Answer Key. Workbook. Pacific Educational Press. MathWorks11

Transcription

1 MathWorks11 Answer Key Workbook Pacific Educational Press

2 MathWorks 11 Workbook ANSWER KEY Pacific Educational Press Vancouver, Canada

3 Copyright Pacific Educational Press 211 Revised September 215 Published by Pacific Educational Press University of British Columbia Telephone: Website: All rights reserved. Pacific Educational Press is a member of Access Copyright. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior written permission of the publisher or a licence from Access Copyright. For a copyright licence, visit or call toll-free Writer Katharine Borgen, PhD, Vancouver School Board and University of British Columbia Design, Illustration, and Layout Sharlene Eugenio Eva Neesemann Five Seventeen Editing Katrina Petrik Nancy Wilson Jordie Yow Cover Photograph Mason Morfix/Getty Images

4 MathWorks 11 Workbook Answer Key 1 Answer Key Chapter 1 Slope and Rate of Change 1.1 Rise Over Run Build Your Skills, p : a) 6:1 b) 8:3 Practise Your New Skills, p Rise Run 18 m 63 m 21 m 49 m As a fraction Slope ( m = rise run ) 1.2 cm.6 cm 2 2 As a decimal c) 8: L cm 12.4 mm 4.6 mm ft 9 ft cups 7. a) 1 6 c) 4 9 e) m cm m cm m b) 1 4 d) Rise Run Slope 15 ft 6 ft cm 32 cm m 16 m 192 in 42 in m 21 m ft 78 ft or approx ft 5. 5 cm m or approx..12

5 MathWorks 11 Workbook Answer Key or m 1.2 Grade, Angle of Elevation, and Distance Build Your Skills, p a) G 23.8, h 4.7 cm b) S 46.4, r 11.3 m c) E 55.3, f 11.4 in 2. a) θ 23.7 ; m = b) θ 64.2 ; m = or.44 or a) 7.6 ft b) a) 6.2 m b) a) 28.8 m b) 28.9 m 6. 18% c) A 53.8 ; B 36.2 ; m = 19 or d) A 54. ; B 36. ; m = 8 11 or approx a) 7.3 m b) a) For 35, m.7; for 45, m = 1 b) 7% and 1% 4. a) m = 3 5 b) 7.2 cm c).34 or.6 5. a) 2987 m b) 9.2% 6. a) 2:5 b).4 c) 4% 7. The roof of the second house is steeper % 7. a) 1 48 or -.21 b) 2.1% 1.3 Rate of Change 8. a).135 b) 7.7 c) 2.3 m m Build Your Skills, p slope l 1 = 3 5 ; slope l 2 = 3 2 ; line l 2 is steeper. 2. slope l 1 = ; slope l 2 is undefined. 1. 4: ft PractiSe Your New Skills, p a) A 5.4 ; B 39.6 ; m = 29 or approx b) A 33.7 ; B 56.3 ; m = 3 2 or 1.5

6 MathWorks 11 Workbook Answer Key 3 3. y 1 c) 3. e George s Earnings based on Sales A Earnings ($) a) 6 km/h x Sales ($) s b) Time c) 6 h 5. a) Let p be the amount owed and w be the number of weeks. p = 6-4w m =.12 or 3 25 d) $ a) 5 gal/min or 3 gal/h b) 27 min or 4.5 h 8. a) 76 km/h b) 96 km/h b) p Amount Owed by Jenita, per Week 9. a) 535 minute or 8 hours 55 minutes 6. b) 72 pages Practise Your New Skills, p. 5 Money owed ($) 1. a) 51 b) 3 8 c) 3 or or Weeks w 2. 5 y The slope of the line is -4. The slope 4 represents the amount of money Jenita pays per week. 6. a) $6., $12., $24. b) earnings =.12 sales The independent variable is the sales x

7 MathWorks 11 Workbook Answer Key 4 3. a) Hours Henrik s earnings Javier s earnings b) 1 $12.2 $ $24.4 $ $36.6 $ $48.8 $ $61. $55.5 Earnings ($) c) Henrik e Earnings per Hours Worked Hours worked Henrik Javier d) Henrik s rate of earning = $12.2/h; Javier s rate of earning = $11.1/h. 4. $ a) 2 km/h b) 115 km 6. a) Sheila is the faster walker. b) 4 d Sheila and Brandy s Walking Speeds Sheila Brandy h 7. a) Time elapsed (minutes) b) Volume of water remaining (L) Volume of water remaining (L) c) m = 15 v Rate of Water Flow Time (min) The slope is the rate at which the water volume decreases, 15 L/min. d) 32 min Chapter Test, p or cm m t Distance walked (km) Time (h) c) Sheila: 2.1 h; Brandy: 2.2 h. t 4. a) 1 ft b) 1.7 ft c) a) 1 or about.33 b) km or 9 m 7. a) m b) 5.4% m

