Applied Math 40S Jun 2019

i G RADE 12 A PPLIED M ATHEMATICS A CHIEVEMENT T EST D ESCRIPTION Time Required to Complete the Test: 3 hours Total Possible Marks: 70 Additional Time Allowed: 30 minutes Unit Marks Relations and Functions 16 Probability 18 Financial Mathematics 19 Design and Measurement 9 Logical Reasoning 8 D IRECTIONS Remember to  indicate your input values by writing them in your booklet or printing a copy if using a technology tool  state any assumptions you make  express your answers in decimal and percentage form to at least the nearest hundredth (two decimal places) when rounding, except for monetary values or when otherwise indicated Example: 15 0.52 or 51.72% 29  Note: Rounding too soon in your solution may result in an inaccurate final answer for which full marks will not be awarded. A “graphic organizer” is a visual representation of information. Examples include a tree diagram, a chart, a list, a Venn diagram, a truth table, Pascal’s triangle, etc. A clearly communicated answer — is easily identified in the response space — includes the parameters in the equation, and “ y =”, “sin”, “ln”, or “ x ”, as applicable — includes the units of measure, where applicable — includes labels, units, scales for the axes on graphs, and key characteristics of functions (e.g., maximum, minimum, intercepts, and appropriate shape) — is expressed as an exact value or is appropriately rounded Marks may be deducted for errors relating to any of the above. Electronic communication between students through phones, email, or file sharing during the test is strictly prohibited.

2 Applied Mathematics: Student Booklet (June 2019) Question 2 Total: 1 mark 102 In an experiment, a water balloon is dropped from the roof of a school. The height of the water balloon from the ground is a function of time. The height is expressed in metres and the time is expressed in seconds. The domain of this function is   0, 1.43 . Give one reason that explains why the domain is restricted.

Applied Mathematics: Student Booklet (June 2019) 5 Question 5 Total: 4 marks A boat is propelled by a paddle wheel with a diameter of 14 feet. Each paddle takes 90 seconds to complete one revolution. The logo on one paddle reaches a maximum height of 11 feet above the water after the boat is in motion for 10 seconds. 107 a) Determine a possible sinusoidal equation that models the height of the logo over time. Show your work. (2 marks) 108 b) Determine how long the logo is underwater during one revolution. Show your work. (2 marks) Time (s) Height (ft.) Diagram is not drawn to scale. logo 14 ft. waterline

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Applied Mathematics: Student Booklet (June 2019) 11 Question 9 Total: 2 marks 115 There are 21 students in an applied math class. On a test, 10 students used an app, 14 students used a graphing calculator, and 4 students used both. What is the probability that a randomly selected student used only an app on the test? Show your work.

14 Applied Mathematics: Student Booklet (June 2019) Question 12 Total: 3 marks Construction work has slowed travel near Dauphin, Manitoba. Harry must drive through the construction zone to get to work. The probability that he will be delayed because of the construction is 45%. If he is delayed, the probability he will get to work on time is 70%. If he is not delayed, the probability he will get to work on time is 85%. 119 a) Use a graphic organizer to show all possible outcomes for this situation. (1 mark) 120 b) Determine the probability that Harry will get to work on time. Show your work. (2 marks)

Applied Mathematics: Student Booklet (June 2019) 17 124 c) What is the total amount Diane will pay to buy the truck? (1 mark)

18 Applied Mathematics: Student Booklet (June 2019) Question 15 Total: 1 mark Select the best answer. 125 Renasha deposits $1200.00 into a savings account that earns simple interest at a rate of 1.72% annually. What is the total value of Renasha’s account at the end of one year? A) $20.64 B) $1220.64 C) $1447.68 D) $3264.00

Applied Mathematics: Student Booklet (June 2019) 19 Question 16 Total: 2 marks 126 Mr. Chen is moving to Manitoba and is looking for a place to live. State two reasons why Mr. Chen would prefer renting a house instead of buying a similar house. Reason 1: Reason 2:

20 Applied Mathematics: Student Booklet (June 2019) Question 17 Total: 3 marks Nadia hopes to save enough money over a 6-year period to go on a trip estimated to cost $11 600.00. To start saving, she deposits $1250.00 into an account that earns an interest rate of 4.21%, compounded monthly. 127 a) If she makes monthly payments of $110.00 into this account, how much money will she have at the end of the 6-year period? Show your work. (2 marks) 128 b) What is the minimum number of additional monthly payments Nadia needs to make in order to save enough money for the trip? (1 mark)

Applied Mathematics: Student Booklet (June 2019) 21 Question 18 Total: 5 marks Marshall and Kim are renting a house that they hope to purchase. They pay $1800.00 in annual heating costs and know that the annual property taxes are $2500.00. Their combined gross income is $5200.00 per month. 129 a) Based on the gross debt service ratio (GDSR), what is the maximum monthly mortgage payment they can afford? Show your work. (2 marks) 130 b) If they have saved $30 000.00 for a down payment, what is the maximum house price they can afford based on a 25-year amortization period at an interest rate of 4.64%, compounded semi-annually? Show your work. (3 marks)

22 Applied Mathematics: Student Booklet (June 2019) Question 19 Total: 5 marks Amor and Angélique each want to retire at age 65. They start investing in tax-free savings accounts (TFSA) at different ages in their lives.  At age 28, Amor starts investing $240.00 per month into a TFSA that earns an interest rate of 2.95%, compounded monthly.  At age 42, Angélique makes an initial deposit of $5000.00 and starts investing $350.00 per month into a TFSA that earns an interest rate of 3.50%, compounded monthly. 131 a) What is the value of each of their TFSAs at age 65? Show your work. (4 marks) 132 b) Explain why a small long-term investment may be worth more than a large short-term investment. (1 mark)

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24 Applied Mathematics: Student Booklet (June 2019) D ESIGN AND M EASUREMENT Question 20 Total: 1 mark Select the best answer. 133 A wheelbarrow is able to transport 6 cubic feet of soil per load. What is the minimum number of loads required to fill the following garden with soil? A) 3 B) 5 C) 14 D) 504 14 ft. 1.5 ft. 4 ft.

