72

10. 150

11. 2.12 • 102

12. 4 • 105

13. 8.2 • 104

14. 9.213 • 103

15. 3.12 • 106

16. 1.1213 • 107

Write in scientific notation. 17. 22,345

18. 510,056

19. 0.00425

20. 914

21. 0.000000009

22. 2,345,000

23. 0.63

24. 5,000,250

25. The fastest speed lightning travels is about 50,400,000 kilometers per second. The speed of light is about 299,792 kilometers per second. How much faster does lightning travel? Express your answer in scientific notation.

26. Mercury is about 36,000,000 miles from the Sun. Venus is about 67,200,000 miles from the Sun. How much farther from the Sun is Venus? Express your answer in scientific notation.

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3-8

LAWS OF EXPONENTS EXERCISES Use the product rule to multiply. 1. 23 • 25

2. 63 • 66

3. 108 • 1010

4. d 4 • d 7

5. n5 • n 2

6. z 6 • z 8

7. 108 105

8. 45 42

9. 718 712

10. x 18 x 10

11. q 9 q 2

12. z10 z 6

13. (68)3

14. (95)5

15. (104)7

16. (x14)2

17. (y 5)11

18. (a 6)5

19. (124)7

20. 26 24

21. 612 65

22. 125 • 110

23. 33 • 315

24. (72)4

25. (5c)2 512

26. 68 6x 62

27. 4m 45 48

28. 88 • 8n 824

29. (45)a 425

30. 12r • 126 1236

Use the quotient rule to divide.

Use the power rule.

Use the laws of exponents.

Find the value of each variable.

31. There are 103 milligrams in a gram and 103 grams in a kilogram. How many milligrams are there in a kilogram?

32. Marri walks 10 m from her house to Keri’s house everyday. Then they walk 1 km from Keri’s house to Robyn’s house. How many times farther is it from Keri’s house to Robyn’s house than from Marri’s house to Keri’s house? (Remember to convert 1 km to m.)

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3-9

SQUARES AND SQUARE ROOTS EXERCISES Find each square. 1. 152

2. 122

3. 102

4. (4)2

5. (1.3)2

6. (0.03)2

7. (0.003)2

8. 1 6

10. (7 )2

2

9. 2 5

11. 2 7

2

2

12. (1 8 )2

Find each square root. 13. 1 6

14. 1 2 1

15. 1 4 4

16. 0 .6 4

17. 0 .0 1

18.

25 19. 36

20.

12956

811 21. 24596

Use the table to find each square root. Round to the nearest tenth. 22. 1 5

23. 2 1

24. 4 4

25. 7

26. 5 0

27. 3 2

CALCULATOR Find each square root. Round to the nearest tenth. 28. 1 4 0

29. 6 0 9

30. 2 1 3

31. 8 4 5

32. 5 5 3

33. 9 6 4

34. The area of a circle can be found by multiplying times the square of the radius. Find the radius of a circle with an area of 36 m2.

35. The volume of a rectangular prism with a square base can be found by multiplying the height, h, times the area of the base. Find the length of each side of the square base of a prism with a volume of 100h ft3.

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MathMatters 1

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4-1

EXTRA PRACTICE

LANGUAGE OF GEOMETRY EXERCISES Draw each geometric figure on your own paper. Then write a symbol for each figure. 1. line RS

2. angle 4

3. ray MN

4. point T

5. angle RST

6. line segment PQ

7. plane MNP

8. angle W

Use symbols to complete the following.

X

Y

Z

9. Name the line four ways. 10. Name two rays with X as an endpoint. 11. Name three different line segments. Draw a figure on your own paper to illustrate each of the following. 12. Line r and line s intersect at point P. 13. Plane Q and segment XY intersect at point X. 14. Angle 1 and angle 2 both have a vertex at point K. Use a protractor to find the measure of each angle.

M

N p

R

S

T

15. PST

16. MST

17. NSP

18. RSM

19. MSP

20. NST

Use a protractor to draw an angle of the given measure on your own paper. 21. 30°

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22. 105°

23. 46°

27

24.

164°

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4-2

POLYGONS AND POLYHEDRA EXERCISES Identify each polygon. State whether it is regular. 1. 2.

4.

Classify each triangle. 7.

3.

5.

6.

8.

9.

Identify the number of faces, vertices and edges for each figure. 10.

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11.

12.

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4-3

VISUALIZE AND NAME SOLIDS EXERCISES Identify each three-dimensional figure. 1. It has six faces that are identical squares. 2. It has one rectangular base and four other faces that are triangles.

3. It has two circular bases and a curved surface. 4. It has two bases that are identical, parallel triangles. The other three faces are rectangles. 5. It has a curved surface and no bases. 6. It has three faces that are triangles. It has one base that is a triangle.

Identify the three-dimensional figure that is formed by each net. 7. 8.

9.

10.

11. Name three everyday objects that have the shape of a cube.

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4-4

EXTRA PRACTICE

NETS AND SURFACE AREA EXERCISES Sketch each solid using isometric dot paper. 1. rectangular prism 3 units high, 3 units long, and 2 units wide

2. triangular prism 3 units high, whose bases are right triangles with legs 2 units and 4 units long

3. For the solid, draw a net and find the surface area.

15

6

9

4. SHIPPING Rawanda needs to wrap a package to ship to her aunt. The rectangular package measures 2 inches high, 10 inches long, and 4 inches wide. Draw a net of the package. How much wrapping paper does Rawanda need to cover the package? 2 10

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4-5

ISOMETRIC DRAWINGS EXERCISES Use the figure to name the following. 1. all of the parallel lines y

2. all of the perpendicular lines x

Complete the following on one drawing. Use your own paper. ↔ 3. Draw XY . ↔ ↔ 4. Draw LM perpendicular to LM at point L. ↔ ↔ 5. Draw line PQ parallel to LM through point N. ↔ ↔ 6. What is the relationship between PQ and XY ?

r

w s

z

On your own isometric dot paper, draw the following. 7. cube: s 4 m 9. cube: s 5.5 in. 11. cube: s 3 units

8. rectangular prism: l 10 cm, w 4 cm, h 8 cm 10. rectangular prism: 12 ft by 9 ft by 15 ft 12. rectangular prism: 4 units by 3 units by 2 units

13. How many 1 unit square cubes would build the cube in Exercise 11? 14. Sketch 1 unit square cubes in your drawing from Exercise 11. 15. How many 1 unit square cubes would build the prism in Exercise 12? 16. Sketch 1 unit square cubes in your drawing from Exercise 12. Make an isometric drawing of each figure. Use your own paper. 17.

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18.

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4-6

PERSPECTIVE AND ORTHOGONAL DRAWINGS EXERCISES Locate and label the vanishing point and horizon line. 1.

2.

3.

4.

Draw each of the following in one-point perspective. Use your own paper. 5. a cone

6. a triangular pyramid

Make an orthogonal drawing of each stack of cubes, showing top, front, and side views. Use your own paper. 7.

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8.

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4-7

VOLUMES OF PRISMS AND CYLINDERS EXERCISES Find the volume of each rectangular prism. 1. l 4 ft, w 12 ft, h 15 ft

2. l 4.5 cm, w 6 cm, h 9.2 cm

3. l 50 m, w 35 m, h 48 m

4. l 16 in., w 13 in., h 9 in.

5. l 0.05 km, w 0.275 km, h 0.8 km

6. l 5.8 yd, w 8 yd, h 4.6 yd

Find the volume of each cylinder. 8. d 12 ft, h 9 ft

7. r 10 m, h 8 m

10. r 6 yd, h 4.5 yd

9. d 0.6 km, h 0.5 km

12. d 7.2 in., h 5.25 in.

11. r 2.1 cm, h 8.3 cm Find the volume. 13.

14.

15.

7 ft

14 cm 9 ft

16 in. 14 cm

8 in.

14 cm 12 in.

Complete the table shown for various cylinders. diameter of base (d ) radius of base (r) 16.

8 in.

height (h) 4 in.

17.

7 cm

6.8 cm

18.

4.7 ft

5 ft

19.

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Glencoe/McGraw-Hill

Volume (V )

10.4 m

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4-8

VOLUMES OF PYRAMIDS AND CONES EXERCISES Find the volume of each figure. If necessary, round to the nearest tenth. 1.

2. 12 in.

7m

10 m

4 in.

3.

4. 6 cm

10.5 ft 7 ft

4 cm

8 ft

5 cm

8 ft 7 ft

Complete each table. Round to the nearest tenth, if necessary. Solid

Base area

Height

5.

Pyramid

16 in.2

7 in.

6.

Pyramid

72 cm2

7.