8 MathWorks 11 Workbook Answer Key 5 9. a) Earnings ($) Rebecca s Earnings per Hour e Hours of work b) m = 15 The slope represents Rebecca s earnings per hour. h 3. a) approx. $ b) The stock was worth most ($12.15) in Week 4. He would have earned $1.4 per share of the stock. Number of copies sold n Canadian Review Magazine Sales Week w c) $12. Chapter 2 Graphical Representations 2.1 Broken Line Graphs Build Your Skills, p a) Wednesday: $3.; Friday: $. b) He spent about $19. for lunch on Sunday. Reasons will vary. He may have gone out to a restaurant with friends. 2. a) The graph shows Katie s heart rate in beats per minute, each hour from 8: am to 9: pm. b) At 8: am, 2: pm, 5: pm, and 9: pm, it was 68 beats per minute. c) Katie s heart rate was highest at 1: pm. She may have just been involved in some physical activity. 5. Sales of the magazine seem to be slowly increasing. Weight (kg) w Jessica s Weight by Week Weeks since birth Jessica lost weight during the first week, and her weight stayed the same between the 8th and 9th weeks. Otherwise, she gained weight each week. t

9 MathWorks 11 Workbook Answer Key 6 6. a) Distance driven (km) d Record of Driving Distances b) The days when he drove km are unusual. These are probably his days off. c) The graph is a fairly good representation of the data. You can see his maximum and minimum daily driving distances, and you can get a general idea of the range in which his driving distances usually fall. 7. Thérèse was driving her car from 8: am until 1: am. It was parked from 1: am to 12: pm, at which time she put gas in the tank. Thérèse then drove for an hour (until 1: pm) and stopped again for an hour until 2: pm. Between 2: and 4: pm, she drove again, and she stopped for the last hour. 8. a) The cost seems to be decreasing slightly. Day b) approximately $325. c) between $3. and $325. t 9. Number of cell phones sold 1. a) c Number of Cell Phones Sold to Males and Females in the Last Year Male Female Jan. Feb. Mar. Apr. May Jun. Month Jul. Aug. Sep. Oct. Nov. Dec. b) The number of cell phones bought fluctuated greatly from month to month, but overall, there seems to be an increase in purchases over time. c) No, there is no real relationship between the number of cell phones purchased and gender. In some months, females bought more, and in other months, males did. d) It is not very useful. A stacked bar graph or a bar graph would better indicate the numbers sold. Stock price ($) s Stock Price Stock A Stock B m.5 Jul. Aug. Sep. Oct. Nov. Dec. Month Jan. Feb. Mar. Apr. May Jun. m

10 MathWorks 11 Workbook Answer Key 7 b) Stock A started off high and made a sudden drop in August and September. It increased again over the next few months and then dropped in March. Stock B prices fluctuated slightly over the year but remained relatively even compared to Stock A. c) Answers will vary. 11. a) The graph represents the amount of money Marcia spent per week on groceries. b) Her spending on groceries increased over the 6 weeks. c) The vertical axis starts at $19.5 rather than $. d) Amount spent ($) s Marcia s Weekly Grocery Expenditures Week 12. a) The first graph makes the decrease look more rapid because one unit on the horizontal axis represents twice as many years as on the second graph. b) The second graph is a better representation because more years are represented. c) about 61% d) about 1952 e) about 17% w Practise Your New Skills, p a) Week 1: 56 steps; Week 13: b) She had fewest steps during weeks 5 and 9, each with about 54 steps. c) With the exception of the two low weeks (weeks 5 and 9), the number of steps generally increased per week. Number of hectares burned (in millions) n Area of Forest Burned in Canada, Year There is no general trend of increase or decrease in the data. However, if one year was high, the following few years tend to be lower. There were a lot of hectares of forest burned from 22 to Answers will vary. At the beginning of the year there was a steady rise in prices, but from June to August they dropped. Prices remained about the same from August to September, then rose again until the end of the year. The highest prices were in December. 4. a) Brand A has no general trend. Brand B has had a steady market with few fluctuations. Brand C has had some of the highest sales at the beginning, but then sales dropped fairly consistently. b) Answers will vary. y

11 MathWorks 11 Workbook Answer Key 8 5. a) 2 Number of Books in the Library Historical fiction Love stories Science fiction 2. a) Answers will vary, but could include: Show height on the vertical axis. Show age on the horizontal axis, and 15 display it from lowest to highest. Number of books 1 b) 2 Jamie s Height 5 15 Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Month b) There is a general, slow trend of increase in number of titles available, indicating that there are more books being added. A decline would likely mean that the librarian got rid of some titles. 2.2 Bar Graphs Build Your Skills, p. 82 Height (cm) Age (years) 3. Answers will vary, but could include: The bars are of different widths, representing different periods of time. The bars are three dimensional, making it harder to tell their heights. 1. Software Installations 4. a) Answers will vary. Percentage of total software installations b) approximately 22.5 billion tonnes c) approximately 27 billion tonnes d) Answers will vary. 5. Will s Test Results p 1 8 In-house IT dept. In-house IT with help from provider Outsourced to service provider Outsourced to development provider How software was obtained and installed Other Percentage Test number t Answers will vary.