Applied Mathematics: Student Booklet (June 2019) 25 Question 21 Total: 3 marks You are in charge of purchasing enough sports drink for the participants of a 5-kilometre race. There are 300 participants and you assume they will each drink the equivalent of 2 cups of sports drink. The cups are cone shaped with the following dimensions: 134 a) What volume of sports drink must you purchase? Show your work. (2 marks) 135 b) Each container of sports drink costs $5.00 and contains 8 L (1 L = 1000 cm 3 ) of drink. How much will you spend on sports drink, before taxes? (1 mark) 8 cm 7 cm

26 Applied Mathematics: Student Booklet (June 2019) Question 22 Total: 5 marks You are to design a bedroom. The bedroom design must satisfy the following conditions:  The bedroom must be rectangular.  The bedroom must include one dresser, one desk, and one bed chosen from the furniture options below. Furniture Options Dresser Desk Bed Tall Wide Small Large Queen King Dimensions (ft.) (width × length) 1.5  4 1.5  6 2  4 2  6 4  6 5  6 Area (ft 2 ) 6 9 8 12 24 30 Cost ($) 559.00 729.00 379.00 449.00 1669.00 1779.00 136 a) Draw or describe the bedroom design, including dimensions, where  one of the dimensions of the bedroom floor must be at least 10 feet  the area of the bedroom must be between double and triple the area occupied by the total of all the furniture (2 marks) Dimensions of bedroom: _______ ft.  _______ ft.

Applied Mathematics: Student Booklet (June 2019) 27 137 b) You must also install flooring in the bedroom. Flooring must be purchased in whole units. You can buy carpet or hardwood.  You must include an additional 10% to the area for installation and waste.  The carpet costs $14.40 per yd 2 .  The hardwood costs $19.80 per yd 2 . Calculate the cost of the flooring before taxes. (2 marks) 138 c) Calculate the total cost of the furniture and the flooring, plus GST and PST. (Note: GST = 5%, PST = 8%) (1 mark)

28 Applied Mathematics: Student Booklet (June 2019) L OGICAL R EASONING Question 23 Total: 2 marks 139 a) Create a true conditional statement using two of the statements given below.  the number is positive  the number is negative  the number is less than zero  the number is prime  the number is odd  the number is even  the number is 5 (1 mark) 140 b) Write the inverse of the statement created in (a). (1 mark)

Applied Mathematics: Student Booklet (June 2019) 29 Question 24 Total: 2 marks 141 The universal set B represents the breakfast items in Pierre’s backpack:   apple, yogurt, granola bar B  Pierre must choose at least one item to eat for breakfast. Write all of Pierre’s breakfast options as subsets.

30 Applied Mathematics: Student Booklet (June 2019) Question 25 Total: 1 mark 142 Students attend a field trip to the Canadian Museum of Human Rights. They have the option of visiting Gallery A, Gallery B, Gallery C, or any combination of these. Their visits can be represented by the Venn diagram below. Shade the Venn diagram to illustrate the students who visited either Gallery B or Gallery C   . B C  U A C B

Applied Mathematics: Student Booklet (June 2019) 31 Question 26 Total: 3 marks A magic square is an array that has the same sum in each row, column, and diagonal. This sum is called the magic number. 7 20 11 12 14 8 23 15 20 6 13 11 9 16 3 22 143 a) Determine the number in the array above that prevents it from being a magic square. (1 mark) 144 b) What number should replace the number found in (a) to make the array a magic square? (1 mark) 145 c) What is the magic number of the resulting magic square? (1 mark) END OF TEST

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Applied Mathematics: Student Booklet (June 2019) 33 Formula Sheet: Applied Mathematics R ELATIONS AND F UNCTIONS F INANCIAL M ATHEMATICS y ax b   2 y ax bx c    3 2 y ax bx cx d     x y ab    ln y a b x     sin y a bx c d    72 t i  I Prt  1 nt r A P n         Net worth Total assets – Total liabilities  Debt-to-equity ratio (%)   Total liabilities – Mortgage 100 Net worth   Gross debt service ratio (%) Monthly Monthly Monthly mortgage property heating payment taxes costs 100 Gross monthly income             Rate of return (%) Current value Previous value – of portfolio of portfolio 100 Previous value of portfolio         P ROBABILITY         – P A B P A P B P A B           P A B P A P B          P A B P A P B A      ! – ! n r n P n r    ! ! – ! n r n C r n r  D ESIGN AND M EASUREMENT Prism: Surface area 2 Volume Ph B Bh    1 Pyramid: Surface area 2 1 Volume 3 B Ps Bh    2 3 Cube: Surface area 6 Volume l l   Rectangular prism: Surface area 2 2 2 Volume lw lh wh lwh       Triangular prism: Surface area 1 Volume 2 bh l a b h bhl      2 2 Square-based pyramid: Surface area 2 1 Volume 3 b bs b h    2 3 Sphere: Surface area 4 4 Volume 3 r r     2 2 Cylinder: Surface area 2 2 Volume r rh r h       2 2 Cone: Surface area 1 Volume 3 r rs r h      

34 Applied Mathematics: Student Booklet (June 2019)