Grade 12 Consumer Mathematics Standards Test. Written Test Student Booklet

Transcription

1 Grade 12 Consumer Mathematics Standards Test Written Test Student Booklet January 2011

2 Manitoba Education Cataloguing in Publication Data Grade 12 Consumer Mathematics Standards Test : Written Test Student Booklet. January 2011 [electronic resource] ISBN: Mathematics Examinations, questions, etc. 2. Mathematics Examinations. 3. Mathematical ability Testing. 4. Consumer education Mathematics Examinations, questions, etc. 5. Educational tests and measurements Manitoba. 6. Mathematics Study and teaching (Secondary) Manitoba. I. Manitoba. Manitoba Education Manitoba Education School Programs Division Winnipeg, Manitoba, Canada Permission is hereby given to reproduce this document for non-profit educational purposes, provided the source is cited. After the administration of this test, print copies of this resource can be purchased from the Manitoba Text Book Bureau. Order online at < This resource will also be available on the Manitoba Education website at < Websites are subject to change without notice. Ce document est disponible en français.

3 Grade 12 Consumer Mathematics Standards Test Written Test Student Booklet (January 2011) DESCRIPTION Total Possible Marks: 40 This component of the test consists of six parts: Maximum Time: 90 minutes Learning Unit Suggested Time to Complete Marks Personal Finance minutes 7 Government Finances minutes 8.5 Statistics minutes 7 Design and Measurement minutes 3 Variation and Formulas minutes 7.5 Investments minutes 7 GENERAL DIRECTIONS You may use the Grade 12 Consumer Mathematics: Written Test Resource Package (2010/2011) containing formulas and tables. Use of a scientific calculator and ruler may be necessary. Graphing calculators are not permitted. Read all instructions on the test carefully. If you need more space to answer a question, extra pages may be provided by your teacher. Write your booklet ID number and question number on any extra page(s) used and staple the additional pages into the booklet where your answer begins. i

4 Remember to show all your work in this booklet use your Written Test Resource Package use a scientific (non-graphing) calculator use a ruler ii

5 DIRECTIONS Show complete answers in the space(s) provided in this booklet. Let the mark values for each question guide you in answering the question. Show all your work. Be sure to include units in your final answer. Use your Written Test Resource Package. Provide explanations and justifications. Use a well-organized method to communicate your answer. Directing Words Some questions may include directing words such as explain, illustrate, and calculate. These words are explained below. The Word identify/list/name/state defend/justify/support describe/explain/express illustrate/sketch draw calculate/convert/determine/find plot The question is asking for a label or title of an item, concept, or method an explanation, information, or evidence that shows why your method, idea, or answer is good words or symbols, diagrams, charts or graphs, or other methods that clearly show what you mean or what you are thinking a reasonably neat picture or diagram (not necessarily to scale) that shows or explains an idea or method a diagram to scale or graph that shows or explains an idea or method a mathematical formula, an algebraic equation, or a numerical calculation to solve a problem placement of a point or points on a graph PLEASE WAIT UNTIL THE TEACHER TELLS YOU TO TURN THE PAGE. iii

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7 Personal Finance 2 Marks 1. Joe borrows $ to buy a house. He has an interest rate of 6.5% on a mortgage amortized over 25 years. A) Calculate Joe s monthly mortgage payment. (1 mark) 115 B) Calculate the total amount of the mortgage payments made, over the 25-year mortgage. 116 (0.5 mark) C) Calculate the total interest paid over the life of the mortgage. (0.5 mark) 117 Consumer Mathematics: Written Test Student Booklet (January 2011) 1

8 2. Roberta, a female smoker, and Doug, a male non-smoker, are 20-year-old twins. They each purchase whole-life insurance policies. 1.5 Marks A) State Roberta s and Doug s issue rates per $1 000 of insurance. (1 mark) 118 Roberta: Doug: B) Explain why Roberta s issue rate per $1 000 unit is lower than Doug s. (0.5 mark) Consumer Mathematics: Written Test Student Booklet (January 2011)