12 MathWorks 11 Workbook Answer Key 9 6. a) The number of tickets sold per day tends to 1. a) Favourite Sport to Watch on TV decrease over time. b) The bar graph is the better representation 3 Boys Girls because it more clearly indicates the number of tickets sold. The line graph is not a good representation, because it makes the data look continuous. Number of students a) Average Weekly Household Expenses, Canada Lowest income households 2. All households with children Football Hockey Basketball Baseball Golf Sport Average weekly household expense ($) Food and drink Clothing Heat and electricity Health Transportation Communication Recreation and culture Education Eating Number of students Favourite Sport to Watch on TV Girls Boys Item b) Answers will vary. 8. a) Most: June, 675 Fewest: January, 125 b) July, a) They represent negative numbers. The temperature was below C. b) There is no black bar on Saturday because the high temperature of the day was C. c) There was no change in temperature. It stayed at 6 C. d) The temperature increased over the week. Football Hockey Basketball Baseball Sport b) 154 c) hockey d) Answers will vary. 11. None of the graphs in questions 7 9 is appropriate for a stacked bar graph. Golf

13 MathWorks 11 Workbook Answer Key 1 Practise Your New Skills, p Histograms 1. Number of Users of Fitness Equipment per day Build Your Skills, p a) approx. 125 Equipment Stationary bike Treadmill Elliptical cross-trainer Stairclimber Number of users b) between $1. and $2. c) The exact value cannot be determined from the graph, but it is over $ a) 38 b) 67 c) 26 d) a) Movies 4 and 5 3. Ages of Employees b) Movie The number of girls taking home economics 2 classes has stayed fairly constant over the time period, while the number of boys taking the classes has increased. Number of people a) The numbers of single-detached house 5 and multiple-unit construction projects started has generally decreased since Age 26. There was a large drop in multipleunit construction projects between 28 and a) 1 Ages of Audience Members at Theatre Presentation 8 b) 1 Housing Construction Projects Started in Abbotsford, BC, per Year Single Multiple Frequency Number of projects 6 4 b) Ages c) The exact age cannot be determined from Year the graph, but he or she was under the age of 2. Answers will vary.

14 MathWorks 11 Workbook Answer Key 11 Practise Your New Skills, p a) 8 b) 9 c) The exact mark cannot be determined from the graph, but it was over 9% and less than or equal to 1%. 2. a) 2 b) Circle Graphs Build Your Skills, p a) 24 b) blue, a) entertainment and savings b) $25. per month 3. a) 15 Fixed Rate Real Estate Housing Sales c) 5 Expenditures 4 Number of houses 1 5 Percentage Selling price (in thousands) ($) b) The exact price cannot be determined from the graph, but it was below $1.. c) 9 Housing Food Clothing Entertainment Item Transportation Savings The circle graph is a better representation of the data. 4. a) Hurricane Occurrences, by Time of Year 3. a) 34% b) 23% Percentage of hurricane occurrences Mar. 21 Jun. 2 Jul. 2 Aug. 2 Dates Sep. 2 Oct. 2 Nov a) c) The toilet and the clothes washer combined to about half the water use, at 48%. Type of Pet 2% 42% Rodent Dog Cat b) between November 2 and March 2 38% c) from August 21 until September 2

15 MathWorks 11 Workbook Answer Key 12 b) 16.4% Type of Pet 34.4% Rodent b) The information could have been displayed on a bar graph. Hairspray Sales in One Month 18.8% None Dog a) 19% Cat 3.4% School Fundraising for International Disaster Relief 6% 9% 44% Classroom donations Concert proceeds Chocolate bar sales Hot lunches Parental donations 22% Hairspray Sales in One Month 3% 11% 3% Brand A Brand B 16% Brand C Brand D Brand E Brand F 18% 22% Number of sales 1 5 Brand A Brand B Brand C Brand Brand D Practise Your New Skills, p a) 137 b) 38% 2. c) 37 15% 15% 1% Deciding Factors for Choosing Greg s Tour 6% Brand E Walk-in Brand F Recommended by friend Recomended by tourism office Travel package 3. 7% Number of Books in Mary s Home Library 4% 3% Autobiography 44% Self-help 14% Biography Poetry Science Fiction 29% Historical Fiction

16 MathWorks 11 Workbook Answer Key 13 Chapter Test, p a) Profit (in thousands of dollars) b) 23 p Company Profits, Year y 3. a) Either a broken line graph or a bar graph (vertical or horizontal) could be used, because the data is discrete. Number of video rentals Video Rentals by Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Month 2. a) c) 23 was the peak year for the company s profits; profits were much higher that year than in 22 or 24. In 24, the profits then dropped down to what they had been during the two previous years (21 22). They made a steady increase over the next three years and seem to have levelled off over the last three years. Number of Motors Bought and Sold Number sold Number bought 4 Number of video rentals n Jan. Feb. Mar. Apr. May b) Most: October (8978) Video Rentals by Month Jun. Month Jul. Aug. Sep. Oct. Nov. Dec. m Number of motors Brand A Brand B Brand C Type b) Brand C, 1 c) Brand B, 1 Brand D Least: May (4199) c) Rentals tend to be lower in the summer months, but are otherwise stable. 4. Housing: $114.; Food: $6.; Car: $48.; Miscellaneous: $39.; Charitable donations: $18.; Entertainment: $12.; Savings: $9..