Pyramid

684 cm3 14 ft

294 ft3 Volume

Solid

Radius

Height

8.

Cone

9 in.

15 in.

9.

Cone

10.

Cone

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Volume

8m

301.4 m3 197.8 ft3

3 ft

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4-9

SURFACE AREA OF PRISMS AND CYLINDERS EXERCISES Find the surface area of each figure. Use 3.14. Round to the nearest whole number. 1. cylinder: r 12 in., h 15 in.

2. rectangular prism: 6 m by 10 m by 14 m

3. cube: s 15.8 ft

4. cylinder: d 12 cm, h 10.5 cm

5. cylinder: r 3.5 cm., h 5.8 cm

6. rectangular prism: l 2.6 m; w 1.7 m, h 1.4 m

7.

8.

5 ft

5 ft

8 ft

8 cm

4 ft

8 cm 6 ft

9.

10.

14 in.

8m 4m

18 in.

11.

12. 4 ft

4 ft

3 ft

3 ft

8 ft

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8 ft

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5-1

INTRODUCTION TO EQUATIONS EXERCISES Tell whether each equation is true, false, or an open sentence. 1. 7 8 x

2. 15 11 4

3. 16 2 4

4. 3 • (7) 21

5. 6(4 3) 24 9 4m 7. 5 2

6. 6 y 3 14 2 1 8. 12 8 4 (16) 2

Which of the given values is a solution of the given equation? 9. c 3 6; 3, 3

10. m 8 1; 7, 7, 9

11. 4 w 2; 6, 2, 4

12. 15 3z; 5, 3, 5 r 14. 12; 6, 8, 24 2 16. 2n 6 n 2; 6, 4, 8 w9 18. 4; 1, 0, 1 2w

13. 4d 24; 8, 6, 4 15. 2x 5 11; 8, 3, 8 a2 17. 4; 10, 14, 16 3 Use mental math to solve each equation. 19. x 2 5

20. m 3 4

21. 4c 20

22. j 7 0

23. 9 t 5

24. 16 g 4

25. 2r 18

26. 5 k 0

27. 7p 49

28. The area of a rectangle whose length is 7 ft is 14 ft2. Use the equation 14 7w, where w represents the width of the rectangle, and these values for w: 2, 4, 98. Determine the width of the rectangle. 29. Fran has $41, which is $12 more than Rafael. Use the equation r 12 41, where r represents the amount of money Rafael has, and these values for r: 29, 53. Determine the amount of money Rafael has. 30. Lee’s dog weighs 36 pounds, which is twice as much as his cat weighs. Use the equation 2c 36, where c represents the weight of Lee’s cat, and these values for c: 9, 18, 72. Determine the weight of Lee’s cat.

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5-2

ADD OR SUBTRACT TO SOLVE EQUATIONS EXERCISES Solve each equation. Check the solution. 1. x 4 15

2. s 10 6

3. 5 r 3

4. 8 w 12

5. m 8 3

6. 0 3 q

7. 3.5 a 7.6

8. 9 d 1

9. s 9.2 1.7

10. 16 x 16

11. 2 5 t

12. 15 a 10

13. k 1 23

14. 0.8 d 0.7

15. 2.1 u 3.5

16. y 28 50

17. 43 m 21

18. 10 10 v

19. 3.4 k 4.3

20. 44.5 35.6 m

1 1 21. m 4 2

2 5 22. w 3 6

2 3 23. f 5 10

3 1 24. t 7 2

Solve each problem by writing an equation. 25. Gina runs 412 mi every weekend. If she runs 234 mi on Saturday, how many miles does she run on Sunday? 26. Harriet and Tomas collect stamps. Harriet has 48 more stamps than Tomas. If Harriet has 83 stamps, how many stamps does Tomas have?

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5-3

MULTIPLY OR DIVIDE TO SOLVE EQUATIONS EXERCISES Solve each equation. Check the solution. w 1. 100 10y 2. 4 3

3. 5a 30

4. 4h 18

5. 20 8g

t 6. 14 5

2 7. b 24 3

8. 5 5c

6 3 9. h 7 4

10. 16 2.5z

y 11. 1 4

12. 15f 18

13. 5.2 0.2s

p 14. 5 2.2

q 3 15. 8 4

16. 15v 30

4 17. 16 j 5

2 18. 14k 7

4 19. m 16 5

20. 14 5t

21. 54 6h

Write an equation for each phrase. 22. the quotient of h and six is negative four 23. five times x equals forty 24. y divided by five is negative five 25. the product of sixteen and g is negative eight 26. Gregg is collecting money for T-shirts. He has collected $105. If each T-shirt costs $7, how many T-shirts has he collected money for? 27. Twain and his friends are sharing some pizzas. There are 6 people in all and each person eats 3 pieces of pizza. How many pieces of pizza did Twain and his friends share in all? 28. Amie works three times as many hours each week as Mia works. If Amie works 15 hours a week, how many hours does Mia work?

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5-4

SOLVE TWO-STEP EQUATIONS EXERCISES Solve each equation. Check the solution. 1. 6t 3 15

2. 2m 5 19

r 3. 4 12 2 12 60 5. 7 d b 7. 7 0 7 1 9. 3v 2 2 y 11. 14 10 3

0.5 1.5 12. 1.7 p

13. 8 8(k 4)

14. 2(c 24) 10

5 d 15. 9 4.5

n 0.2 16. 0.24 4.8

4. 10 4 7f 6. 10 5k 10 8. 9 8t 25 10. 2(x 12) 4

17. Thea spent $10.80 on 5 notebooks and some pens. If the pens cost $4.80, how much did each notebook cost? 18. Jack spent $32 to rent a bicycle. He paid a $8 deposit and then $3 an hour for the rental. How many hours did he rent the bicycle? Use the figure shown for Exercises 19–21. 19. The length of this rectangle is twice as long as the width. Write an equation to model this situation.

14 x+4

20. Solve the equation to determine the value of x.

21. Use the value of x to find the width, length, perimeter, and area of the rectangle.

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5-5

COMBINE LIKE TERMS EXERCISES Simplify. 1. 5d 3d

2. 6x 5y 2x

3. y 7y

4. 9w 4 7 5w

5. n n2 3n2 5n

6. 2p p 6p

7. 4t 3t 2

8. 6m 5n 4m 5n 10. 4(x 3) 5x

9. 7b (3a) 5a (9b) 11. 2(t 2) 4(5 3t)

12. 9h 7k 2k hk

13. 4 (r 2s) 4r

14. 2z 3z2 5z z

15. f 2 3(f 2) 5f 2

16. 4n 5(3n 2) 12

Solve each equation. Check the solution. 17. 4x 3x 1 7

18. 4r 2 r 8

19. d 5 5d 17

20. w 2 6 w

21. 10 6c 5c 2

22. 5x 3 31 2x 1 24. m m 10 2 26. 4q 3q 1 5 q 2 28. (k 15) 2k 2 3

23. 3d 4 2 2d 25. 2(r 4) 5r 2 27. 5(2.5 x) 7.5x

Write and solve an equation to represent the following phrases. 29. Eight more than a number is six less than twice the number.

30. Four times a number less five is ten minus twice the number.

31. Six more than three times a number is half of the number plus twelve.

32. Maria has twice as many nickels as dimes. Together she has 24 nickels and dimes. How many of each does she have? ©

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5-6

FORMULAS EXERCISES 1. The formula for the perimeter of a square is A 4s, where s length of a side. A square has a perimeter of 24 in. Find the length of a side. 2. The formula for the volume of a prism is V lwh, where l length of the base, w width of the base, and h height of the prism. A prism has a volume of 60 cm3, a length of 4 cm, and a width of 3 cm. Find its height. 3. Rita traveled 252 miles in 4.5 hours. Use the formula d rt to determine her rate.

Ned earns $320 each week plus $9.50 an hour for working overtime. 4. Write a formula for Ned’s weekly pay, represented by the variable p, when he works a certain number of overtime hours, represented by h. 5. One week Ned worked 6 hours of overtime. What was his pay for that week? 6. How many hours of overtime did Ned work if his weekly pay is $434? The charges for a certain long distance plan are $15 a month plus $0.10 per minute. 7. Write a formula for the monthly long distance charges, represented by c, when m minutes of long distance phone calls are made. 8. One month, 124 minutes of long distance calls were made on this plan. What were the long distance charges for this month? 9. How many minutes of long distance calls were made if the monthly long distance charges are $24? Solve each formula for the indicated variable. 10. I prt, for p

11. T p prt, for t

12. y mx b, for b

13. P a b c, for a

RM 14. O , for R 2

15. Ax By C, for y

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5-7

SOLVING ADDITION AND SUBTRACTION EQUATIONS EXERCISES 1. AGE Walter lived 2 years longer than his brother Martin. Walter was 79 at the time of his death. Write and solve an addition equation to find Martin’s age at the time of his death.

