https:www.edu.gov.mb.ca:k12:assess:archives:ap_sb_jan_20

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 17 Probability 18 Design and Measurement 7 Financial Mathematics 20 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 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.

iv 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 c 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      

Applied Mathematics: Student Booklet (January 2020) 1 R ELATIONS AND F UNCTIONS Question 1 Total: 1 mark Select the best answer. 101 Identify which equation the graph represents. A) 3 2 2 – 5 3 y x x x    B) 3 2 –2 – 5 3 y x x x    C) 3 2 2 – 5 – 3 y x x x   D) 3 2 –2 – 5 – 3 y x x x   y x

4 Applied Mathematics: Student Booklet (January 2020) Question 4 Total: 4 marks In 2020, the elk population in Riding Mountain National Park can be predicted by the following exponential equation: ( ) 3500 1.03 t P = where P represents the elk population and t represents the time (in years) starting in January 2020. 105 a) Create a clearly labelled graph of the predicted elk population over the next 50 years. (3 marks)

Applied Mathematics: Student Booklet (January 2020) 7 109 c) State the range and explain its meaning in this situation. (2 marks)

10 Applied Mathematics: Student Booklet (January 2020) Question 8 Total: 2 marks 114 A student enters a maze and needs to make 4 turns. She must turn left or right at each intersection. Determine how many different paths are possible if she makes either 1 or 2 right turns. Use a graphic organizer to show your work.

Applied Mathematics: Student Booklet (January 2020) 13 Question 11 Total: 3 marks Your school requires a group of 4 actors for a play. 118 a) Determine how many ways the group of 4 actors can be chosen from 23 interested students. (1 mark) 119 b) You and your best friend are 2 of the 23 interested students. Determine the probability that you both are chosen. Show your work. (2 marks)

14 Applied Mathematics: Student Booklet (January 2020) Question 12 Total: 4 marks A dance studio has 9 students: 4 students are ballet dancers and 5 students are hip-hop dancers. They are arranging themselves in a row for a year-end photo. 120 a) Determine how many ways the dancers can be arranged for the photo if they must alternate between their type of dance. Show your work. (2 marks) 121 b) Determine how many ways the dancers can be arranged for the photo if the ballet dancers must all stand together. Show your work. (2 marks)

Applied Mathematics: Student Booklet (January 2020) 15 Question 13 Total: 4 marks Kyla wants to buy a cup of tea for $2. She has the following coins in her pocket:  2 identical toonies ($2 coin)  6 identical loonies ($1 coin)  3 identical quarters (25¢ coin) 122 a) Determine the probability of randomly drawing 2 loonies, one after the other, if the first coin is not replaced in her pocket before drawing the second coin. Show your work. (2 marks) 123 b) Once she has paid for her tea using the 2 loonies, Kyla decides to stack all of the remaining coins in a tower. Determine the number of different ways she can stack the coins. Show your work. (2 marks)

16 Applied Mathematics: Student Booklet (January 2020) D ESIGN AND M EASUREMENT Question 14 Total: 1 mark Select the best answer. 124 A frozen dessert is made of ice and syrup. Shauna wants to estimate the amount of ice and syrup in her frozen dessert. Identify the expression that will help her with her estimation. A) 2 3 4 3 3 r h r    B) 2 3 2 3 3 r h r    C) 2 2 rs r    D) 2 4 rs r   

Applied Mathematics: Student Booklet (January 2020) 17 Question 15 Total: 2 marks 125 Sarah has prepared 7000 cm 3 of soup in a pot. She uses a ladle, in the shape of a hemisphere, to serve the soup into bowls. The ladle has a diameter of 10 cm. Determine the number of full ladles of soup that she can serve. Show your work. 7000 cm 3 10 cm ladle pot

18 Applied Mathematics: Student Booklet (January 2020) 9 ft. 9 ft. 12 ft. 24 ft. 12 ft. 18 ft. Question 16 Total: 6 marks Nashida wants to build an outdoor kitchen. She is going to place patio stones in the layout shown to the right. The patio stones  are in the shape of a square with 18-inch sides  cost $3.00 each 126 a) Determine the number of patio stones Nashida needs. Show your work. (2 marks) Nashida must buy a grill, a countertop, and a patio set for the outdoor kitchen. She has the following options: Grill Countertop Patio Set Propane $1400.00 Granite $2700.00 Basic $600.00 Pellet $3000.00 Soapstone $3600.00 Elegant $1000.00 She also plans to buy three of the following items: Side Burner Fridge Cabinet Sink Warming Drawer Single $400.00 Small $800.00 30-inch $700.00 Single $350.00 Small $800.00 Double $650.00 Large $1100.00 42-inch $1250.00 Double $500.00 Large $1300.00

Applied Mathematics: Student Booklet (January 2020) 19 127 b) Nashida can spend a maximum of $11 000.00, taxes included. Calculate the total cost, plus GST and PST, of the patio stones and components of the outdoor kitchen. Show your work. (Note: GST = 5%, PST = 7%) (2 marks) F INANCIAL M ATHEMATICS 128 c) Nashida is financing the outdoor kitchen with a financial institution that gives her an interest rate of 5.00%, compounded monthly. She wants to make $300.00 monthly payments on the loan. Calculate how many payments it will take Nashida to pay off the loan. Show your work. (2 marks)

20 Applied Mathematics: Student Booklet (January 2020) Question 17 Total: 1 mark 129 Kazoo is looking for a house. He has the following options: Option 1: He can buy a house with a monthly mortgage payment of $1150.00 amortized over 25 years. Option 2: He can rent a similar house for $1150.00 per month. State which option Kazoo should choose. Provide one reason for your choice.