17 MathWorks 11 Workbook Answer Key a) 6 Number of Hours Spent per Month Doing Volunteer Work 3. a) in 2 b) 36.6 m m 1.8 m Number of respondents m 2 5 Hours m b) m 8.8 m 1.8 m c) 33% Chapter 3 Surface Area, Volume, and Capacity 3.1 Surface Area of Prisms 6.2 m 2.6 m 2.4 m 3.6 m Build Your Skills, p m 1. a) circle, mm m 1.8 m b) triangle, 26.5 m 2 c) parallelogram, 78.4 cm 2 d) triangle, 72 in m 2.4 m 2. a) rectangle, 44.2 m m b) parallelogram, 44.2 m m 1.8 m c) triangle, 22.1 m 2 d) triangle, 22.1 m m e) triangle, 22.1 m m f) Areas of rectangles and parallelograms are the same if they have the same base and height. Areas of triangles are the same if they have the same height and base. A triangle with the same base and height as a rectangle has half the area of the rectangle. 2.6 m Area 46 m 2 7. m

18 MathWorks 11 Workbook Answer Key Prism Shape of base Right or oblique Shape of lateral Name of prism faces a) triangular oblique parallelogram oblique triangular prism b) rectangular right rectangular right rectangular prism c) pentagonal right rectangular right pentagonal prism d) trapezoidal oblique parallelogram oblique trapezoidal prism e) octagonal right rectangular right octagonal prism f) rectangular oblique parallelogram oblique rectangular prism 6. a) 5 in 7. Ralph is correct. Manon s net is missing one of the side panels. 8. a) 6 cm 15 in 8 cm 5 in 6 cm 6 cm 6 cm 5 in b) 3 cm 3 cm 8 cm 3 cm 1 cm SA 376 cm 2 b) 14 cm 5 in 5 in 4 in 5 in 2.6 cm 3 in 3 in 3 in 8 in SA 18 in 2

19 MathWorks 11 Workbook Answer Key 16 c) 12 cm b) 15 cm 48 cm 15 cm 8 cm 9 cm 12 cm 2 cm 25 cm 25 cm 15 cm 25 cm 15 cm SA 318 cm 2 SA 726 cm m cm a) 31 8 cm 2 b) cm ft 2 Practise Your New Skills, p a) 42 cm 3 cm 3 cm 3 cm ft m ft Surface Area of Pyramids, Cylinders, Spheres, & Cones Build Your Skills, p ft cm mm 2 25 cm m 2 3 cm 25 cm cm mm cm cm 2 SA 612 cm cm cm cm cm

20 MathWorks 11 Workbook Answer Key cm cm in mm m cm 4. 7 trips 5. a) 9.4 cm cm cm m 2 V cm mm 2 V cm m 2 b) 16.8 cm 6.6 cm 7.4 cm ft cm cm 2 V 2 Practise Your new Skills, p cm V in cm ft ft ft cm Volume and Capacity of Prisms and Cylinders Build Your Skills, p a) V 369 cm 3, capacity 3.69 L b) V 34 m 3, capacity 34 L c) V 12.7 in 3, capacity.55 US gal or V 28 cm 3, capacity 28 ml 16.8 cm m cm cm 3, 6.4 L cm 3, 33 L cm Practise Your Skills, p a) cm 3 b) 34.6 cm 3 c) 81.4 m 3 2. rectangular prism ft 3 4. a) 4.1 m 3 b) 984 kg 6.6 cm

21 MathWorks 11 Workbook Answer Key cm Chapter Test, p m 1. a) 3.4 Volume and Capacity of Spheres, 8 cm Cones, and Pyramids 8 cm Build Your Skills, p cm 7.4 cm 1. a) 2572 cm 3 b) cm 3 8 cm 6 cm 2. a) cm 3 b) 1431 L 8 cm 3. a) 1615 in 3 b) 4 ft 3 c) cm 3 4. V 484 ft 3, capacity US gal or V m 3, capacity L SA = cm 2 b) 15 cm 8 cm in 3 6. a) 739 mm 3 b) 2663 in 3 c) 637 in 3 d) 86 mm 3 8 cm 8 cm 8 cm 8 cm 7. a) in 3 b) 1583 cm 3 8 cm c) 198 m mm cm 3 c) SA = 68 cm 2 Practise Your New Skills, p a) 147 mm 3 b) 515 mm 3 c) 3.6 mm 3 d 271 mm 3 18 cm US gal 5 cm 8 cm 9.4 cm 3. a) 631 cm 3 b) 631 ml 5 cm 9.4 cm m 3 SA = 443 cm cm 3

