Applied Math 40S Jan 2017

Applied Mathematics: Student Booklet (January 2017) 1 G RADE 12 A PPLIED M ATHEMATICS A CHIEVEMENT T EST D ESCRIPTION Total Possible Marks: 61 Time: 3 hours Unit Description Marks A Relations and Functions 15 B Probability 15 C Financial Mathematics 17 D Design and Measurement 9 E Logical Reasoning 5 R ESOURCES You may use the following resources: • Formula Sheet (tear-out page at the back of this booklet) • one 8½ ″ × 11 ″ study sheet • ruler • graphing calculator, computer software, and/or app • Internet access for tools such as applets or mortgage payment calculators Use of the Internet to communicate or access other content, including but not limited to course notes, definitions, or conceptual information is not permitted during the test. Electronic communication between students through phones, email, or file sharing during the test is strictly prohibited.

4 Applied Mathematics: Student Booklet (January 2017)

Applied Mathematics: Student Booklet (January 2017) 7 Question 3 Total: 4 marks Stephanie experiments with the frequency of waves in a ripple tank during her Physics class. At the beginning of the experiment, she places a ruler into the tank and measures the median height of the water to be 10 cm. The water then rises to a maximum height of 13 cm at 1 second. 103 a) Determine the sinusoidal regression equation that models the relationship between the height of the water and time. Show your work. (2 marks) 104 b) Determine the height of the water at 15 seconds. (1 mark) 105 c) Stephanie changes the settings of the motor to generate waves more quickly. Write an equation that can model this change if all other conditions remain the same. (1 mark) motor (generates waves)

10 Applied Mathematics: Student Booklet (January 2017) Question 5 Total: 6 marks Pam drives her car over a nail. As a result, one of the tires on her car starts to lose air pressure. Her tire pressure sensor provides the following data: t (h) 0 1 2 3 6 10 P (psi) 40 32 26 21 10 5 where P represents the air pressure (in psi) and t represents the time (in hours). 108 a) Create a clearly labelled graph by plotting the given data. Draw a curve of best fit. (3 marks) 109 b) Determine the regression equation that best models the data in this situation. (1 mark)

Applied Mathematics: Student Booklet (January 2017) 13 P ROBABILITY Question 6 Total: 1 mark Select the best answer. 111 Which of the following expressions represents the number of ways to create a 4-digit passcode for your phone using the digits 0 to 9, if repetition is allowed? A. 10 9 8 7 × × × B. 4 10 C. 10 4 C D. 10 4 P Question 7 Total: 1 mark Select the best answer. 112 Scott can choose from 8 toppings to make a pizza. How many pizzas can be made with 3 different toppings? A. 6 B. 56 C. 336 D. 6720

16 Applied Mathematics: Student Booklet (January 2017) Question 9 Total: 2 marks 116 If 4 coins are tossed at the same time, what is the probability that they will land as either all heads or as all tails? Show your work.

Applied Mathematics: Student Booklet (January 2017) 19 Question 12 Total: 3 marks A coach randomly selects 5 players from a team of 18 to line up for a shot on goal. 120 a) How many different 5-player arrangements are possible? (1 mark) 121 b) If Dustin and Andrew are 2 of the 18 players, what is the probability that Dustin will shoot first and Andrew will shoot second? Show your work. Express your answer as a fraction or round to the nearest thousandth (three decimal places). (2 marks)

20 Applied Mathematics: Student Booklet (January 2017) F INANCIAL M ATHEMATICS Question 13 Total: 1 mark Select the best answer. 122 Which of the following graphs shows the total amount of interest paid over the course of a 25-year mortgage? A. C. B. D. Years Interest (in thousands) Years Interest (in thousands) Years Interest (in thousands) Years Interest (in thousands)

Applied Mathematics: Student Booklet (January 2017) 21 Question 14 Total: 1 mark Select the best answer. 123 According to the Rule of 72, a reasonable estimate for the time it would take to double an investment of $24 000.00 at an interest rate of 6.00%, compounded monthly is A. 3 years B. 4 years C. 12 years D. 18 years

22 Applied Mathematics: Student Booklet (January 2017) Question 15 Total: 4 marks 124 Imani is going to buy a car. She can afford monthly payments of $600.00. The dealer offers two financing options: Option 1: financing over 60 months at a rate of 0.90% compounded monthly Option 2: financing over 60 months at a rate of 2.90% compounded monthly with an instant rebate of $3000.00 at the time of purchase Which option allows Imani to purchase a more expensive car? Show your work.

Applied Mathematics: Student Booklet (January 2017) 23 Question 16 Total: 2 marks 125 Your friend has $10 000.00 and is considering an investment in stocks, a guaranteed investment certificate (GIC), or rare collectibles. Choose one of the three investments mentioned above and indicate one advantage and one disadvantage for your choice.