2. CIVICS New York has 21 fewer members in the House of Representatives than California. New York has 33 representatives. Write and solve a subtraction equation to find the number of California representatives.

3. GEOMETRY Two angles are supplementary if the sum of their measures is 180°. Angles A and B are supplementary. If the measure of angle A is 78°, write and solve an addition equation to find the measure of angle B.

4. BANKING After you withdraw $40 from your checking account, the balance is $287. Write and solve a subtraction equation to find your balance before this withdrawal.

m A 78˚

180˚ B A

5. WEATHER After the temperature had risen 12°F, the temperature was 7°F. Write and solve an addition equation to find the starting temperature.

6. CHEMISTRY The atomic number of mercury is the sum of the atomic number of aluminum and 67. The atomic number of mercury is 80. Write and solve an addition equation to find the atomic number of aluminum.

7 F

7. ELEVATION The lowest point in Louisiana is 543 feet lower than the highest point in Louisiana. The elevation of the lowest point is 8 feet. Write and solve a subtraction equation to find the elevation of the highest point in Louisiana.

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8. POPULATION The population of Honduras is the population of Haiti decreased by 618,397. The population of Honduras is 6,249,598. Write and solve a subtraction equation to find the population of Haiti.

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5-8

EXTRA PRACTICE

GRAPH OPEN SENTENCES EXERCISES Graph each open sentence on a number line on your own paper. 1. x 3

2. c 4

3. t 5

4. j 1

5. r 0

6. m 3

10. n 6

3 8. m 4 11. k 6 10

13. x 1

14. y 4 3

16. 5y 1 4

17. m 9

7. r 3 2

9. q 2.5 12. 2 h 6 15. 1 u 9 3 18. k 4 4

Write three solutions to the following inequalities. 19. x 3

20. q 9

21. n 0

1 22. k 2 24. m 3.5

23. r 10 Write an inequality to describe each situation. 25. Joan cannot spend more than $40. 26. Dennis saves at least $50 each month.

27. The auditorium seats a maximum of 450 people. Write an open sentence for each graph. 28. –7 –6 –5 –4 –3 –2 –1 0

1

2

3

4

5

6

7

29. –7 –6 –5 –4 –3 –2 –1 0

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1

2

3

4

5

6

7

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5-9

SOLVE INEQUALITIES EXERCISES Solve and graph each inequality on your own paper. 1. x 3 7

2. 4t 16

3. m 7 12

p 4. 2 5

5 5. g 10 6

6. 5p 4

7. 8 r 6

8. h (3) 2 10. 12 3c 3

9. 4 2t 0 11. 8 3y 2

12. 2b 4 8

13. 2(x 4) 6

14. 3 2x 1 4x

15. 2 8n 10n

16. 12(w 3) w 25

Write and solve an inequality. 17. Alan has saved $75 and wants to use it to buy a stereo. The stereo he wants to buy sells for $399. Determine the least amount Alan must still save. 18. Kendra has at most $400 to spend on software for her computer. She bought a package for her children that cost $59. Determine the most Kendra still has to spend on software. 19. Jon is scheduled to work more than 28 hours this week. He worked 6 hours on Monday. Determine the minimum number of hours he will work the rest of the week. 20. Lana studies at least 4 hours each weekend. She studied 1.5 hours on Saturday morning. Determine the minimum number of hours she will study the rest of the weekend. 21. Uri borrowed $1650 to buy a computer. He plans to pay $75 a month on this loan. Determine the number of months it will take before the balance due on his loan will be less than $100.

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6-1

PERCENTS AND PROPORTIONS EXERCISES Write and solve a proportion. 1. 55% of 125 is what number?

2. 16.8 is what percent of 28?

3. What percent of 48 is 36?

4. 28% of 34 is what number? 6. 125 is what percent of 200?

5. 14 is 15% of what number? 7. 12% of 16 is what number?

8. What percent of 81 is 9?

9. What number is 64% of 80?

10. 1% of what number is 4? 4

11. 10 1% of 50 is what number? 2

12. 3.5 is 20% of what number?

13. What percent of 3.7 is 2.96?



16. 5.76 is 24% of what number?

17. 92% of what number is 82.8?

18. 66 2% of what number is 24? 3


20. 108 is what percent of 144?

21. 78 1% of what number is 39 1? 2 4

22. 4% of what number is 6?


24. What percent of 42 is 28.56?

25. WEATHER Last February it snowed 12 out of 28 days. What percent of days did it snow last February? 26. Andrea left a $4.50 tip for a bill of $25.00. What percent of the bill did she leave as a tip? FITNESS Last Monday 38 of the 80 members who came to the health club attended an aerobics class. Last Tuesday 40% of the 105 members attended an aerobics class. 27. On which day did the greatest percentage of members attend an aerobics class?

28. On which day did the greatest number of members attend an aerobics class?

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6-2

WRITE EQUATIONS FOR PERCENTS EXERCISES Write and solve an equation. 1. 40% of what number is 6?


3. 80% of 16 is what number?





8. 18 is 21% of what number? 2 10. 0.9 is 0.5% of what number?

9. What percent of 169 is 135.2? 11. 67.5 is what percent of 150?

12. 8% of what number is 18,500?

13. 2% of 63 is what number?

14. What number is 0.2% of 240?

15. 8 is what percent of 21? 2


17. Nora answered 4 out of 52 questions on a history test incorrectly. What percent of the questions did she answer correctly? 18. Last year 35% of the computers Miquel sold were notebooks. If he sold 140 notebook computers last year, how many computers did he sell in all? Grace earns $1800 a month. 19. She spends $600 a month on rent. What percent of her monthly income does she spend on rent? 20. She spends 5% of her income on entertainment. How much does she spend on entertainment each month? 21. Her monthly car payment is $275. What percent of her monthly income does she spend on her car payment? 22. How much does she spend on all other monthly expenses? 23. What percent of her monthly income does she spend on her other expenses?

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6-3

DISCOUNT AND SALE PRICE EXERCISES Find the discount and the sale price. Round your answers to the nearest cent 1. Regular price: $165.00 Percent of discount: 10%

2. Regular price: $85.50 Percent of discount: 20%


4. Regular price: $1500.49 Percent of discount: 17.5%





Find the percent of discount. 9. Regular price: $65.99

10. Regular price: $3500.00

Sale price: $56.09

Sale price: $2275.00



Sale price: $637.50

Sale price: $278.60



Sale price: $67.95




Sale price: $110.99




Sale price: $743.75

Sale price: $84.60

19. The regular price of a television is $295. The price is reduced by 23%. How much will you save with the reduced price? 20. Which is cheaper, a $36 software package that is 20% off, or a $32 package that is 25% off? ©

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6-4

TAX RATES EXERCISES Find the amount of the sales tax and total cost of each item. 1. Jeans: $45.00

2. Stereo system: $369.99

Sales tax rate: 8%

Sales tax rate: 6.5%

3. DVD player: $950.00

4. Leather coat: $269.75


Sales tax rate: 7%

5. Bicycle: $168.99

6. Telephone: $69.50


Sales tax rate: 5%

Find the income tax and net pay for each. 7. Income: $600/wk

8. Income: $55,000/yr

Income tax rate: 28%


9. Income: $425/wk

10. Income: $28,000/yr



11. Income: $42,800/yr

12. Income: $530/wk


Income tax rate: 16.5%

Find the property tax paid by each homeowner. 14. Home value: $65,000

13. Home value: $105,000

Property tax rate: 2%


16. Home value: $145,500

15. Home value: $98,000


Property tax rate: 2% Find the sales tax rate. 17. Price: $32.28

18. Price: $1250.00

Total cost: $35.50 ©

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Total cost: $1356.25 48

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6-5

SIMPLE INTEREST EXERCISES Find the interest and the amount due. Principal

Annual rate

Time

1.

$550.00

6%

2.

$55.00

4.5%

3.

$1450.00

8%

4.

$3000.00

9.5%

18 mo

5.

$9450.50

4.6%

24 mo

6.

$75.50

4%

6 mo

7.

$10,900.00

10.5%

5 yr

8.

$865.00

12%

3 yr

9.

$2400.75

15%

6 yr

10.