22 MathWorks 11 Workbook Answer Key SA = 87 m 2, V = 45 m 3 3. a) cm 2 b) cm 3 c) ml 4. a) mm 2 b) mm 3 5. SA = cm 2, V = 6149 cm m 3 7. $2484. Chapter 4 Trigonometry of Right Triangles 4.1 Solving for Angles, Lengths, and Distances Build Your Skills, p a) tan θ.6423; θ 32.7º b) sin θ.7826; θ 51.5º c) cos θ.797; θ 44.8º cm cm x = 7.1 m, z = 3.7 m , 19.5 cm m m m m 2 Practise Your New Skills, p a) 18.4 m b) 5.4 m c) 21.3 cm d) 4.4 e) 8.7 f) 19.2 cm g) 8.6 m h) m m , m 5. a = 2.5 ft, b = 1.5 ft, c = 53, d = 3.5 ft 4.2 Solving Complex Problems in the Real World Build Your Skills, p m 2. a) x 12.7 cm, y 19. cm b) x 11.6 m, y 1. m 3. x 8.5 cm, y 6.4 cm, h 17.1 cm m 5. a) 12.7 ft b) 5.9 ft m or 439 m 7. a) 65. m b) 82.6 m 8. a) 21.4 km b) m Practise Your New Skills, p a) x 7.1 cm, y 8.4 cm

23 MathWorks 11 Workbook Answer Key 2 b) θ = 33, x = 4 cm, y 47.7 cm c) θ 42., x 78.4 ft, y 81.1 ft 2. G 43.2, x = 8.5 ft, y = 11. ft 3. a) 43.7 m b) a) 36.4 m b) 49.9 m m Chapter Test, p a) 2.8 m b) 35. c) 73.9 d) 39.8 in 2. a) x 1.1 cm, Y 47.7 b) X 53.6, y 8.4 cm, z 1.4 cm c) x 5.9 cm, Y 48, z 2.9 cm m cm m 6. a) 67.5 m b) a) 83. km b) 4.1 Chapter 5 Scale Representations 5.1 Scale Drawings and Models Build Your Skills, p a) 63 b) 1 c) 2 d) 918 e) 11 f) a) 14.4 b) 19.3 c) 1.8 d) years km 5. 1:5 6. a) 2:1 b).1 cm 7. 1: m 9. a) The picture is 5 cm long. Scale = 1:84 b) 5. m c) 2.3 cm 1. a).3 cm or 3 mm b) 375 cm or 3.75 m c) It is unlikely that the same scale would be used because the sizes are very different. For the cat, you would probably use a scale of 1:c. That is, you would represent it smaller than it actually is. The only time you might use the same scale for them is if, for some reason, you needed to compare how small the mite would be on the cat. Practise Your New Skills, p cm

24 MathWorks 11 Workbook Answer Key a) 1:88.8 b) in in or 1.2 ft 15.7 ft c) in 99.9 in or 9.7 ft 8.3 ft 4. a) 1:254 b) 2.3 cm 5. height: 234 cm; width: 162 cm; depth: 3 cm m 5.2 Two-Dimensional Representations Build Your Skills, p b) No, there might be some blocks we cannot see, hidden by the tower. 4 in 8 in 8 in 1 in 4 in 24 in Top View 8 in 1 in 4 in 3 in 7 in 24 in Front View 2 in TOP 1 in 4. 5 cm 1 in SIDE VIEW 1 m FRONT SIDE 2. a) 1 m Side View 1.2 m.5 m FRONT 1 m Front View

25 MathWorks 11 Workbook Answer Key cm 3 cm 6 cm Practise Your New Skills, p cm A 2 9 cm B 4 9 cm C 1 Top View SHELF COMPONENT 18 cabinet screws KICK PLATE COMPONENT Side View 2. a) Front View 6. a) 1:6 SIDE COMPONENT b) She can make a quilt that will have square patches, but it will be smaller than she planned because she forgot about the seam allowance. c) Scale 1:2 9 cm 6 cm Top View Side View Front View b) No, you can t draw the back view because there could be additional blocks or gaps that you cannot see from the current diagram. A 2 8 cm B 4 15 cm

26 MathWorks 11 Workbook Answer Key SCALE 1:6 6. SCALE 1:2.9 m.3 m TOP.9 m Top View.55 m LID.9 m Front View.7 m FRONT 4. a) 1:35 b) width: 7 cm; height: 14 cm c) No, you do not have enough information to draw top and side views of the house. 5. a) She will need to provide a front view. She does not need to provide side views, since all the sides are the same. She does not need to provide a top view, because the roof can be seen on the front view. b).9 m.9 m BACK.9 m.8 m BASE Scale statements will vary.

27 MathWorks 11 Workbook Answer Key m.9 m 5.3. Three-Dimensional Representations Build Your Skills, p x = 2 ft, y = 1 ft, z = 16 ft, h = 8 ft.7 m SIDE 2.9 m 2. SCALE 1:2.8 m 7. Scale 1:5 5 cm 5 cm 2 cm 22 cm 3. SCALE 1:6 4 cm A 2 62 cm C 1 B 2

28 MathWorks 11 Workbook Answer Key A 6. Answers will very depending on the location of the vanishing point. Two possible answers: B The two drawings will not look exactly alike because they depend on the location of the vanishing point and how deep you choose to make your boxes. Even if you choose to make the boxes the same depth, they will look slightly different because of the angle to the vanishing point. 5. V 7. 8.