9 1 Mark 3. Cynthia was approved for a $ mortgage. In addition to her down payment she has 120 $600 saved for additional costs involved in purchasing this home. Justify why $600 is not enough money to pay for the initial costs in purchasing a home. Consumer Mathematics: Written Test Student Booklet (January 2011) 3

10 2.5 Marks 4. Elmer wants to make monthly payments of $ on a house. His gross monthly income is $8 000, the monthly property taxes are $300 and the monthly heating is $150. A) Calculate Elmer s Gross Debt Service Ratio (GDSR). (1.5 marks) 121 B) Elmer really wants this house. Identify what he could do to lower his GDSR. 122 (1 mark) 4 Consumer Mathematics: Written Test Student Booklet (January 2011)

11 Government Finances 2 Marks 5. A) Name one expenditure for each of the three levels of government. (1.5 marks) 123 Level of Government Expenditure Federal Provincial Municipal B) Identify one source of revenue the government receives to pay for these expenditures. 124 (0.5 mark) Consumer Mathematics: Written Test Student Booklet (January 2011) 5

12 2.5 Marks 6. Connie is planning a trip to England. A) Connie has $7 000 Canadian. Convert her money into pounds ( ). (1 mark) 125 B) While on her trip to England, Connie spent pounds ( ). When she arrives home 126 she converts the money she has left into Canadian dollars. Calculate the amount of money Connie has left. (1.5 marks) 6 Consumer Mathematics: Written Test Student Booklet (January 2011)

13 2.5 Marks 7. Doreen s property has a portioned assessed value of $ and the municipal mill rate is A) Calculate the amount of property tax Doreen will pay. (1 mark) 127 B) The property has a 50-foot frontage and the local improvement tax for street lighting 128 is $3.50 per foot. Calculate the cost of local improvements for Doreen s property. (0.5 mark) C) Doreen paid a total of $ for municipal and education taxes. Calculate the 129 amount of education tax she paid. (1 mark) Consumer Mathematics: Written Test Student Booklet (January 2011) 7

14 1.5 Marks 8. A Manitoba municipality has a total taxable portioned assessment base of $ The municipality requires revenue of $ to meet its budget requirements. A) Calculate the property tax rate in mills. (1 mark) 130 B) Express this mill rate as a percentage. (0.5 mark) Consumer Mathematics: Written Test Student Booklet (January 2011)

15 Statistics 2 Marks 9. Tyler is one of 360 players in a basketball league. He is six feet seven inches tall. There are 31 other players who are the same height as Tyler and 316 players that are shorter than Tyler. A) Calculate Tyler s percentile rank. (1.5 marks) 132 B) How tall is the tallest player in the basketball league? (0.5 mark) 133 Consumer Mathematics: Written Test Student Booklet (January 2011) 9

16 1 Mark 10. A car manufacturer builds the Nano, a small car that is economical to drive. A specific car part in the Nano has a lifespan that follows a normal distribution as shown in the diagram below. Lifespan km km Determine the standard deviation of the car part s lifespan in km Consumer Mathematics: Written Test Student Booklet (January 2011)

17 11. A college course entrance test was used to sort the applicants. The mean on the test was 74 and the standard deviation was 5. The scores followed a normal distribution pattern. 2 Marks A) State the scores for the spaces given below the curve. (1 mark) 135 Distribution of Student Scores B) Calculate the number of students that scored between 69 and 79, if 300 students wrote 136 the test. (1 mark) Consumer Mathematics: Written Test Student Booklet (January 2011) 11

18 1 Mark 12. A study shows a positive correlation between the number of sugared drinks consumed by 137 young people and the onset of Type II diabetes. Carolyn is a teenager concerned about her health. According to this study, describe a change she can make to decrease her chances of developing Type II diabetes. 12 Consumer Mathematics: Written Test Student Booklet (January 2011)