24 Applied Mathematics: Student Booklet (January 2017) Question 17 Total: 4 marks When she turned 25, Alexa began investing $400.00 monthly into a mutual fund account producing average returns of 6.00%, compounded monthly. Alexa will stop contributing when she retires at age 55. 126 a) How much money will her investment be worth at retirement? Show your work. (2 marks) 127 b) Alexa will withdraw $2500.00 per month from her account after retiring. If the average return rate stays the same, how old will she be when the account balance is zero? Show your work. (2 marks)

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26 Applied Mathematics: Student Booklet (January 2017) Question 18 Total: 5 marks Shirley and Cameron have just moved to Brandon and are considering the two following housing options: Option 1: House for purchase • purchase price of $249 000.00 • down payment of $50 000.00 required • 25-year mortgage at an interest rate of 3.00%, compounded semi-annually Option 2: Apartment for rent • monthly payments of $1300.00 • monthly parking fees of $60.00 128 a) What would be Shirley and Cameron’s monthly mortgage payment with Option 1? Show your work. (2 marks)

Applied Mathematics: Student Booklet (January 2017) 27 129 b) What will be the total amount paid for each option at the end of 10 years? (2 marks) 130 c) State one advantage of renting the apartment. (1 mark)

28 Applied Mathematics: Student Booklet (January 2017) D ESIGN AND M EASUREMENT Question 19 Total: 2 marks 131 Eleni is placing cups onto a 7 in. by 10 in. tray. Each cup has a circumference of 10 in. Determine the maximum number of cups she can place on the tray. Show your work.

Applied Mathematics: Student Booklet (January 2017) 29 Question 20 Total: 4 marks 132 You want to build a garden. • The garden is square. (Diagram is not drawn to scale.) • The side length is between 8 ft. and 10 ft. • The garden is enclosed using boards stacked two boards high. • There are 12 metal supports used to connect the structure. • The garden is filled with soil to a depth of 15 in. Below is the price list for materials: Item Cost (plus GST and PST) metal supports $2.00 each boards $2.50/linear foot soil 3 $12.00/yd Determine the total cost of building your garden. All items must be purchased in whole units. Show your work. (Note: GST 5%, PST 8%) = = 15 in. side length: _______ ft.

30 Applied Mathematics: Student Booklet (January 2017) Question 21 Total: 3 marks 133 a) What is the volume of a rubber hockey puck? (Diagram is not drawn to scale.) (1 mark) 134 b) How many pucks can be produced for $1000.00 if it costs $0.24 to print a logo on each puck and rubber costs $0.003 6 per cm 3 ? (2 marks) 7.62 cm 2.54 cm

Applied Mathematics: Student Booklet (January 2017) 31 L OGICAL R EASONING Question 22 Total: 1 mark Select the best answer. 135 Given the following pattern: Which of the following continues this pattern? A. B. C. D.

32 Applied Mathematics: Student Booklet (January 2017) Question 23 Total: 2 marks 136 You have 3 pails with volumes of 2 L, 3 L, and 5 L. The 5 L pail is filled with water. The other pails are empty. Using only these pails, explain how to measure out exactly 4 L of water into the 5 L pail. 3 L 2 L 5 L

Applied Mathematics: Student Booklet (January 2017) 33 Question 24 Total: 2 marks Consider the original statement: “If students are in Grade 12, then they will graduate this June.” 137 a) Write the converse of the statement. (1 mark) 138 b) Determine if a biconditional statement is possible. If yes, write the biconditional statement. If not, provide a counterexample. (1 mark) END OF TEST

34 Applied Mathematics: Student Booklet (January 2017) NO MARKS WILL BE AWARDED FOR WORK DONE ON THIS PAGE.

Applied Mathematics: Student Booklet (January 2017) 35 Formula Sheet: Applied Mathematics Relations and Functions y ax b = + 2 y ax bx c = + + 3 2 y ax bx cx d = + + + x y ab = ( ) ln y a b x = + log b y a x = ( ) sin y a bx c d = + + ( ) cos y a bx c d = + + Financial Mathematics 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       = × Probability ( ) ( ) ( ) ( ) or – and P A B P A P B P A B = + ( ) ( ) ( ) and P A B P A P B = × ( ) ( ) ( ) and P A B P A P B A = × ( ) ! – ! n r n P n r = ( ) ! ! – ! n r n C r n r = Design and Measurement Prism: Surface area 2 Volume Ph B Bh = + = Pyramid: Surface area ( slant height) 2 Volume 3 Ps B s Bh = + = = 2 3 Sphere: Surface area 4 4 Volume 3 r r π π = = 2 2 Cylinder: Surface area 2 2 Volume rh r r h π π π = + = 2 2 Cone: Surface area Volume 3 r rs r h π π π = + =

36 Applied Mathematics: Student Booklet (January 2017)