29 MathWorks 11 Workbook Answer Key c) The perspectives and the angles to the vanishing point are different cm 32 cm A 2 Practise Your New Skills, p See diagram on the next page cm 14 cm B 3 3. a) SCALE 1:5 5. a) SCALE 1:5 8 cm 1 cm 1 cm A 4 1 cm B 4 b) 6 cm 6 cm C 2

30 MathWorks 11 Workbook Answer Key Three-Dimensional Representations, Practise Your New Skills, Question 1. SCALE 1:1

31 MathWorks 11 Workbook Answer Key 28 b) 7. Chapter Test, p a) : cm b) 384 cm or 38.4 m 8. a) Scale may vary. SCALE 1:1 4. a) 1:15 b) c) 8.4 cm 45 cm 25 cm A 1 27 cm 7 cm B 4 TOP b) 6. SIDE FRONT

32 MathWorks 11 Workbook Answer Key 29 Chapter 6 Financial Services 6.1 Choosing an Account Build Your Skills, p a) $5.5 b) $ 2. a) $33.75 b) $ $ See table on the next page. End of month balance: $ $ $ Practise Your New Skills, p $1. 2. $ 3. Full-Service Account or Self-Service Account 4. a) See table on the next page. b) No, she should switch to a Full- Service Account. 5. $ Simple and Compound Interest Build Your Skills, p a) $25. b) $5. c) $5. d) $5. e) The interest doubles. f) The interest doubles. 2. $ $ $ $ $ a) $ b) $ c) $ d) $ $ Interest Table Interest period Investment value at beginning of period Interest earned (I = Prt) Investment value at end of period 1 $3. $24.38 $ $ $24.57 $ $ $24.77 $ $ $24.97 $ $ $25.18 $ $ $25.38 $ $ $25.59 $ $ $25.8 $ a) 18 years b) 29.4 years c) 36.9 years Practise Your New Skills, p a) I = $4., A = $44. b) I = $13.13, A = $ c) I = $45., A = $145. d) I = $426.6, A = $ a) $442.5 b) $86.42 c) $ d) $

33 MathWorks 11 Workbook Answer Key Choosing an Account, Build Your Skills, Question 4. Transaction Description Withdrawal Deposit Balance $ Direct deposit Paycheque $ $ ATM Cash $2. $331.4 Bank card Groceries $63.95 $ Bank card Clothes $75.32 $ Bank card Movie $24.5 $ Teller Hydro bill $89.56 $ Direct deposit Paycheque $ $ ATM Cash $1. $ Auto-withdrawal Loan payment $ $ Bank card Groceries $ $358.3 Bank card Gas $56.23 $ Bank card Dinner $25.38 $ Auto-withdrawal Rent $575. $ Bank card Books $ $ Auto-withdrawal Monthly banking fee $24.5 $ Choosing an Account, Practise Your New Skills, Question 4. Transaction Description Withdrawal Deposit Balance $ ATM Cash $25. $ Bank card Dinner $25.32 $ Bank card Groceries $ $ Direct deposit Paycheque $ $ Bank card Movie $12.98 $ ATM Cash $1. $ Bank card Gas $48.96 $ Teller Utilities $ $ Auto-withdrawal Rent $55. $ Direct deposit Paycheque $ $ Bank card Groceries $ $ ATM Cash $1. + $.5 $ Teller Phone $ $1. $ Bank card Misc) $ $.5 $ Bank card Dinner $ $.5 $ ATM Cash $2. + $.5 $ Bank card Prescription $ $.5 $421.7

34 MathWorks 11 Workbook Answer Key Interest Table Interest period Investment value at beginning of period Interest earned (I = Prt) Investment value at end of period 1 $1. $19.25 $ $ $19.62 $ $ $2. $ $ $2.38 $ a) $ b) $ a) 26 years b) $ a) $1133. b) 28.8 years % per annum compounded annually 8. a) $ b) $ c) $ d) $ Credit Cards and Store Promotions Build Your Skills, p a) $16.64 b) $22.55 c) $ $ a) $127.5 b) $6.35 c) $ a) 12 days b) $554.5 c) $ $ % 7. Option %Practise Your New Skills, p. 313 Practise Your New Skills, p a) $79.19 b) $ $ a) $ b) $ a) $66.1 b) $ Option Personal Loans, Lines of Credit, and Overdrafts Build Your Skills, p % 2. a) 137% b).375% 3. $ $ days 6. a) $13. b) 182.5% 7. a) monthly payment = $137.4, total paid = $ , finance charge = $ b) monthly payment = $65.85, total paid = $237.6, finance charge = $245.6 c) monthly payment = $263.58, total paid = $ , finance charge = $ a) $18. b) $8.19 c) $ d) $324.56

35 MathWorks 11 Workbook Answer Key 32 Practise Your New Skills, p a).98% b) 358% 2. $ a) monthly payment = $78.35, total paid = $282.6, finance charge = $32.6 b) monthly payment = $194.5, total paid = $11 67., finance charge = $167. c) monthly payment = $64.97, total paid = $ , finance charge = $ a) $ b) $ c) $ a) $ b) She should choose Option 1. Chapter Test, p See table below. 2. a) $125. b) $ $ $ $ a) $18.28 b) $ a) $ b) $ a) 1.14% b) 417.% 9. a) $74.34 b) 5.6 % c) Option 1 = $ Option 2 = $216. He should choose Option Personal Loans, Lines of Credit, and Overdrafts, Chapter Test, Question 1. Transaction Description Withdrawal Deposit Balance $ ATM Cash $2. $ Direct deposit Paycheque $ $ Bank card Groceries $ $ Bank card Gas $42.54 $ ATM Cheque $ $ reimbursement Bank card Dinner $32.42 $ ATM Cash $1. $ Auto-withdrawal Hydro $ $ Direct deposit Paycheque $ $ Auto-withdrawal Rent $645. $ Bank card Car repairs $ $ Bank card Movie $28.12 $ ATM Cash $2. $216.22