$5764.00

16.5%

Interest

Amount due

2 yr 6 mo 4 yr

30 mo

Find the rate of interest. 12. Principal: $1250.00

11. Principal: $302.50 Interest: $30.20

Interest: $318.75

Time: 2 yr

Time: 3 yr 14. Principal: $2895.50

13. Principal: $10,500.00 Interest: $1968.75

Interest: $579.10

Time: 18 mo

Time: 5 yr 16. Principal: $1400.00

15. Principal: $14,500.00

©

Interest: $5220.00

Interest: $332.50

Time: 54 mo

Time: 30 mo

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6-6

COMMISSION EXERCISES Complete the table. Sale

Commission rate

1.

$1500.00

2%

2.

$700.00

Commission

$56.00

3.

8%

4.

$460.00

5.

$1235.00

$48.40 $23.00

4%

6.

3.5%

7.

$800.00

8.

$950.00

7.5%

9.

$325.00

21% 2

10.

$3055.00

$128.80 $42.00

$213.85

Find the total income. 12. Base salary: $900/mo

11. Base salary: $350/wk Total sales: $2500/wk

Total sales: $15,000/mo

Commission rate: 3%

Commission rate: 5.5% 14. Base salary: $1250/mo

13. Base salary: $15,000/yr Total sales: $25,000/yr

Total sales: $3000/mo

Commission rate: 4%

Commission rate: 8.2% 16. Base salary: $225/wk

15. Base salary: $20,000/yr

©

Total sales: $54,560/yr

Total sales: $1750/wk

Commission rate: 12%

Commission rate: 6%

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6-7

PERCENT OF INCREASE AND DECREASE EXERCISES Find the percent of increase. 1. Original rent: $450

2. Original price: $0.50

New rent: $495

New price: $0.65

3. Original price: $220

4. Original weight: 110 lb

New price: $286

New weight: 132 lb


6. Original number: 70

New price: $60

New number: 98

7. Original fare: $140


New fare: $210

New price: $28 10. Original population: 980


New population: 1127

New price: $66 11. Original airfare: $225

12. Original score: 80

New airfare: $270

New score: 84

Find the percent of decrease. 13. Original score: 190

14. Original weight: 180 lb

New score: 152

New weight: 162 lb


16. Original airfare: $340

New price: $28

New airfare: $255

17. Original population: 600

18. Original enrollment: 360

New population: 510

New enrollment: 342 20. Original number: 80


New number: 44

New fare: $99 21. Original membership: 75


New membership: 60

New price: $45

23. Original time: 40 min


New time: 38 min

New price: $51

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6-8

SIMPLE INTEREST EXERCISES

©

1. SAVINGS ACCOUNT How much interest will be earned in 3 years from $730 placed in a savings account at 6.5% simple interest?

2. INVESTMENTS Terry’s investment of $2,200 in the stock market earned $528 in two years. Find the simple interest rate for this investment.

3. SAVINGS ACCOUNT Lonnie places $950 in a savings account that earns 5.75% simple interest. Find the total amount in the account after four years.

4. INHERITANCE William’s inheritance from his great uncle came to $225,000 after taxes. If William invests this money in a savings account at 7.3% interest, how much will he earn from the account each year?

5. RETIREMENT Han has $410,000 in a retirement account that earns $15,785 each year. Find the simple interest rate for this investment.

6. COLLEGE FUND When Melissa was born, her parents put $8,000 into a college fund account that earned 9% simple interest. Find the total amount in the account after 18 years.

7. MONEY Jessica won $800,000 in a state lottery. After paying $320,000 in taxes, she invested the remaining money in a savings account at 4.25% interest. How much interest will she receive from her investment each year?

8. SAVINGS Mona has an account with a balance of $738. She originally opened the account with a $500 deposit and a simple interest rate of 5.6%. If there were no deposits or withdrawals, how long ago was the account opened?

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7-1

EXTRA PRACTICE

GRAPHS AND FUNCTIONS EXERCISES 1. The graph below represents the height of a 2. The graph below represents a tsunami (tidal wave) as it approaches shore. student taking an exam. Describe Describe what is happening in the graph. what is happening in the graph. Number of Questions Answered

Height

Time

Time

3. FOREST FIRES A forest fire grows slowly at first, then rapidly as the wind increases. After firefighters answer the call, the fire grows slowly for a while, but then the firefighters contain the fire before extinguishing it. Which graph represents this situation? A B C Area Burned

Area Burned

Area Burned

Time

Time

Time

INTERNET NEWS SERVICE For Exercises 4–6, use the table that shows the monthly charges for subscribing to an independent news server. Number of Months Total Cost ($)

1

2

4.50

9.00

3

4

5

13.50 18.00 22.50

4. Write the ordered pairs the table represents. 5. Draw a graph of the data. Total Cost ($)

27.00 22.50 18.00 13.50 9.00 4.50 0

1 2 3 4 5 6 Number of Months

6. Use the data to predict the cost of subscribing for 9 months. 7. SAVINGS Jennifer deposited a sum of money in her account and then deposited equal amounts monthly for 5 months, nothing for 3 months, and then resumed equal monthly deposits. Sketch a reasonable graph of the account history.

Account Balance ($)

Time ©

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7-2

COORDINATE PLANE EXERCISES Use the coordinate grid shown. Give the coordinates of each. y

1. point B

I

7

H

2. point D

A

5

K

3

3. point H

D

4. point C

-7

5. point E

-5

C

6. point G J

B

1 -3

-1-1

G

1

3

x 7

F

-3 -5

5

E

-7

7. point I

8. point L

9. point A

10. point K

11. point F

12. point J

L

13. two points in the fourth quadrant 14. a point whose y-coordinate is 0 15. a point on the y-axis 16. two points in the second quadrant Graph each point on a coordinate grid. Use your own paper. 17. X(1, 5)

18. N(5, 0)

19. V(2, 2)

20. T(5, 4)

21. U(6, 2)

22. Z(0, 4)

23. M(7, 10)

24. P(3, 9)

25. W(6, 6)

Sketch each figure on a coordinate grid. Use your own paper. 26. rectangle LMNP with a diagonal having endpoints at L(2, 3) and N(4, 2) 27. square ABCD with a diagonal having endpoints at B(6, 4) and D(0, 2) 28. circle with center at M(1, 3) and radius with a length of 6 units 29. Which pair of points is closer together: (1, 4) and (3, 4), or (3, 6) and (8, 6)? Explain your answer.

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7-3

EXTRA PRACTICE

RELATIONS AND FUNCTIONS EXERCISES Does the mapping show that the relation is a function? 1. Texas Ohio

Houston Cleveland Dallas Columbus

2.

–5 3 4 –1

3.

4 –4 3 –1

Joe Kathy Ron Kara

Tigers Hawks

Use the vertical line test to determine if each relation is a function. 4.

5.

y

x

7.

y

x

8.

y

6.

y

x

9.

y

x

x

y

x

State the domain and range of each relation. Then state whether each relation is a function. 10. (7, 2), (4, 3), (3, 4), (2, 4) 11. (0.9, 1.4), (1.4, 0.8), (3.2, 1.4)

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7-4

LINEAR GRAPHS EXERCISES Make a table of three solutions for each equation. Then graph the equation on your own paper. 1. y x 2 x

y

4. y x 4 x

y

7. y 4x 3 x

y

2. y 2x 1 x

3. y x 5

y

x

5. y 3x 2 x

6. y 4x

y

x

y

1 9. y x 2 2 x y

8. y 2x 3 x

y

y

Find the x-intercept and y-intercept of each equation.

10. y 3x 2

11. y 2x 2

12. y 2x 1

13. y x 7

3 14. y x 6 4

15. y 2x 5

16. y 8x 2

17. y 3x

18. y x 5

19. y 2 3x 4

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7-5

SLOPE OF A LINE EXERCISES Find the slope of each line on the coordinate grid shown. y 7

w

1. r

t

5

v

2. s

3

r

1 -7

-5

-3

3. t s

-1-1

1

3

5

7x

-3 -5

4. v

-7

5. w Identify the slope of each line as positive, negative, zero or undefined. y

m

6. l 7. m

l

p 8. n

x

9. p 10. q

n

q

Find the slope of the line that passes through each pair of points. 11. A(3, 4) and B(5, 8)

12. C(1, 4) and D(2, 2)

13. M(3, 5) and N(4, 2)

14. W(8, 0) and Z(2, 3)

15. B(4, 5) and C(1, 2)

16. P(5, 7) and Q(1, 1)

On a coordinate grid on your own paper graph the point (2, 2). Then graph lines through (2, 2) with each of the following slopes. 3 17. 4

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4 18. 3

3 19. 4 57

4 20. 3

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7-6

SLOPE-INTERCEPT FORM OF A LINE EXERCISES Find the slope and y-intercept of each line. Then graph the line on your own paper. 1. y 2x 3

2. y x 2

2 3. y x 1 3

4. y 1

5. y 3x 1

1 6. y x 2 4

7. y 2x

2 8. y x 4 3

5 10. y x 5 3 Name the slope and y-intercept of each line. Write an equation of the line. 11. 12. 13. y y 9. y 3x 4

-4

4

4

4

2

2

2

-2

2

-4

4x

-2

-2

-2

-4

-4

14.

