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# In how many ways can a student choose one course in

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In how many ways can a student choose one course in each of these three subjects? Solution 4 1 5 1 2 1 4 5 2 40 ways C C C or or i i i i Question 37 E1 1 mark Simplify: 11! 9! Solution 11 10 110 or i

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Pre-Calculus Mathematics: Marking Guide (January 2009) 41 Question 38 F1 1 mark Identify the conic section described by 2 3 6 12 0 y x y + = . Solution parabola Note(s): give ½ mark for vertical parabola Question 39 G2 1 mark Mark is playing a game on his computer in which he wins one out of six times. If Mark plays this game twice, what is the probability that he loses both times? Solution Question 40 C2 1 mark Find the exact value of 5 5 cos cos sin sin π π π π + 8 8 8 8 . Solution 0 Note(s): give ½ mark for 4 cos or cos 8 2 π π ( ) 5 5 P lose, lose 6 6 25 36 = = i
42 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 41 A4, C1 Solve for x on the interval [ ] 0, 2 π : 2 2 2sin 3cos cos 4 x x x + = + Solution Part 2: Long-Answer Questions ( ) ( ) ( ) 2 2 2 2 2 2 1 cos 3cos cos 4 0 2 2cos 3cos cos 4 0 cos cos 2 0 cos 2 cos 1 0 cos 2 cos 1 no solution x x x x x x x x x x x x x + = + = = + = = = − = π 1 mark for identity ½ mark for factoring ½ mark for solving for cos x 2 marks for consistent solutions of trigonometric equations (1 mark for each solution) 4 marks

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Pre-Calculus Mathematics: Marking Guide (January 2009) 43 Exemplar Mark: 2½ out of 4 Note(s): gave 1 mark for identity gave ½ mark for solving for cos x gave ½ mark for one consistent solution of 1 cos 2 x = gave 1 mark for the consistent solution of cos 1 x = − deducted ½ mark for arithmetic error in line 2
44 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 42 B4 Sketch a clearly labelled graph of at least one period of sec y x = . Solution Note(s): no additional deduction for missing horizontal scale (correctly placed asymptotes require a scale) deduct ½ mark if graph crosses or curls away from the asymptote 1 mark for correctly placed asymptotes ½ mark for general shape ½ mark for correct range 2 marks y x 2 − π −π π 2 π 2 π 3 π 2 1 1 3 π 2

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Pre-Calculus Mathematics: Marking Guide (January 2009) 45 Exemplar Mark: 1½ out of 2 Note(s): gave full marks deducted ½ mark for not labelling the graph of sec y x =
46 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 43 A6, B3 Sketch a clearly labelled graph of at least one period of cos y x = − . Solution ½ mark for sinusoidal shape ½ mark for correct period 1 mark for the reflection without a shift 2 marks y x 2 π − π 1 2 π π

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Pre-Calculus Mathematics: Marking Guide (January 2009) 47 Exemplar Mark: ½ out of 2 Note(s): gave ½ mark for sinusoidal shape
48 Pre-Calculus Mathematics: Marking Guide (January 2009)

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• Spring '12
• A.Young
• Trigonometry, Logarithm, New Testament chapters, pre-calculus mathematics

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