36 MathWorks 11 Workbook Answer Key 33 Chapter 7 Personal Budgets 7.1 Preparing to Make a Budget Build Your Skills, p Answers may vary. Item Classification Reason Semimonthly paycheque Regular This paycheque will happen twice a month. Birthday gift Variable You don t know what you ll get for your birthday and it only happens once a year. Tips Variable You don t know how many tips you ll get in a shift. Interest from investment Regular Your investments will have regular interest payments. Tax refund Variable You don t know how much tax you ll pay or get refunded each year until you do your taxes. 2. Answers may vary. Item Classification Reason Rent Recurring You will have to pay the same rent every month. New shoes Variable You don t need to buy new shoes often enough to plan on this. Loan payments Recurring You will have an agreement with whoever issued the loan on a repayment schedule. Car repairs Unexpected You can t plan when your car will break down. Groceries Variable You don t know how much you ll spend on groceries each trip, but you do have to do it regularly. Meal at restaurant Replacing broken cell phone Car insurance Variable Unexpected Recurring You don t know how much you ll spend every time you go for dinner, but you can budget for it. You can t plan when you break your cell phone. You will have an agreed rate of car insurance with your insurance broker. 3. Item Income Expense Paycheque: $25.98 Regular John's birthday: $54.25 Variable Commission: $75. Variable Babysitting: $4. Variable Paycheque: $ Regular Loan payment: $125. Regular Donation to earthquake relief Variable fund: $25. Car insurance: $ Regular Savings: $5. Variable Rent: $45. Regular Cell phone bill: $45. Regular Meal at restaurant: $56.76 Variable 4. $ $217.56, 7.1% 6. No, she will have $ saved months 8. She will be $18. short of her goal. Practise Your New Skills, p Item Income Expense Paycheque Regular Rent Regular Car insurance Regular Gas Variable Clothing Variable Cell phone bill Regular Mother s Day gift for mom Variable Groceries Variable Present for Joan Variable Entertainment Variable Mowing lawns Variable Utilities Variable 2. a) $215. b) 17% c) Yes, she will have $129. saved.

37 MathWorks 11 Workbook Answer Key $25./month 4. a) Income Expenses Babysitting $4. Cell phone $4. Babysitting $4. Entertainment $15. Paycheque $375. Food $195. Paycheque $375. Loan payment $65. Tutoring $5. Rent $425. Tutoring $1. Renter s $25. insurance Tutoring $5. Transportation $8. b) Total income: $13.; total expenses: $935. c) $114. d) 9% 7.2 The Budgeting Process Build Your Skills, p a) Answers will vary. A possible budget: Craig and Stéfanie s Monthly Budget Income Expenses Craig s $28. Mortgage $185. monthly pay Payment Stéfanie s $277. Utilities $175. monthly pay Cat care $5. Clothing $15. Food $4. Gas $15. Car insurance $112. Gifts $15. Entertainment $12. Loan payment $15. Home $122. insurance Trip fund $25. Cell phones $135. Miscellaneous $475. Savings $1281. Total income $557. Total expenses $557. b) Answers will vary depending on the budget you create. For the values given above, they would save $ a) Answers will vary. A possible budget: Minh s Monthly Budget Income Expenses Regular $1665. Rent $64. Tips $3. Utilities, phone, $115. cable, internet Food $3. Transportation $11. Entertainment $21. Other $5. Savings $9. Total income $1965. Total expenses $1965. b) Answers will vary. Based on this budget, he will be $ short. 3. a) Answers will vary. A possible budget: Georgina s Monthly Budget Income Expenses Monthly pay $35. Mortgage $125. payment Car insurance $122. House repairs $7. House taxes $35. Gifts $45. Charity $3. Gas $125. Loan payment $22. Miscellaneous $16. Entertainment $16. Home insurance $125. Clothing $13. Car $5. maintenance Food $375. Skiing season s $55. pass Savings $8. Total income $35. Total expenses $35.

