Applied Math 40S Jun 2018

i G RADE 12 A PPLIED M ATHEMATICS A CHIEVEMENT T EST D ESCRIPTION Total Possible Marks: 61 Time: 3 hours Unit Marks Relations and Functions 15 Financial Mathematics 16 Design and Measurement 7 Probability 17 Logical Reasoning 6 D IRECTIONS Remember to • indicate your input values by writing them in your booklet or printing a copy if using a technology tool • express your answers in decimal and percentage form to the nearest hundredth (two decimal places) when rounding, unless otherwise indicated Example: 15 0.52 or 51.72% 29 = • state any assumptions you make 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, and scales for the axes on graphs — 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 2018) Question 2 Total: 1 mark Select the best answer. 102 A cubic function has two x -intercepts and a positive y -intercept. The graph that has these characteristics is: A) C) B) D) y x y x y x y x

Applied Mathematics: Student Booklet (June 2018) 5 106 b) The standard height for a basketball net is 10 feet. Sarah shoots the ball and it goes directly through the net on its way down. Using the given equation, determine how far, horizontally, the ball was from the net when it was shot. Show your work. (2 marks) horizontal distance

8 Applied Mathematics: Student Booklet (June 2018) F INANCIAL M ATHEMATICS Question 6 Total: 1 mark Select the best answer. 111 The table below shows the value of a luxury vehicle over a two-year period. Year Value 0 $58 500 1 $42 100 2 $30 300 The value of this vehicle depreciates at an annual rate of: A) 72% B) 52% C) 39% D) 28%

Applied Mathematics: Student Booklet (June 2018) 11 Question 9 Total: 2 marks 116 Mr. Smythe makes a one-time donation to a university. The university decides to invest this money and use only the amount earned in simple interest from the investment to finance a scholarship. • The initial amount of the donation was $650 000.00. • The amount earned in simple interest annually is $40 000.00. • The university awards the scholarship to one student each year. At what interest rate must the donation be invested to obtain the $40 000.00 needed to award the scholarship each year? Show your work.

14 Applied Mathematics: Student Booklet (June 2018) D ESIGN AND M EASUREMENT Question 12 Total: 1 mark Select the best answer. 121 Melia baked the following cake and will ice the top and the sides. The surface area that needs to be iced is: A) 1290 cm 2 B) 1680 cm 2 C) 2580 cm 2 D) 5400 cm 2 6 cm 20 cm 45 cm

Applied Mathematics: Student Booklet (June 2018) 17 P ROBABILITY Question 15 Total: 1 mark Select the best answer. 125 There are 16 girls and 11 boys enrolled in a physical education class. A volleyball team of 4 girls and 2 boys will be formed from this class. Which of the following expressions could be used to determine the number of teams possible? A) 27 6 C B) 27 6 P C) 16 4 11 2 C C × D) 16 4 11 2 P P × Question 16 Total: 2 marks 126 Rylan rolls two 4-sided dice with sides numbered 1 through 4. What is the probability that the sum of the rolled numbers is greater than or equal to 6? Show your work.

18 Applied Mathematics: Student Booklet (June 2018) Question 17 Total: 2 marks 127 How many different routes can Martin take to the mall if he can only travel north and east and wants to meet Amy on the way? Show your work. Amy Martin N Mall

Applied Mathematics: Student Booklet (June 2018) 19 Question 18 Total: 2 marks Arif, Simba, and Maritza ran for student council treasurer. Of the 650 students who voted: • 44% voted for Arif • 36% voted for Simba • the remaining students voted for Maritza 128 a) Determine the number of students that voted for Maritza. (1 mark) 129 b) One of the students is selected at random. Determine the odds against this student having voted for Arif. (1 mark)

20 Applied Mathematics: Student Booklet (June 2018) Question 19 Total: 3 marks Jack is late for the bus 15% of the time. When he is late for the bus, the probability that he will see Jill at the bus stop is 8%. When he is not late, the probability that he will see Jill at the bus stop is 82%. 130 a) What is the probability that Jack did not see Jill today? Show your work. (2 marks) 131 b) Jack did not see Jill today. Using your answer in (a), what is the probability that Jack was late for the bus? (1 mark)

Applied Mathematics: Student Booklet (June 2018) 21 Question 20 Total: 2 marks Guy’s baseball team is playing in a tournament. There are six teams entered in the tournament. All teams play each other once and each game is played on the same baseball field. 132 a) Determine the total number of games played in the tournament. (1 mark) 133 b) Determine the probability that Guy’s team plays the first game of the tournament. (1 mark)

22 Applied Mathematics: Student Booklet (June 2018) Question 21 Total: 3 marks Shivani needs to create a new password for her computer. The password must begin with three upper case letters followed by five digits. 134 a) How many passwords are possible if repetition is not allowed? Show your work. (2 marks) 135 b) How many passwords are possible if repetition is not allowed and the password must begin with the letter M? (1 mark)

Applied Mathematics: Student Booklet (June 2018) 23 Question 22 Total: 3 marks Joe is getting dressed in the dark. The only socks in his drawer are 12 white socks and 10 green socks. He randomly picks two socks from the drawer, one after the other. 136 a) What is the probability that both socks are the same colour? Show your work. (2 marks) L OGICAL R EASONING 137 b) Using logical reasoning, what is the minimum number of socks Joe would have to pick to guarantee a pair of the same-coloured socks? (1 mark)

24 Applied Mathematics: Student Booklet (June 2018) Question 23 Total: 1 mark Select the best answer. 138 Given the following sets: { } { } { } 3, 4, 5, 6, 7, 8, 9, 10 8, 9, 10, 11, 12 8, 9, 10 A B C = = = Which of the following statements represents set C ? A) A B ′ ′  B) B A ⊂ C) A B  D) A B 

Applied Mathematics: Student Booklet (June 2018) 25 Question 24 Total: 2 marks 139 Given hypothesis, p , and conclusion, q , complete the truth table below. p q ~ p ~ p ↔ q True True True False False True False False

26 Applied Mathematics: Student Booklet (June 2018) Question 25 Total: 2 marks 140 Mrs. Dela Cruz teaches German and Spanish. She has 31 students of which 21 study German and 17 study Spanish. How many of Mrs. Dela Cruz’s students study German only? Show your work. END OF TEST

Applied Mathematics: Student Booklet (June 2018) 27 NO MARKS WILL BE AWARDED FOR WORK DONE ON THIS PAGE.

28 Applied Mathematics: Student Booklet (June 2018) NO MARKS WILL BE AWARDED FOR WORK DONE ON THIS PAGE.

Applied Mathematics: Student Booklet (June 2018) 29 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 = + =

30 Applied Mathematics: Student Booklet (June 2018)