15.

y

4

2 -4

©

2

-2

4x

-4

-2

4x

-4

-2

16.

y

4

2

4x

-4

-2

-2

-2

-4

-4

-4

58

4x

2

4x

y

2

-2

Glencoe/McGraw-Hill

2 -2

2 2

y

MathMatters 1

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7-7

DISTANCE AND THE PYTHAGOREAN THEOREM EXERCISES Graph each set of points on a coordinate grid on your own paper. Then use the Pythagorean Theorem to find the distance between each pair of points. 1. D(4, 5) and E(2, 1)

2. P(1, 1) and Q(5, 2)

3. L(0, 1) and M(4, 2)

4. R(2, 3) and S(1, 4)

5. A(4, 2) and B(2, 0)

6. T(3, 2) and V(2, 4)

7. S(9, 2) and T(2, 2)

8. H(1, 2) and I(2, 3) 10. J(4, 2) and K(5, 2)

9. X(1, 8) and A(3, 2)

Use the distance formula to find the distance between each pair of points. 11. L(4, 2) and M(1, 3)

12. B(3, 6) and D(1, 4)

13. F(3, 0) and G(4, 3)

14. Z(5, 1) and W(1, 8)

15. A(3, 1) and B(1, 4)

16. U(2, 5) and V(5, 4)

17. Q(4, 3) and R(2, 3)

18. T(3, 7) and V(4, 1)

19. S(2, 2) and T(4, 1)

20. M(2, 6) and N(3, 3)

21. J(1, 1) and K(4, 4)

22. P(2, 3) and Q(5, 1)

23. C(3, 1) and D(5, 3)

24. T(3, 4) and U(5, 2)

25. A guy wire is attached from the top of a pole to a point 8 ft from the base of the pole. If the pole is 12 ft high, how long is the wire? 26. Dani leaves her home and travels 3 mi east, 2 mi north, 5 mi west and 6 mi south to the library. What is the shortest distance between the library and Dani’s home?

27. The bottom of a 16-ft ladder is 6 ft from the base of the wall against which it is leaning. How high up the wall is the top of the ladder from the bottom of the wall?

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7-8

EXTRA PRACTICE

SOLUTIONS OF LINEAR AND NONLINEAR EQUATIONS EXERCISES Determine if the ordered pair is a solution. 1.

2, 4 1 3

2. (1, 2)

1 5 y x 4 8

y4x

3. (0.2, 1.2)

4. (1, 1)

y 4x 2

y|x| 6. (4, 0)

5. (4, 16)

y|x|4

y x2

8. (1, 3)

7. (3, 4) 4

y

4

y

x -2

2

-2

4x

-2

-2

-4

-4

10. (0, 1)

9. (2, 3) 4

y

4

y

2

2

x

x -4

©

-2

Glencoe/McGraw-Hill

2

-4

4

-2

2

-2

-2

-4

-4

60

4

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8-1

ANGLES AND TRANSVERSALS EXERCISES Find each measure. 1. m2 118° 2 3

4

2. m3 3. m4 In the figure, m | | n, m2 67°, and m14 112°. Use the figure to answer Exercises 4–20.

p

q

4. Identify a pair of vertical angles.

5. Identify a pair of corresponding angles.

6. Identify a pair of supplementary angles.

1

2

4

3 13 14 16 15

5 6 8 7

7. m1

8. m3

9. m4

10. m5

11. m6

12. m7

13. m8

14. m9

15. m10

16. m11

17. m12

18. m13

19. m15

20. m16

In the figure, a c and m1 69°. Find each measure.

m

9 10 12 11

n

c b

21. m2 a

22. m3

1

6 5

23. m4

2 4

3

24. m5 25. m6

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8-2

BEGINNING CONSTRUCTIONS EXERCISES Using a protractor and your own paper, construct each angle. Then bisect the angle. 1. mRST 126°

2. mMNP 54°

3. mHJK 140°

4. mXYZ 28°

5. mDEF 172°

6. mGHI 88°

Trace each segment. Then copy it and construct the perpendicular bisector. 7.

8. A

B

Y

X

↔ Trace each figure. Then construct a line perpendicular to RS from point T. 9.

10.

T R

T

S

R

S

Trace each triangle and construct the perpendicular bisectors through each side. Label the intersection point P. 11.

X

©

12.

Y

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Z

K

J

62

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8-3

DIAGONALS AND ANGLES OF POLYGONS EXERCISES Draw all of the diagonals from one vertex of each polygon. 1.

2.

Find the unknown angle measure in each figure. 3.

4. 78°

84° 70°

102° 111°

x° 128°

x°

82°

5.

6.

x°

44°

110°

x°

x°

7. What is the measure of each angle of a regular pentagon? 8. What is the measure of each angle of a regular octagon? 9. What is the measure of each angle of a regular heptagon? 10. What is the measure of each angle of a regular decagon? ©

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8-4

COMBINATIONS EXERCISES 1. ENTERTAINMENT During one month, a movie theater is planning to show a collection of 9 different Cary Grant movies. How many different double features (two-film showings) can they choose to show from this collection?

2. SCHOOL For a history test, students are asked to write essays on 4 topics. They must choose from a list of 10 topics about the European countries they have been studying. Is this situation a permutation or a combination? Explain. How many ways can a student choose 4 topics?

3. MARKET RESEARCH A taste test of 11 different soft drinks is held at a shopping mall. Each taster is randomly given 5 of the drinks to taste. How many combinations of soft drinks are possible?

4. BOOK FAIR A school book fair is offering a package deal on the opening day. For a special price, students may purchase any 6 different paperback books from a list of 30 books that have won the Newbery Medal. How many packages are possible?

GARDENING For Exercises 5 and 6, use the shipping list at the right that shows the rosebushes Mrs. Lawson ordered for her front yard. She wants to plant 9 of them along the walkway from her driveway to her front porch.

Shipping List (1 each) Aquarius Purple Tiger Candy Apple Roundelay Desert Dawn Scarlet Knight Fragrant Plum Shining Hour Golden Girl Sonia Supreme Linda Ann Sundowner Mount Shasta Viceroy Pink Parfait Winifred

5. How many ways can she plant the rosebushes along the walkway if order is not important?

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6. How many ways can she plant the rosebushes along the walkway if order is important?

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8-5

TRANSLATIONS IN THE COORDINATE PLANE EXERCISES For Exercises 1–3, use your own grid paper. 1. Graph the image of the point A(3, 0) under a translation 3 units right and 2 units up. 2. Graph the image of RST with vertices R(1, 3), S(2, 5), and T(3, 2) under a translation 4 units left and 1 unit down. 3. Graph the image of ABC with vertices A(1, 1), B(4, 2), and C(0, 4) under a translation 2 units right and 4 units down. Copy each set of figures on a coordinate plane. Then graph the image of each figure under the given translation. 4. 6 units left, 4 units up 4

5. 2 units right, 6 units down

y

4 2

2 -4

-2

y

2

-4

4x

-2

2

4x

-2

-2

Determine the direction and number of units of the translation for each image shown. 6.

7. A' C

C'

A

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8-6

REFLECTIONS AND LINE SYMMETRY EXERCISES Give the coordinates of the image of each point under a reflection across the given axis. 1. (3, 2); x-axis

2. (1, 2); x-axis

3. (5, 3); x-axis

4. (6, 5); x-axis

5. (2, 3); y-axis

6. (3, 4); y-axis

7. (1, 6); y-axis

8. (2, 1); y-axis

Graph the image of each figure under a reflection across the given axis. 9. a. x-axis 10. a. x-axis b. y-axis

b. y-axis 4

y

4

2 -4

-2

y

2 2

4x

-4

-2

-2

2

4x

-2

Tell whether the dashed line is a line of symmetry. 11.

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12.

13.

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8-7

ROTATIONS AND TESSELLATIONS EXERCISES For Exercises 1–5, use your own grid paper. 1. Graph the image of ABC with vertices A(4, 5), B(5, 2) and C(1, 1) after a rotation of 180° clockwise about the origin. 2. Graph the image of LMN with vertices L(3, 2), M(2, 1) and N(0, 2) after a rotation of 180° clockwise about the origin. 3. Graph the image of RST with vertices R(2, 2), S(1, 2) and T(2, 1) after a rotation of 180° clockwise about the origin. 4. Graph the image of XYZ with vertices X(0, 4), Y(3, 3) and Z(1, 1) after a rotation of 180° clockwise about the origin. 5. Graph the image of DEF with vertices D (1, 2), E(1, 3) and F(3, 1) after a rotation of 180° clockwise about the origin. Give the order of rotational symmetry for each figure. 6. 7.

