Applied Math 40S Jun 2015

Applied Mathematics: Student Booklet (June 2015) 1 G RADE 12 A PPLIED M ATHEMATICS A CHIEVEMENT T EST D ESCRIPTION Total Possible Marks: 60 Time: 3 hours Unit Description Marks A Relations and Functions 16 B Probability 15 C Financial Mathematics 17 D Design and Measurement 7 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 (June 2015)

Applied Mathematics: Student Booklet (June 2015) 7 Question 3 Total: 2 marks 103 Sam is studying the characteristics of quadratic functions. She states the following: Statement 1: A quadratic function always has a degree of 2. Statement 2: The graph of a quadratic function always extends from quadrant II to quadrant I. Statement 3: The graph of a quadratic function always has one turning point. Statement 4: A quadratic function always has two x -intercepts. Two of these statements are incorrect. Identify which statements are incorrect and provide a counterexample for each.

10 Applied Mathematics: Student Booklet (June 2015) Question 6 Total: 6 marks The top of a flagpole moves back and forth on a windy day. It sways 15 cm to the left (–15 cm) and 15 cm to the right (+15 cm) from its resting position (0 cm). It moves back and forth every two (2) seconds. At t = 0, the pole was at its resting position before swaying to the left. 108 a) Determine a sinusoidal equation that models this situation. Show your work. (2 marks)

Applied Mathematics: Student Booklet (June 2015) 13 Question 9 Total: 1 mark 113 The probability of rain is 60%. What are the odds against rain? Question 10 Total: 1 mark 114 A pizza place offers the following choices: • 3 types of crust • 2 types of sauce • 5 types of cheese • 6 meat toppings • 8 vegetable toppings Charles would like to create a pizza by choosing one item from each category. Determine how many different pizzas can be made.

16 Applied Mathematics: Student Booklet (June 2015) Question 13 Total: 3 marks On January 21, the probability of the overnight low temperature being below –27  C is 11%. If the temperature is below –27  C, the probability of Cara’s car starting is 55%. If it is not below –27  C, the probability of Cara’s car starting is 91%. 117 a) Create a graphic organizer to represent all possibilities for this situation. (1 mark) 118 b) What is the probability that Cara’s car will not start on January 21? Show your work. (2 marks)

Applied Mathematics: Student Booklet (June 2015) 19 F INANCIAL M ATHEMATICS Question 16 Total: 1 mark Select the best answer. 123 The value of a house appreciates 4.10% per year. If the house was purchased for $180 000 in June 2010, what is the approximate value of the house in June 2015? A. $184 000 B. $220 000 C. $937 000 D. $1 003 000

20 Applied Mathematics: Student Booklet (June 2015) Question 17 Total: 4 marks Deema is saving for a home renovation. She deposits $50.00 every month into a new high-interest savings account that earns 4.60%, compounded monthly. 124 a) What will be the value in Deema’s account after 4 years? Show your work. (2 marks) 125 b) How much interest will she have earned after 4 years? Show your work. (2 marks)

Applied Mathematics: Student Booklet (June 2015) 21 Question 18 Total: 2 marks 126 Lisette is 50 years old and would like to retire at age 55. Her assets include $60 000.00 in a guaranteed investment certificate (GIC), $78 000.00 in a chequing account, and $192 000.00 in stocks. Make two recommendations to help Lisette strengthen her investment portfolio. Justify your recommendations.

22 Applied Mathematics: Student Booklet (June 2015) Question 19 Total: 2 marks 127 Serge invests $12 000.00 on his 30th birthday. If his investment earns 6.00% interest, compounded annually, apply the Rule of 72 to estimate how much money he will have when he retires on his 66th birthday.

Applied Mathematics: Student Booklet (June 2015) 23 Question 20 Total: 3 marks Harsimran invested $20 000.00 in a simple interest savings bond. After 12 years, the future value of the bond was $26 768.00. 128 a) Determine the annual interest rate. (2 marks) 129 b) Determine the rate of return. (1 mark)

24 Applied Mathematics: Student Booklet (June 2015) Question 21 Total: 5 marks Maurice needs a truck for his new job that will last four years. He has the following two options: Option 1: He can purchase the truck for $45 194.35 (taxes included) with no down payment, at an interest rate of 4.00%, compounded monthly, for four years. Option 2: He can lease the same truck for four years with a down payment of $5000.00 and monthly payments of $850.00 (taxes included). He would be allowed 20 000 km per year and there is a $0.18 per km (taxes included) charge above this limit. 130 a) What would be Maurice’s total cost in Option 1 if he makes monthly payments? Show your work. (2 marks) 131 b) If Maurice drives 25 000 km annually, what would be his total cost in Option 2? Show your work. (2 marks) 132 c) Which option would you suggest to Maurice and why? (1 mark)

Applied Mathematics: Student Booklet (June 2015) 25 D ESIGN AND M EASUREMENT Question 22 Total: 1 mark Select the best answer. 133 How many cubic yards are in 54 cubic feet? A. 2 B. 3 C. 6 D. 18 Question 23 Total: 1 mark 134 One can of paint can cover an area of 200 ft 2 . How many cans need to be purchased to paint a 60 ft. by 8 ft. wall?

26 Applied Mathematics: Student Booklet (June 2015) Question 24 Total: 5 marks James is landscaping his 50 ft. by 40 ft. yard. He will construct a concrete walkway with a uniform width of x around the centre of the yard which is to be covered in sod, as illustrated below. (Diagram is not drawn to scale.) Consider the following: • The walkway must be at least 3.5 feet wide. • The concrete must be poured 6 inches deep. • The concrete costs $3.00 per cubic foot, plus GST and PST. • The sod costs $0.40 per square foot, plus GST and PST. • The budget for this project is $2150.00. 135 a) Design a walkway that fits within the budget. Indicate the width of the walkway and the dimensions of the sod below. (1 mark) Width of the walkway ( x ): _______ ft. Dimensions of the sod: _______ ft. by _______ ft. Sod x x x x Concrete

Applied Mathematics: Student Booklet (June 2015) 27 136 b) Calculate the total cost of your design. (Note: GST 5%, PST 8%) = = (4 marks)

28 Applied Mathematics: Student Booklet (June 2015) L OGICAL R EASONING Question 25 Total: 1 mark Select the best answer. 137 What values of m and n correctly complete the following truth table? p q p q → True True True True False m False True n False False True A. True True m n = = B. True False m n = = C. False True m n = = D. False False m n = =

Applied Mathematics: Student Booklet (June 2015) 29 Question 26 Total: 1 mark 138 Consider this conditional statement: “If x has a positive value, then 2 . x x ≥ ” Provide a counterexample to the statement above.

30 Applied Mathematics: Student Booklet (June 2015) Question 27 Total: 3 marks A universal set is defined as: { } 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 S = Two subsets are given below: { } { } odd whole numbers of prime numbers of O S P S = = 139 a) Draw a Venn diagram to represent S , O , and P . (1 mark) 140 b) Determine . O P  (1 mark) 141 c) Determine ( ) . n O P ′  (1 mark) END OF TEST

Applied Mathematics: Student Booklet (June 2015) 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 (June 2015)