19 1 Mark 13. Scores on math and language arts exams have a correlation coefficient of 138 r = Identify the strength and type of this correlation. Consumer Mathematics: Written Test Student Booklet (January 2011) 13

20 Design and Measurement 3 Marks 14. A manufacturer purchases a rectangular sheet of cardboard that has dimensions of 30 cm 50 cm. 30 cm 50 cm The manufacturer cuts 5 cm 5 cm squares out of each corner. The sides are folded up to create an open-top box. A) State the length, width, and height of the box and calculate its volume in cm (2 marks) B) Calculate the percent of the original sheet that was wasted in cutting out the corners. 140 (1 mark) 14 Consumer Mathematics: Written Test Student Booklet (January 2011)

21 Variation and Formulas 1 Mark 15. The time needed to manufacture DVDs varies directly with the number of DVDs manufactured. Sketch this variation. 141 Number of DVDs Time Consumer Mathematics: Written Test Student Booklet (January 2011) 15

22 2 Marks 16. Identify the type of variation that matches each table. A) x y (0.5 mark) 142 B) x y (0.5 mark) 143 C) x y (0.5 mark) 144 D) x y (0.5 mark) Consumer Mathematics: Written Test Student Booklet (January 2011)

23 1.5 Marks 17. Allen was stopped for driving at a speed of 120 km/h in a 100 km/h zone. His fine for speeding is based on a flat rate of $100 for exceeding the limit and $10 for every km/h over the limit. A) Identify the type of variation represented. (0.5 mark) 146 B) Sketch the variation that represents this situation. (1 mark) 147 Cost Speed over 100 km/h Consumer Mathematics: Written Test Student Booklet (January 2011) 17

24 1 Mark 18. The length of an arc can be found using the formula: s s = π θ r 180 θ r where s is the arc length θ is the angle measure in degrees r is the radius of the circle Find the arc length, in centimetres, of the circle if the angle is 30º and the radius is 12 cm Consumer Mathematics: Written Test Student Booklet (January 2011)

25 2 Marks 19. A solid cone is to be completely covered in paint. Calculate the surface area to be painted if 149 the cone has a diameter of 5 cm and a slant height of 7 cm. Consumer Mathematics: Written Test Student Booklet (January 2011) 19

26 Investments 20. A young couple both have well-paying jobs. Their main financial goal is to retire early. 1 Mark State one type of investment that would meet their financial goal and explain why it is a 150 good choice. 20 Consumer Mathematics: Written Test Student Booklet (January 2011)

27 1 Mark 21. Given the following list of investment options: Investment Options T-bills stocks mutual fund GIC savings account real estate Choose an investment type that is a: A) Short-term investment (0.5 mark): 151 B) Long-term investment (0.5 mark): 152 Consumer Mathematics: Written Test Student Booklet (January 2011) 21

28 2 Marks 22. Wednesday s information from Grinnell Inc. stock is given below: Symbol High Low Close Net Change Volume (000 s) GRI A) State the opening price of Grinnell Inc. on Wednesday. (0.5 mark) 153 B) State the number of Grinnell Inc. shares sold on Wednesday. (0.5 mark) 154 C) On Wednesday, Michael purchased 600 Grinnell Inc. shares at the highest price 155 and sold them at the lowest price. Calculate the amount he lost, not including commission. (1 mark) 22 Consumer Mathematics: Written Test Student Booklet (January 2011)

29 3 Marks 23. Braeden s bank has the following information about his financial situation: Stocks $ RSPs $ Home $ Personal Loan $ Car $6 500 Car Loan $1 800 Mortgage $ A) Determine his net worth. (1.5 marks) 156 B) Calculate his Debt-Equity Ratio (DER). (1.5 marks) 157 Consumer Mathematics: Written Test Student Booklet (January 2011) 23

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