9.

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10.

8.

11.

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9-1

MONOMIALS AND POLYNOMIALS EXERCISES Write each polynomial in standard form. 1. 4x 2x 2 3 2. 8n 3 5n 5 3n 3. r 3 2r 2 5 4. 5t 2 t 4 4t 3 5. 2s 2 4s 7 3s 4 2 1 1 6. d 4 d 6 d 2 d 7 2 3 7. 0.7w 0.2w 3 4.5w 2 3 5 7 8. z 2 z 1 z 9 4 6 8 Tell whether the terms in each pair are like or unlike terms. 9. 7w, 7w 2

10. r 3, 4r 3

11. mn, 5mn

12. 5x 2y, 3xy 2

13. 4st, 3st

14. 12a 3b, a 3b

Simplify. Be sure your answer is in standard form. 15. 8x 4 5x 16. t 3 6t 3 t 4t 17. 10 4fg 3 fg 3 5 18. 3y 3 3y 6y 3 2y 4 19. 8q 5q 4 q 4 7q 2 10 6q 20. 3 4c 4 2c 2 3c 3 c 2 c 4 21. 8n 4n3 5n2 7n 4n2 5n3 22. 10y 6 4y 7y 3 y 4 5y 6 2y 3 23. 2.5r 2 0.5r 7.6 0.9r 2 2.8r 5.2 ©

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9-2

ADD AND SUBTRACT POLYNOMIALS EXERCISES Simplify. 1. 4x (3x 4) 2. 8j (5j 6) 3. 5t (6t 9) 4. (5d 4f ) (4d f ) 5. (6x 4y) (5x 3y) 6. (5h2 3) (6h2 4) 7. (7x 2 4z) (5x 2 z) 8. (6w 2) (8w 3) 9. (r 2 4r 3) (2r 2 4) 10. (5v 2 3v 3) (v 2 4v 8) 11. (p 2 6p 2) (2p 2 p) 12. 9r (5r) 13. 8p (7p 3) 14. 4uv (6uv 7v) 15. (9 4n) (7 3n) 16. (x y) (7x 2y) 17. (5d 2 4d ) (d 2 3d ) 18. (3k 2 4k 4) (4k 2 k 2) 19. (4a 2ab 2b) (a 5ab 4b) 20. (2m3 m2 m) (2m3 3m 2 2m) 21. A deck has a length of 5x 2, and its width measures 2x 5. Find the amount of railing needed to go around the edge of the deck. 22. A triangle has sides of length 5y 3z, 2y z and 6y 5z. Find the perimeter of the triangle.

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9-3

MULTIPLY MONOMIALS EXERCISES Simplify. 1. (4x)(3y) 3. (3r)(5t) 5. (6m)(n) 7. (0.5r)(3s) 9. (4s)2 11. (d 5)(5d 2) 13. (2c 4)2 15. (4y)4 17. (2z 2)5 19. (2x)(3x)3 21. (4v 5)3 23. (m4)2(3m6)2 25. (6xy 4)(x 4y 6) 1 27. 4r 3t (16rt 3)

12xy 15rt 6mn 1.5rs 16s 2 5d 7 4c 8 256y 4 32z 10 54x 4 64v 15 9m 20 6x 5y 10 4r 4t 4

2. (5k)(4k) 4. (2x)(7z) 6. (2f )(1.5g) 8. 1c (4d) 2 10. (3c 2)(c 3)

12. (3w 4)(w) 14. (6t 4)(2t 3) 16. (2y 4)3 18. (2d)3(3d)2 20. (2a3)(2a)3 22. (2k 3)2(5k)4 24. (4a 2b 3)(5ab 4) 26. (7m4n2)(2mn)2 7 28. (3pq)2 9p 4q 3

20k 2 14xz 3fg 2cd 3c 5 3w 5 12t 7 8y 12 72d 5 16a 6 2500k 10 20a 3b 7 28m 6n 4 7p 6q 5

Write an expression for the area of each figure. 29.

30.

5a

6x

3c

6x

36x 2

15ac 31.

32. 6p

5w

7p

8w

21p 2

20w 2 © Glencoe/McGraw-Hill

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MULTIPLY A POLYNOMIAL BY A MONOMIAL EXERCISES Simplify. 1. 3x(x 2x 2)

2. 3(t 4t 3)

3. m(m 2 6m)

4. r(r 4 5r 2)

5. 3(w 6)

6. 4(2c 7)

7. 5d(d 3 d 2)

8. 3w(4w 6) 10. y(y 2 y 3)

9. 2x(x 2 4x 3) 11. 4(p 2 2p 4) 12. 3r(5r 2 5r 4) 13. m(3 m 2m 2) 14. 2t(6 7t 4t 2) 15. 3x(4x 2 2x 2) 16. 5w 2(w 2 w 1) 17. 4x 2(1 x x 2) 18. 3y 3(2 y y 2) Write an expression for the area of each figure. 19.

20.

x+8

4a

4a –2

21.

22.

x2+ 5

x

©

2x

x+3

2

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x3

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9-5

FACTOR USING GCF EXERCISES Find the greatest common factor of the monomials. 1. 6z and 3yz 2

2. 4a 2 and 12ab

3. 15zw 3 and 20z 2w

4. 3f 2g and 7fg

5. 16x 2y 2 and 24xy 3

6. 9mn 4 and 21m 2n 2

Match each set of monomials with their greatest common factor. 7. 3x 2, 3x 2y, 3xy

a. xy 2

8. 5xy 2, 5x 2y 2, 10x 3y 2

b. xy

9. 2xy 3, x 2y 2, 4xy 2

c. 3x d. 5xy 2

10. xy 3, x 2y 4, 3x 2y 2, 6xy Factor each polynomial. 11. 12 9x

12. 5x 2 2x

13. 32a 8

14. 6w 3 30w

15. 6y 2 21y

16. 6s 2 3s 12

17. 30a 2b 25ab 2

18. 2x 2 6x 2y 8xy

19. 4m 3n 3 12mn 3 4m2n 20. 10r 2s 2 15r 2s 25rs 2t Factor each expression. 21. m(m 1) 3(m 1) 22. 5(x 3) x(x 3) 23. (y 4)y 2(y 4) 24. 10(h 7) h(h 7) 25. d 2(d 1) d(d 1) 4(d 1) 26. (w 6)w 2 (w 6)w (w 6)5 Find the missing factor. 27. 10x 6 (5x 3)(

)

28. 8a 5b 3 (4a 3b 2)(

)

29. 16d 6f 5 (8d 2f 3)(

)

30. 24c 6d 4 (6c 4d )(

)

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EXTRA PRACTICE

DIVIDE BY A MONOMIAL EXERCISES Simplify. 24xy 2. 12y

15ab 1. 3b

5b

36bc 4. 4b

9c

30rs 5. 6r

45 z8 7. 5z 6

9z 2

y 3z 8. y z m2n5p 11. mn3

mn

r 2s 3 13. r 2s

s2

3c 4 14. 2 9c

3x 15 16. 3

x5

16g 8 17. 4

24r 16s 40t 21. 8

6y 2

23.

30a 2b 3 24ab 2 36a 2b 2 6ab

24.

15m 2n 2p 3 6mn 2p 2 12m 2n 2p 3mn 2p

2d 2

xy 4 9. 2 xy

y2

mn 2p 2 c 3

j 3k 2 12. 2 j

jk 2 2 d c3

4g 2

10m 12n 18. 5m 2

d4 15. 32 c d

18x 2 6x 4 20. 2 4x 3 12x 2 6x 22. 2x

3r 2s 5t

7m

16d 4 6. 8d 2

5s y2

mn4 10. n3

36y 2 12y 19. 6y

14mn 3. 2n

2x

6n

9x 2 3x 2 2x 2 6x 3

5ab 2 4b 6ab 5mp 2 2p 4m

25. A rectangle has area 18xy square units. The length is 6x units. Write an expression

3y

for the width of the rectangle.

26. A rectangle has area 32a 2b square units. The width is 4a units. Write an expression

8ab

for the length of the rectangle.

27. A rectangle has area 48p 2q 3 square units. The length is 16p 2q 2. Write an expression

3q

for the width of the rectangle.

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9-7

MULTIPLYING MONOMIALS AND POLYNOMIALS EXERCISES 1. GEOMETRY Write an expression in simplest form for the area of the rectangle. What is the area of the rectangle if c 5 units?

