Math 506 SN. Competency Two Uses Mathematical Reasoning. Mathematics Science Option. Secondary 5. Student Booklet

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1 Mathematics Science Option Secondary 5 Math 506 SN Competency Two Uses Mathematical Reasoning TEACHER USE ONLY Part A /24 Part B /16 Part C /60 Total /100 Student Booklet Parts A, B and C June 2014 Name: Group: Date:

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3 Instructions 1. Write all the required information in this Student Booklet. Answers written in the Question Booklet will not be evaluated; only the Student Booklet will be evaluated. 2. In Part C you must show all your work to justify your answers. The steps in your procedure must be organized and clearly presented. Always write down your procedure and reasoning along with aspects of the situation that you think are relevant. Do this even if you are unsure of how to complete your solution. 3. You have 3 hours to complete this evaluation situation. 4. Permitted materials: Note: Graph paper Geometry set (ruler, compass, set square, protractor) Calculator (with or without graphic display) Before the exam starts, data and programs stored in the calculator s memory must be deleted. Using a calculator containing stored data or programs will be considered as cheating. Students may not share their calculators. Communication between calculators is prohibited. Handwritten memory aid that you have prepared prior to the evaluation situation. The memory aid consists of one letter-sized sheet of paper (8½ x 11 ). Both sides of the sheet may be used. Any mechanical reproduction of this or any other memory aid is prohibited. The use of any other materials is prohibited. Figures have not necessarily been drawn to scale. The following are the evaluation criteria required to complete the tasks in this booklet. Evaluation Criteria Competency Two: Uses Mathematical Reasoning Cr. 2 Cr. 3 Cr. 4 Cr. 5 Correct use of appropriate mathematical concepts and processes Proper implementation of mathematical reasoning suited to the situation Proper organization of the steps in an appropriate procedure Correct justification of the steps in an appropriate procedure BIM GRICS Page 1

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5 Part A Questions 1 to 6 Darken the letter that corresponds to your answer. Each question is worth 4 marks. 1. [A] [B] [C] [D] 2. [A] [B] [C] [D] 3. [A] [B] [C] [D] 4. [A] [B] [C] [D] 5. [A] [B] [C] [D] 6. [A] [B] [C] [D] Part B Questions 7 to 10 Write your answer in the space provided. Each question is worth 4 marks a) The rule of the inverse of the function is = b) The domain of is 9. The conic in its standard form is The rule of the function is BIM GRICS Page 2

6 Part C This part of the examination consists of Questions 11 to 16. For each question, you must show all your work to justify your answer. The work you show on all the pages of Part C will be considered. Your work must be organized and clearly presented; it cannot simply involve listing the calculator applications or programs used to obtain results or information. Each question in Part C is worth 10 marks. 11. Dog-Walking Over the summer, Paige started a dog-walking business. Once the summer had ended, she was able to track her clientele using an absolute value function. Paige started her business with one client. Three weeks later, she added five more clients to her list. The number of clients peaked and then declined. During its decline, 6.6 weeks into the summer, the number of clients was 10. For how many weeks did Paige s dog-walking business have 8 or more clients? BIM GRICS Page 3

7 Show all your work. Paige s dog-walking business had 8 or more clients for weeks. Evaluation Criteria Uses mathematical reasoning Observable indicators correspond to level LEVEL A B C D E Cr Cr Cr. 4 Cr BIM GRICS Page 4

8 12. Piecing it together! Calvin the chipmunk is being chased by his brother Isidore according to the piecewise function shown below. At point E, Isidore catches Calvin. y Distance (dm) D (22, 12) A (2, 6) (h 1, k 1 ) B (10, 0) C (18, 0.5) (15, k 2 ) E (?, 0) x Time (sec) How many seconds does it take Isidore to catch Calvin? BIM GRICS Page 5

9 Show all your work. Isidore catches Calvin in seconds. Evaluation Criteria Uses mathematical reasoning Observable indicators correspond to level LEVEL A B C D E Cr Cr Cr. 4 Cr BIM GRICS Page 6

10 13. Terrific Tides Lobster fishermen dock at a small fishing harbor on the Bay of Fundy. The depth of the water varies according to the tides. A sinusoidal function can be used to predict the water s depth. The Bay of Fundy has the highest tidal range in the world. At low tide, the depth of the water is 2 metres. Six hours later, at high tide, the depth of the water is 14 metres. The fishermen leave from and return to the harbor when the depth of the water is at least 5 metres. For how many hours can the fishermen be at sea between two consecutive low tides? BIM GRICS Page 7

11 Show all your work. The fisherman can be at sea between two consecutive low tides for hours. Evaluation Criteria Uses mathematical reasoning Observable indicators correspond to level LEVEL A B C D E Cr Cr Cr. 4 Cr BIM GRICS Page 8

12 14. Sailing through the Storm A ferry is leaving port A to bring passengers to port B. In order to avoid a storm, the captain must plan a route of two sailing paths and involving a change in direction. The two ports are represented in the Cartesian plane below. The planned route between the two ports is represented by a dotted line. The scale of this graph is in kilometres. The captain has defined the sailing paths by the following vectors: = ( 8, 15). = (3, 4) and In kilometres, what is the difference in the distances between the usual path and the redirected path? BIM GRICS Page 9

13 Show all your work. The difference in the distances between the usual path and the redirected path is km. Evaluation Criteria Uses mathematical reasoning Observable indicators correspond to level LEVEL A B C D E Cr Cr Cr. 4 Cr BIM GRICS Page 10

14 15. Treasure Hunt For their grade eleven math exam, Miss Fray s class was asked to create a treasure hunt using conics. Arnold and Keisha chose to hide their treasure in the fountain (F) located at the intersection of the parabola and the ellipse according to the illustration below. Arnold and Keisha used the following to describe the location of the treasure: The parabola has a vertex of (0, 2). The directrix of the parabola corresponds to the fence located along the line y = The equation of the ellipse is (0, 2) Fence y = 2.25 F (?,?) What are the exact coordinates of the fountain? BIM GRICS Page 11

15 Show all your work. The exact coordinates of the fountain are. Evaluation Criteria Uses mathematical reasoning Observable indicators correspond to level LEVEL A B C D E Cr Cr Cr. 4 Cr BIM GRICS Page 12

16 16. Animal Hotel Meowoof is a pet hotel that cares for cats and dogs when their owners go on vacation. Meowoof accepts cats and dogs only. The manager of the pet hotel noticed the following: There are always a minimum of 7 cats and a maximum of 13 dogs. There are always more than 17 animals at the hotel at any given time. Twice the number of cats added to five times the number of dogs is at most 81. The number of dogs is at least 27 less than 3 times the number of cats. Meowoof charges their clients a weekly fee of $100 per cat and $200 per dog. For the care of the animals, Meowoof incurs a weekly expense of $12 per cat and $24 per dog. Let x represent the number of cats at the hotel Let y represent the number of dogs at the hotel This week, Meowoof maximized its profit. What are all the possible combinations for the number of cats and dogs that stayed at Meowoof this week? BIM GRICS Page 13

17 Show all your work. y x The possible combinations for the number of cats and dogs that stayed at Meowoof this week are. Evaluation Criteria Uses mathematical reasoning Observable indicators correspond to level LEVEL A B C D E Cr Cr Cr. 4 Cr BIM GRICS Page 14