Applied Mathematics: Student Booklet (January 2020) 21 Question 18 Total: 6 marks Ham and Sylvie each had $10 000.00 to invest. 130 a) Ham invested $10 000.00 in a mutual fund at an interest rate of 6.00%, compounded monthly. Determine the value of the mutual fund at the end of the first year. Show your work. (2 marks) 131 b) Sylvie invested $10 000.00 in a guaranteed investment certificate (GIC) with interest compounded semi-annually. The value of the GIC was $11 261.62 at the end of the third year. Determine the interest rate for the GIC. Show your work. (2 marks) 132 c) Using the Rule of 72, determine approximately how much longer it will take for Sylvie’s GIC to reach a value of $40 000.00 compared to Ham’s mutual fund. Show your work. (2 marks)

22 Applied Mathematics: Student Booklet (January 2020) Question 19 Total: 6 marks Simba wants to purchase a bed for $2200.00 (taxes included). The store offers him a promotion of 0% interest with no payments for one year. If Simba does not pay the amount in full within one year, interest will be charged from the date of purchase at an interest rate of 19.99%, compounded monthly. 133 a) If Simba does not make any payments during the first year, calculate the amount the store will bill him one year after the date of purchase. Show your work. (2 marks) 134 b) If Simba makes monthly payments over the second year to pay off the amount calculated in (a), determine his monthly payment. Show your work. (2 marks)

Applied Mathematics: Student Booklet (January 2020) 23 135 c) Using your answer in (b), calculate the interest Simba would pay over the two-year period. Show your work. (1.5 marks) 136 d) Give one reason why Simba would buy his bed using the promotion. (0.5 mark)

24 Applied Mathematics: Student Booklet (January 2020) Question 20 Total: 3 marks The Ramilo family moved to The Pas. They bought a house with a purchase price of $229 000.00 and made a down payment of $20 000.00. Their mortgage has an interest rate of 3.15%, compounded semi-annually, and is amortized over 25 years. 137 a) Calculate their monthly mortgage payment. Show your work. (2 marks) 138 b) Calculate the balance owing on the mortgage after 10 years if they have been making regular monthly payments. (1 mark)

Applied Mathematics: Student Booklet (January 2020) 25 Question 21 Total: 2 marks 139 In 2009, the value of a cottage was $325 000.00. In 2019, the same cottage had a value of $425 000.00. Determine the average annual appreciation rate. Show your work.

26 Applied Mathematics: Student Booklet (January 2020) L OGICAL R EASONING Question 22 Total: 1 mark Select the best answer. 140 Ari, Boba, and Cora are shopping at a farmer’s market. The Venn diagram below represents the items found in their shopping baskets. Identify which of the following statements is true. A)     n A n C  B)       n B n A n C    C)     n C n B  D)       n C n B n A    mangoes strawberries apples cherries beans carrots oranges kiwis limes corn squash zucchini cucumbers A B C

Applied Mathematics: Student Booklet (January 2020) 27 Question 23 Total: 1 mark 141 An arithmagon is a puzzle in which the number in each box is the sum of the two numbers in the circles adjacent to that box. Here is an example: Given: Becomes: Therefore, given: Fill in each circle above with an appropriate number. 9 18 13 9 18 13 11 7 2 15 13 26

28 Applied Mathematics: Student Booklet (January 2020) Question 24 Total: 2 marks 142 There are 7 students in Ms. Sanduk’s class. She knows that some of her students have part-time jobs and some of her students participate in extra-curricular activities. However, 2 students neither have a part-time job nor participate in extra-curricular activities.       students with part-time jobs students who participate in extra-curricular activities 1 A B n A B     Fill in the blank diagrams below to show two possibilities in this situation. B A B A

Applied Mathematics: Student Booklet (January 2020) 29 Question 25 Total: 2 marks 143 Complete the truth table, including the missing symbol in the box, based on the following logical statement: A number is even if and only if a number is a multiple of two. p q p q True True True False False True False False

30 Applied Mathematics: Student Booklet (January 2020) Question 26 Total: 2 marks To form a group, 4 students are randomly chosen from 7 students. Jean writes the following conditional statement: “If all 7 students have an equal chance of being chosen, then there are 840 different groups that could be formed.” 144 a) Write the contrapositive of the conditional statement. (1 mark) 145 b) Is the original conditional statement true? Justify your answer. (1 mark) END OF TEST