2. GEOMETRY Write an expression in simplest form for the area of the triangle. What is the area of the triangle if z 2 units?

c

4z 4c 5

3. SWIMMING POOLS The Marshalls’ pool is 5 feet longer than twice its width w. Write two expressions for the area of the pool. What is the area of the pool if it is 12 feet wide?

5z 8

4. BUSINESS When a factory makes t bicycles in a month, the gross profit on each bicycle is 25 2t dollars. Write an expression in simplest form for the total gross profit the factory makes in a month that it produces t bicycles. What is the gross profit if the factory makes 40 bicycles?

5. FUND-RAISING When the Science 6. GROUP RATES If Mr. Casey buys Club members charged p dollars to t tickets for his class to see a play, each wash each car at their car wash, ticket will cost 0.5t 1 dollars. If he they had 8p customers. When they buys three times as many tickets so doubled their price, they had 12 fewer that all three eighth grade classes can customers. Write expressions go, the price for each ticket is 2 dollars representing the new price and the less. Write an expression for the total new number of customers. Then write cost of the tickets for all three classes. an expression in simplest form If there are 20 students in Mr. Casey’s representing the amount of money class, how much will the tickets for all they made at the new price. How three classes cost? much money did they raise at the new price if the original price was $5 for each car?

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10-1

PROBABILITY EXERCISES Find each probability using the spinner. Give your answer as fractions and percents.

8 1. P(1)

2. P(2 or 3)

3. P(not 4)

4. P(1 or 8)

5. P(even number)

6. P(less than 4)

7. P(not 5 or 6)

8. P(6, 7, or 8)

1

7

2

6

3 5

4

Use the spinner to find the odds in favor of each event. 9. 1 or 2 12. 5

10. odd number

11. greater than 2

13. multiple of 3

14. less than 3

One card is drawn randomly. Find each probability.

P(C)

P

T A C

16. P(consonant)

I

R C

E

17. P(vowel)

18. P(T or I)

19. P(X)

20. P(a letter in the word PRACTICE)

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10-2

EXTRA PRACTICE

EXPERIMENTAL PROBABILITY EXERCISES The table shows the number of bagels purchased at a bagel shop one day at lunch. Find the experimental probability of each event. Wheat

Egg

Plain

Rye

Cinnamon Raisin

Oat Bran

Other

16

18

24

8

6

12

16

1. P(egg)

2. P(not plain)

3. P(cinnamon raisin)

4. P(wheat or rye)

5. P(other)

6. P(not oat bran or egg)

7. P(not cinnamon raisin)

8. P(not wheat) 10. P(not egg, plain, or rye)

9. P(wheat, egg, or plain)

Randi chose a colored pencil from a box 50 times. The outcomes are recorded in the table. Find each experimental probability. Color

red

blue

green

other

Number of outcomes

19

16

7

8

11. P(red)

12. P(blue)

13. P(other)

14. P(green)

15. P(not red or blue)

16. P(not blue or other)

17. P(red or other)

18. P(blue or green)

19. Alyn made 15 out of the 32 field goals he attempted in his last basketball game. What is the experimental probability that he will make the next field goal he attempts?

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10-3

SAMPLE SPACES AND TREE DIAGRAMS EXERCISES List each sample space.

U O

1. picking a card from those shown

T E

O

C

2. spinning Spinner 1

S

M

3. spinning Spinner 2 Use a tree diagram to find the number of possible outcomes in each sample space.

4

1

A

3

2

B

4. tossing two pennies 5. tossing a penny and tossing a

Spinner 1

Spinner 2

number cube 6. tossing two pennies and tossing a number cube 7. picking a card from those shown and tossing a penny 8. spinning Spinner 1 and tossing a penny 9. spinning Spinner 1 and Spinner 2 10. tossing a penny, tossing a cube, and spinning Spinner 1 Suppose you spin both Spinner 1 and Spinner 2. Find each probability. 11. P(1 and A)

12. P(2 and B)

13. P(even number and B) 14. P(a number less than 5 and A) Suppose you spin Spinner 1 and pick a card from those shown. Find each probability. 15. P(1 and a vowel)

16. P(3 and a consonant)

17. P(even number and O)

18. P(odd number and M)

19. P(even number and T)

20. P(prime number and S)

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10-4

COUNTING PRINCIPLE EXERCISES Use the counting principle to find the number of possible outcomes. 1. Choose a meal from three meats, two vegetables, and two types of potatoes. 2. Choose a sandwich from four cheeses, two luncheon meats, and six condiments. 3. Choose an outfit from five T-shirts, three pairs of jeans, and two pairs of shoes. 4. Choose a computer system from four monitors, three CPUs, and six printers. 5. Toss a six-sided number cube three times. 6. Toss a coin five times. 7. Toss a six-sided number cube eight times. 8. Toss a coin twenty times. Use the counting principle to find the probability. 9. A coin is tossed five times. Find P(all tails).

10. A six-sided number cube is tossed three times. Find P(all odd numbers).

11. A six-sided number cube is tossed four times. Find P(all even numbers).

12. A six-sided number cube is tossed three times. Find P(1, 2, 3).

13. A coin is tossed twice and a six-sided number cube is tossed twice. Find P(all heads and prime number).

14. How many different four-letter “words” can be made using any of the letters A through Z? (Assume that a letter may be repeated.)

15. How many different four-letter “words” can be made using any of the letters A through Z? (Assume that a letter may not be repeated.)

16. How many different three-digit numbers can be made using the digits 1 through 9? (Assume that a digit may be repeated.)

17. How many different 3-digit numbers can be made using the digits 1 through 9 if each digit can only be used once and the first digit must be even? ©

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10-5

EXTRA PRACTICE

INDEPENDENT AND DEPENDENT EVENTS EXERCISES A game is played by spinning the spinner then randomly choosing a card. After each turn, the card is replaced. Find the probability of each event.

4

1

4

1

3

1 3

A

A

A

B

B

C

C

D

D

D

E

E

E

F

2

1. P(1 then A)

2. P(4 then C)

3. P(3 then B)

4. P(2 then E)

5. P(1 then F)

6. P(3 then D)

7. P(4 then A)

8. P(2 then C)

9. P(3 then A)

10. P(1 then D)

11. P(2 then B)

12. P(4 then F)

13. P(3 then C)

14. P(1 then B)

State whether the pairs of events are independent or dependent. 15. You slept 8 hours last night. You will sleep 8 hours tonight. 16. There is no snow on the ground now, but it will snow on Friday. You will go sledding on Friday with your friends. Eight cards lettered A through H are in a box. A card is taken from the box and not replaced. Then a second card is chosen. Find the probability of each event. 17. P(A then B)

18. P(B then a vowel)

19. P(E then a consonant)

20. P(a vowel then a vowel)

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10-6

EXPERIMENTAL PROBABILITY EXERCISES

ENTERTAINMENT For Exercises 1 and 2, use the results of a survey of 120 eighth grade students shown at the right.

1. Explain how to find the probability

that a student plays video games more than 6 hours per week. Then find the probability.

3. DINING Only 6 out of 100 Americans say they leave a tip of more than 20% for satisfactory service in a restaurant. Out of 1,500 restaurant customers, how many would you expect to leave a tip of more than 20%?

Video Game Playing Time Per Week Hours Number of Participants 0 18 1–3 43 3–6 35 more than 6 24

2. Out of 400 students, how many would you expect to play video games more than 6 hours per week?

4. PLANTS Jason has a packet of tomato seeds left over from last year. He plants 36 of the seeds and only 8 sprout. What is the experimental probability that a tomato seed from this packet will sprout?

SPORTS For Exercises 5 and 6, use the results in the table at the right. In a survey, 102 people were asked to pick their favorite spectator sport.

5. What is the probability that a person’s favorite spectator sport is professional baseball? Is this an experimental or a theoretical probability? Explain.

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Favorite Spectator Sport Sport Number professional football 42 professional baseball 27 professional basketball 21 college football 12

6. Out of 10,000 people, how many would you expect to say that professional baseball is their favorite spectator sport? Round to the nearest person.

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10-7

EXPECTED VALUE AND FAIR GAMES EXERCISES 1. A sample space has four equally likely outcomes. The payoffs for the outcomes are 1, 2, 3 and 4. What is the expected value of the sample space? 2. A sample space has six equally likely outcomes. The payoffs for five of the outcomes are 3. The expected value of the sample space is 6. What is the payoff for the sixth outcome? 3. A sample space has eight equally likely outcomes. The payoffs for four of the outcomes is $4. The payoffs for four of the outcomes is $6. What is the expected value of the sample space? 4. A charity raffles off a $2500 computer system by selling 4000 tickets for $5 per ticket. What is the expected value?

