Applied Math 40S Jan 2016

Applied Mathematics: Student Booklet (January 2016) 1 G RADE 12 A PPLIED M ATHEMATICS A CHIEVEMENT T EST D ESCRIPTION Total Possible Marks: 65 Time: 3 hours Unit Description Marks A Relations and Functions 16 B Probability 15 C Financial Mathematics 14 D Design and Measurement 9 E Logical Reasoning 11 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 2016)

Applied Mathematics: Student Booklet (January 2016) 7 Question 3 Total: 2 marks 103 In a diving competition, Tracy’s first dive can be modelled by the equation: 2 – 4.90 2.72 10 h t t = + + where t represents the dive time (in seconds) and h represents the diver’s height (in metres) above the water. How much time does it take for Tracy to reach the water? Show your work.

10 Applied Mathematics: Student Booklet (January 2016) Question 6 Total: 6 marks Bailey launched his remote control plane. He recorded the height of the plane at different times during the flight. Time (s) Height (ft.) 0 0 1 9 2 7 3 3 4 7 5 26 108 a) Determine the cubic regression equation that models this data. (1 mark) 109 b) Create a clearly labelled graph of the equation in (a). (3 marks)

Applied Mathematics: Student Booklet (January 2016) 13 Question 9 Total: 3 marks Lena runs every day. If it is sunny, the probability she will run outside is 75%. If it is not sunny, the probability that she will run outside is 20%. A 45% probability of sunshine has been announced for tomorrow. 114 a) Use a graphic organizer to show all the possible outcomes for this situation. (1 mark) 115 b) Determine the probability that Lena runs outside tomorrow. Show your work. (2 marks)

16 Applied Mathematics: Student Booklet (January 2016) Question 12 Total: 4 marks There are 18 girls and 12 boys trying out for a debate team. 120 a) How many different teams of 4 members can be formed if there are no restrictions? (1 mark) 121 b) How many different teams of 4 members can be formed if exactly two members must be girls? (1 mark) 122 c) How many different teams of 4 members can be formed if at least two members must be girls? Show your work. (2 marks)

Applied Mathematics: Student Booklet (January 2016) 19 Question 16 Total: 2 marks 127 Pedro has a tax-free savings account (TFSA) with a balance of $5000.00. Interest is earned at a rate of 4.00%, compounded monthly. If Pedro contributes $400.00 to the TFSA at the end of every month, how long will it take him to save $20 000.00? Show your work.

20 Applied Mathematics: Student Booklet (January 2016) Question 17 Total: 3 marks Kira purchases a sofa for $1015.87 (taxes included). The department store offers her a promotion of 0% interest with no payments for one year. If Kira does not pay the amount in full within one year, interest will be charged from the date of purchase at an annual rate of 28.80%, compounded monthly. 128 a) If Kira does not make any payments, what will the department store bill her one year after the date of purchase? Show your work. (2 marks) 129 b) State a different compounding period such that the overall cost of the sofa is lower than if the annual interest rate were compounded monthly. (1 mark)

Applied Mathematics: Student Booklet (January 2016) 21 Question 18 Total: 5 marks Bill and Celine purchase a new home. They obtain a $375 000.00 mortgage amortized over 25 years with their credit union. The initial 5-year term of the mortgage requires monthly payments. Interest is calculated at a rate of 3.25%, compounded semi-annually. 130 a) Calculate Bill and Celine’s mortgage payment. Show your work. (2 marks) 131 b) How much will Bill and Celine owe at the end of their 5-year term? (1 mark) 132 c) Bill and Celine make an additional $10 000.00 payment on the principal at the end of the 5-year term. How much sooner will they pay off their mortgage if they keep the same payments and interest rate over the life of the mortgage? Show your work. (2 marks)

22 Applied Mathematics: Student Booklet (January 2016) D ESIGN AND M EASUREMENT Question 19 Total: 1 mark Select the best answer. 133 The volume of a freezer is 0.46 m 3 . This volume can also be expressed as: A. 46 cm 3 B. 460 cm 3 C. 4600 cm 3 D. 460 000 cm 3

Applied Mathematics: Student Booklet (January 2016) 23 Question 20 Total: 2 marks 134 Sophie wants to install carpet in her bedroom. The 12 ft. by 9 ft. carpet she wants to install costs $32.50/yd 2 , plus GST and PST. Calculate the total cost of the carpet. Show your work. (Note: GST 5%, PST 8%) = =

24 Applied Mathematics: Student Booklet (January 2016) Question 21 Total: 6 marks The Menard family has a grain farm. They own 5 bins for grain storage. Each bin • is composed of a cone and a cylinder • is 30 feet tall (from the top of the cone to the bottom of the cylinder) • has a diameter of 20 feet • has a cylinder 22 feet tall (Diagram is not drawn to scale.) 135 a) Calculate the volume of one grain bin. Show your work. (2 marks) 22 ft. 30 ft. 20 ft.

Applied Mathematics: Student Booklet (January 2016) 25 136 b) Mr. Menard decides to paint the exterior (sides and top) of the bins. • Each bin needs 2 coats of paint. • One can of paint covers 400 ft 2 . • Each can of paint costs $67.99, plus GST and PST. Calculate the total cost of the paint for the 5 bins. Show your work. (Note: GST = 5%, PST = 8%) (4 marks)

26 Applied Mathematics: Student Booklet (January 2016) L OGICAL R EASONING Question 22 Total: 1 mark Use the information below to answer the following question and select the best answer. 137 Students were surveyed about the technology they own. A = owns a notebook computer B = owns a tablet computer Which of the following statements is true? A. ( ) 21 n A = B. ( ) 36 n B = ′ C. ( ) 9 n A B =  D. ( ) 76 n A B =  10 21 9 36 A B U

Applied Mathematics: Student Booklet (January 2016) 27 Question 23 Total: 2 marks 138 A class of 28 students was surveyed to discover the type of music to which they listen. • 12 students said they listen to country • 18 students said they listen to pop • 2 students said they listen to neither country nor pop Determine the number of students who listen only to pop. Show your work.

28 Applied Mathematics: Student Booklet (January 2016) Question 24 Total: 2 marks Consider the original statement: “If the end behaviour of a function extends from quadrant II to quadrant I, then the function is quadratic.” 139 a) Is the original statement true? If not, provide a counterexample. (1 mark) 140 b) Write the contrapositive of the original statement. (1 mark)

Applied Mathematics: Student Booklet (January 2016) 29 Question 25 Total: 3 marks Given the following sets: { } { } { } 1, 3, 5, 7, 9, 13, 17, 21 1, 9, 13, 21 1, 7, 9, 17, 21 U A B = = = 141 a) Illustrate these sets using a Venn diagram. (1 mark) 142 b) Determine . A B ′  (1 mark) 143 c) Create a set C with 3 elements, where . C B ⊂ (1 mark)

30 Applied Mathematics: Student Booklet (January 2016) Question 26 Total: 3 marks 144 a) Use the numbers 1, 2, 3, 4, 5, 6 only once to complete the chart. (2 marks) 7 + + 9 = 22 + + + + + = 7 + + + + 8 + = 16 = = = 13 18 14 145 b) What were the first two numbers you obtained? Explain the strategy you used to obtain these numbers. (1 mark) END OF TEST and

Applied Mathematics: Student Booklet (January 2016) 31 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 = + =

32 Applied Mathematics: Student Booklet (January 2016)