38 MathWorks 11 Workbook Answer Key 35 b) Answers will vary. Based on this budget, $96.. c) Answers will vary. Based on this budget,.3%. d) Answers will vary. 4. a) $444. b) 13.5% 5. a) $324. b) 5 months 6. 7 months Practise Your New Skills, p a) Answers will vary. A possible budget: Pierre s Monthly Budget Income Expenses Semi-monthly pay Semi-monthly pay $1475. Mortgage $145. Payment $1475. Utilities/phone $15. Groceries $325. Loan $25. repayment Charity $4. Entertainment $15. Clothing $15. Transportation $22. Miscellaneous $8. Savings $135. Total income $295. Total expenses $295. b) $135./month; $162./year 2. a) Answers will vary. A possible budget: Chantal s Monthly Budget Income Expenses Semi-monthly $111. Rent $675. pay Semi-monthly $11. Utilities, phone, $15. pay cable, internet Tips $135. Food $4. Transportation $3. Entertainment $15. Other $375. Savings $35. Total income $2355. Total expenses $2355. b) Answers will vary. Based on this budget, 13%. c) Answers will vary. Based on this budget, 4 months. 3. a) $86.5 b) 9 months 7.3 Analyzing a Budget Build Your Skills, p a) 14 months b) 17.5% 2. a) $ b) $ a) Answers will vary. b) Answers will vary. A possible graph: Petra s Monthly Expenses 4% 2% 5% 5% 5% 7% 13% 2% 39% Rent Food Utilities, phone, cable, internet Savings Clothing Miscellaneous Transportation Entertainment Charitable donations

39 MathWorks 11 Workbook Answer Key a) Sammy needs to lower his spending on transportation, entertainment, and other expenses. He needs to increase his savings. b) $6. c) Answers will vary. A possible budget: Sammy s Monthly Budget Income Expenses Pay $15. Housing $4. Food $275. Transportation $2. Entertainment $15. Charitable $125. donations Savings $15. Other $2. Total income $15. Total expenses $15. b) Willa s Monthly Expenses $285. $3. $375. $215. $235. $42. $45. $125. Practise Your New Skills, p a) $44. b) $ a) $45. b) $ a) Total income = $275.; total expenses = $275.. Yes, his budget is balanced. Housing Food Debt repayment Savings Health and personal Transportation Utilities Recreation $15. $15. $2. $125. $2. Sammy s Monthly Expenses $4. $275. Housing Food Transportation Other Entertainment Savings Charitable donations 5. a) Answers will vary. A possible budget: Willa s Monthly Budget Income Expenses Regular $353. Housing $125. Utilities $235. Transportation $285. Debt repayment $42. Savings $375. Food $45. Recreation $215. Health and $3. personal care Total income $353. Total expenses $353. b) Sean s Monthly Expenses $1. $5. $1. $125. $15. $15. $175. $175. $2. Housing Food Savings Clothing Utilities Phone, cable, internet $325. $12. Charitable donations Miscellaneous Medical/health and other emergencies Entertainment Transportation c) No, Sean is spending 44% of his income on housing. He should be spending no more than $ d) Answers will vary.

40 MathWorks 11 Workbook Answer Key a) Gabriella s Montly Expenses Chapter Test, p. 367 $15. $175. $175. $125. $175. $75. $275. $84. b) She is spending too much on: housing (by about $145.) Savings Transportation Miscellaneous Food Clothing Entertainment Loan payments Housing debt repayment (by about $36.); and personal expenses (clothing and miscellaneous) (by about $9.). She is spending below the guidelines on: transportation (by about $115.); savings (by about $125.) She is within the guidelines for: food; and entertainment c) Current rate: 14 months. If she wanted to save $1. in 6 months, she would need to save $91.67 more per month. Her savings would still be lower than the guidelines suggest. 1. Item Income Expense Biweekly paycheque: $735. Regular Monthly bus pass: $75. Recurring Gas: $42.95 Variable Cell phone bill: $39.96 Recurring New jacket: $69.95 Variable Tips: $52. Variable Debt repayment: $75. Recurring Emergency vet bill for cat: Unexpected $25. Movie ticket and snack: $2. Variable Dinner at restaurant: $27. Variable Charitable donation: $25. Variable Commission: $1. Variable 2. a) Answers will vary. A possible budget: Tamara s Monthly Budget Income Expenses Semi-monthly $975. Rent $575. Semi-monthly $975. Utilities, phone, $155. cable, internet Groceries $275. Debt repayment $1. Transportation $325. Personal $465. Savings $55. Total income $195. Total expenses $195. b) Answers will vary. Based on this budget, $66./year. c) Answers will vary. Based on this budget, 3%. 3. a) $ b) 26%

41 MathWorks 11 Workbook Answer Key a) Madeleine s Montly Income & Expenses Income Expenses Semi-monthly $885. Rent $595. Semi-monthly $885. Utilities, phone, $275. cable, and internet Tips $25. Food $295. Transportation $1. Entertainment $225. Other $35. Savings $18. Total income $22. Total expenses $22. b) Rent: 29.5%; Utilities, phone, cable, and internet: 13.6%; Food: 14.6%; Transportation: 5.%; Entertainment: 11.1%; Other: 17.3%; Savings: 8.9% c) $ a) Noah would need to spend $14. less on food, $15. less on transportation, $6. less on other expenses, and save $9. more per month. b) He should put at least $12. into savings per month. c) Answers will vary. A possible budget: Noah s Monthly Budget Income Expenses Semi-monthly $12. Rent $795. Semi-monthly $12. Utilities $15. Food $36. Transportation $36. Entertainment $15. Clothing $1. Savings $245. Other $24. Total income $24. Total expenses $24. Noah s Montly Expenses $15. $15. $24. $1. $795. Clothing Utilities Entertainment Other Savings $245. Transportation $36. $36. Food Rent