Suppose a public service group raffles off 100 tickets for a $50 gift certificate. 5. What is the expected value for the purchase of one ticket? 6. Would $1 be a fair price to pay for a ticket? Explain. 7. A carpenter bids on a home remodeling project. There is a 0.6 probability of making $5000 profit, and a 0.2 probability of losing $1000. What is the expected value? 8. Using a fair six-sided number cube, what is the expected value of the cube landing with a 3 up? 9. Suppose an employee has a 0.1 probability of being late to work. The boss docks the employee’s weekly pay by $50 for each time an employee is late but adds $5 to their pay each time an employee is on time for work. What is the average amount of weekly pay the employee is docked?

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11-1

OPTICAL ILLUSIONS EXERCISES A

1. Write a statement about segments AB and CB. Check to see if it is true. B

C

2. Write a statement about segments XZ and XY. Check to see if it is true.

X

Z

Y

3. Write a statement about segments MN and NP. Check to see if it is true.

M N

P

4. Write a statement about figure XYZW. Check to see if it is true.

X

Y

W

Z

5. Write a statement about the two vertical segments shown. Check to see if it is true.

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Date ____________________________

11-2

INDUCTIVE REASONING EXERCISES Use inductive reasoning to find the ones digit of the following.

5

1. 1512

0

2. 2010

3. the seventh power of power of 8

2

4. any power of 16

3

5. the fifteenth power of 7

6

6. any even numbered power of 9

1

For Exercises 7–10, use the given examples to complete each conjecture. 7. 32 9 52 25 112 121 172 289 odd The square of an odd number is an number. 2 2 2 2 8. 4 16 8 64 14 196 20 200 even number. The square of an even number is an 9. 2 7 9 15 4 19 22 13 35 14 37 51 odd The sum of an odd number and an even number is an number. • • • • 10. 5 10 50 13 10 130 18 10 180 23 10 230 even number. The product of any number and 10 is an Examine each sequence of numbers. Describe a pattern or rule for the sequence and give the next four numbers.

12 , 9 Subtract 3, add 5. 800, 400, 600, 300, 500, 250, 450 , 225 , 425 , 212.5 Divide by 2, add 200. 68 , 136 , 140 , 280 Add 4, 1, 5, 10, 14, 28, 32, 64, multiply by 2.

11. 4, 1, 6, 3, 8, 5,

12.

13.

10

,

7

,

For Exercises 14–15, find the first four products. Study the pattern and use the first four products to predict the fifth product. 14. 123,456 • 9 123,456 • 18 123,456 • 27 123,456 • 36 123,456 • 81 © Glencoe/McGraw-Hill

1,111,104 2,222,208 3,333,312 4,444,416 9,999,936

242 24,642 111 222 2,468,642 1111 2222 11,111 22,222 246,908,642 111,111 222,222 24,691,308,642

15. 11 • 22 •

•

•

•

83

MathMatters 1

Name _________________________________________________________

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11-3

DEDUCTIVE REASONING EXERCISES State whether the following conditional statements are true or false. If false, give a counterexample. 1. If two numbers are even, then their quotient is even. 2. If a shape has three sides that are not congruent, then it is a scalene triangle. 3. If two lines intersect, then they are perpendicular.

Is this argument valid or invalid? Use a picture to help you decide. 4. If an animal is a golden retriever, then it is a dog. Mac is a dog. Therefore, Mac is a golden retriever. 5. If the temperature is below 32°F, then water will freeze. The temperature is 23°F. Therefore, water will freeze. 6. If a figure has four sides, then it is a quadrilateral. A pentagon does not have four sides. Therefore, this figure is not a quadrilateral. Write each of the following statements as an if-then statement. 7. All prime numbers are divisible by 1 and the number itself. 8. All basketball players can dribble. 9. All cats meow. Is the argument valid or invalid? Use a picture to help you decide. 10. All students must study. Patti studies. Therefore, Patti is a student. 11. All trees have leaves. An oak is a tree. Therefore, an oak has leaves.

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84

MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

11-4

VENN DIAGRAMS EXERCISES Use the Venn diagram shown.

Girls on the Basketball or Volleyball Team

1. How many girls are on the basketball team? 2. How many girls are on the basketball team, but not on the volleyball team?

Basketball 12

Volleyball 14

3

3. How many girls are on both the basketball team and the volleyball team?

4. How many girls are on the volleyball team? 5. How many different girls are on the basketball team or on the volleyball team? Car Ownership

The results of a survey of car owners are shown in the Venn diagram. 6. How many people own a van and a sedan?

Van 15

7. How many people own only a sports car?

5 1

8. How many people own just a van?

Sedan 36

6

2 Sports 24

9. How many people own a van, a sedan, and a sports car? 10. How many people were surveyed? 11. In a survey of 34 families, 17 own only a desktop computer, 12 own only a laptop, and 5 own both. Make a Venn diagram of the results of the survey.

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85

MathMatters 1

Name _________________________________________________________

EXTRA PRACTICE

Date ____________________________

11-5

LOGICAL REASONING EXERCISES Draw a conclusion from the given information without using a table. 1. Either Meagan or Neil play softball only. Neil plays basketball.

2. Tim, Todd, and Tia took first, second, and third places at a track meet, but not necessarily in that order. Tim finished between Todd and Tia. Tia did not finish in first place.

3. Either Lance, Leah, or Luke is Len’s cousin. Len has only one cousin. Lance and Leah are cousins.

Make a table to help solve each problem 4. Four friends, Mandi, Marti, Mark, and Matt, are attending the same university. One is studying to be a dentist, another a doctor, another a nurse, and another a surgeon. Mark studies with the future surgeon and dentist every weekend. Marti eats dinner with the future nurse and surgeon every Tuesday. Mandi is not studying to be a surgeon. Mandi is not studying to be a nurse or a doctor. Who is studying to be the nurse?

5. Beki, Belinda, and Beth all play basketball, but none play the same position. Beki practices with her sister, the guard, everyday after their team practice. Neither Belinda nor Beth are centers. Beth and Beki are sisters. Who plays forward?

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MathMatters 1

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EXTRA PRACTICE

Date ____________________________

11-6

A PLAN FOR PROBLEM SOLVING EXERCISES Use the five-step plan to solve each problem. SKATEBOARDING For Exercises 1 and 2, use the table at the right. It shows the results of a recent survey in which teenagers were asked who the best professional skateboarder is.

Skater

Votes

Bob Burnquist

18

Danny Way

15

Bam Margera

11

Arto Saari 1. Estimate the total number of teenagers who voted.

©

9

2. How many more teenagers preferred Burnquist to Saari?

3. HISTORY The area of Manhattan Island is 641,000,000 square feet. According to legend, the Native Americans sold it to the Dutch for $24. Estimate the area that was purchased for one cent.

4. TRAVEL Britney’s flight to Rome leaves New York City at 5:15 P.M. on Wednesday. The flight time is 7.5 hours. If Rome is 6 hours ahead of New York City, use Rome time to determine when she is scheduled to arrive.

5. OFFICE SUPPLIES At an office supply store, pens are $1.69 per dozen and note pads are $4.59 per dozen. Can Shirley buy 108 pens and 108 note pads for $50? Explain your reasoning.

6. SHOPPING Yoshi bought two pairs of shoes. The regular price of each pair was $108. With the purchase of one pair of shoes at regular price, the second pair was half price. How much did Yoshi pay altogether for the two pairs of shoes?

Glencoe/McGraw-Hill

87

MathMatters 1

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EXTRA PRACTICE

Date ____________________________

11-7

NON-ROUTINE PROBLEM SOLVING EXERCISES For Exercises 1 and 2, suppose you are tiling a floor. You start by making the square shown at the right. 1. You continue the pattern shown by placing one strip of tiles all around the square to make a larger square. How many tiles will you use for this larger square? How many white tiles will you use? How many gray tiles?

2. You continue tiling by placing one more strip of tiles all around the square from Exercise 1 to make a larger square. How many tiles will you use for this larger square? How many white tiles will you use? How many gray tiles?

3. Use the figure shown below. Add three straight lines to get six triangles not counting those that overlap.

4. How many cuts does it take to cut a 12-foot piece of ribbon into pieces that are each 1 foot long?

5. The elevator at Mira’s office building is not working properly. Every time it goes up, it only goes up 3 floors and stops, and then goes down 1 floor and stops. This pattern continues until it gets to the top floor, which is the 20th floor, and then it goes all the way back down to the first floor. Mira starts at the first floor and needs to go to the 12th floor. How many stops will the elevator make between the time Mira gets on the elevator and the time she gets off?

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