Principles of Mathematics 12 August 2006 Form A Provincial Examination Answer Key
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1 Principles of Mathematics August 006 Form A Provincial Eamination Answer Key Cognitive Processes K Knowledge U Understanding H Higher Mental Processes Weightings 0% 70% 0% Question Type 44 Multiple Choice (MC) 6 Written Response (WR) Topics. Problem Solving. Patterns and Relations 3. Shape and Space 4. Statistics and Probability Prescribed Learning Outcomes (PLOs) A B, C, D E, F G A Problem Solving and Cross Topic Problems B Geometric Sequences and Series C/D Logarithms and Eponents C/D Trigonometry E Conics F Transformations G Combinatorics G Probability G Statistics Question Number Keyed Response Cognitive Process Mark Topic PLO Question Type. D K. D6 MC. B U. C3 MC 3. D U. D6 MC 4. A U. D6 MC. B U. C8 MC 6. A H. C MC 7. B K. D MC 8. A U. D4 MC 9. C U. C MC 0. B H. C MC. A U. 3 E MC. A U. 3 E MC 3. D H. 3 E MC 4. B H. 3 E3 MC. A U. 3 F MC 6. B U. 3 F3 MC 7. B K. 3 F MC 8. A U. 3 F MC 9. B H. 3 F6 MC 0. C K. 3 E MC. D U. 3, E; F3; A MC. C U. D MC 3. C H., A9, D7 MC Principles of Mathematics 0608 Form A Key Page
2 Question Number Keyed Response Cognitive Process Mark Topic PLO Question Type 4. A U. B3 MC. A U. B MC 6. C U. B MC 7. B U. B MC 8. D H. B MC 9. A U. D3 MC 30. A H. D3 MC 3. A U. 4 G6 MC 3. B U. 4 G4 MC 33. D U. 4 G8 MC 34. D U. 4 G7 MC 3. D H. 4 G, G6 MC 36. B U. 4 G0 MC 37. C U. 4 G3 MC 38. D H. 4 G8 MC 39. C U. 4 G MC 40. C U. 4 G MC 4. B H. 4 G MC 4. D U. 4 G MC 43. C U. 4 G MC 44. B U. 4 G3 MC Principles of Mathematics 0608 Form A Key Page
3 Principles of Mathematics August 006 Provincial Eamination Written-Response Key / Scoring Guide Cognitive Processes K Knowledge U Understanding H Higher Mental Processes Weightings 0% 70% 0% Question Types 44 Multiple Choice (MC) 6 Written Response (WR) Topics. Problem Solving. Patterns and Relations 3. Shape and Space 4. Statistics and Probability Prescribed Learning Outcomes (PLOs) A B, C, D E, F G A Problem Solving and Cross Topic Problems B Geometric Sequences and Series C/D Logarithms and Eponents C/D Trigonometry E Conics F Transformations G Combinatorics G Probability G Statistics Question Number Keyed Response Cognitive Process Mark Topic PLO Question Type. U 3 3 F, F6 WR. U 3 F4 WR 3. U D WR 4. U 4 G WR. U 4 C, C6 WR 6. H C7, C8 WR Principles of Mathematics 0608 Written-Response Key Page
4 The graph of y Use the following graph to answer questions and. f is shown below. y y f Principles of Mathematics 0608 Written-Response Key Page
5 . On the grid provided, sketch the graph of y f +. (3 s) y : absolute value : vertical epansion : vertical translation Note: deduct if graph does not stop on the left side or does not continue on the right side Principles of Mathematics 0608 Written-Response Key Page 3
6 . On the grid provided, sketch the graph of y. ( s) f y : invariant points each half : shape each half Principles of Mathematics 0608 Written-Response Key Page 4
7 3. A radioactive substance has a half-life of 7 d. How long will it take for 300 g of this substance to decay to 9 g? (Solve algebraically using logarithms. Answer accurate to at least decimal places.) ( s) Ê ˆ Ë Ê ˆ Ë d 7 Ê 9 ˆ Ë 300 Ê ˆ log log Ë d 7 d 7 Ê 9 ˆ Ë 300 d Ê ˆ log log 7 Ë s d Ê 9 ˆ 7 log Ë 300 Ê ˆ log Ë d 8. 0 days Principles of Mathematics 0608 Written-Response Key Page
8 4. It is known that 3% of graduating students are boys. Three grads are chosen at random. Given that at least two of the three grads are boys, determine the probability that all three of the grads are boys. (Answer accurate to at least 4 decimal places.) ( s) B G B G B G B G B G B G B G P 3 boys at least boys OR P 3 boys at least boys P ( 3 boys and at least boys P at least boys) (. ) ( 047. ) + ( 0. 3) s P ( 3 boys and at least boys P at least boys) - binompdf 3, 03., 3 binomcdf 3, 03., s Principles of Mathematics 0608 Written-Response Key Page 6
9 . Determine the general solution algebraically. (Solve over the set of real numbers.) 3cos - 8cos (Answer accurate to at least decimal places.) (4 s) ( - ) 3cos - cos 0 Æ cos cos , 44. mk mk fl reject np, np, n is an integer Principles of Mathematics 0608 Written-Response Key Page 7
10 6. Prove the identity: tan cos + cot sec + tan sin sin - cos ( s) Æ Æ LEFT SIDE tan cos + cot sec + tan Æ sin + + sin cos sin Ê cos ˆ cos + cos Ë sin sin + cos cos Ê cos ˆ Æ ( sin + ) Ë + sin RIGHT SIDE sin sin - cos sin sin cos ( - cos ) sin cos sin cos Æ cos LS RS Principles of Mathematics 0608 Written-Response Key Page 8
11 6. Prove the identity: tan cos + cot sec + tan sin sin - cos ( s) alternate solution LEFT SIDE RIGHT SIDE tan cos + cot sec + tan sin sin - cos Æ Æ sin Ê cos ˆ cos + cos Ë sin sin + cos cos cos ( sin + ) cos Ê sin ˆ + Ë cos cos cos sin + + sin sin sin cos ( - cos ) sin cos sin cos Æ cos LS RS END OF KEY Principles of Mathematics 0608 Written-Response Key Page 9
Principles of Mathematics 12 Sample 2007/08 Provincial Examination Multiple-Choice Key
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NOTICE TO CUSTOMER: The sale of this product is intended for use of the original purchaser only and for use only on a single computer system. Duplicating, selling, or otherwise distributing this product
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