Give your answer as a whole number b how many 6

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Give your answer as a whole number. b) How many 6-letter arrangements end with TT? Give your answer as a whole number. c) How many 6-letter arrangements can be made if the letters {M, T, T, R} must be together? Give your answer as a whole number. Briefly explain your calculations. Solution a) b) c) Note(s): deduct ½ mark if no explanation in c) 1 mark 6! 360 2! = T T 4! 4! 24 = 1 mark 2 marks ( ) 4! 3! 2! consonants for two T ’s 3 groups = 72 arrangements ½ mark for 3! ½ mark for 4! ½ mark for 2! ½ mark for consistent answer
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Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 Page 25 EXEMPLARS a) b) c) Mark: 1 out of 2 Note(s): This case arrangement would work, but the student neglected to divide each 4! by 2! for the identical T ’s. Mark: 0 out of 1 Mark: 1 out of 1
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Page 26 Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 Question No. 10 Outcomes: C1, H3 a) Find the common ratio of the geometric series given below. Express your answer in terms of a single trigonometric function. 2 2 cos cos sin sin x x x x + + + b) Find a trigonometric expression for the fourth term of the geometric series: 2 2 cos cos sin sin x x x x + + + Solution a) b) 2 cos sin tan cos x x r x x = = 1 mark for division of terms ½ mark for simplifying ½ mark for tan x 2 marks ( ) ( ) ( ) 3 2 2 3 cos tan sin tan sin cos or or x x x x x x 1 mark ( ) cos 0, sin 0 x x
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Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 Page 27 EXEMPLARS a) b) Mark: 1 out of 2 Note(s): gave ½ mark for simplifying gave ½ mark for cot x Mark: 0 out of 1 Note(s): multiple notation errors
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Page 28 Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 11. In the triangle below, the measure of Q is: a) 54 ° b) 70 ° c) 72 ° d) 82 ° 12. The expression ( )( ) csc cot x x is equivalent to: cos sin x x sin cos x x 13. On the interval [ ] 0, 2 π , which of the following lines will intersect the curve 3sin 2 y x = + exactly once? Q P R 10 π Part 2—Multiple-Choice Questions
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Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 Page 29 14. Which of the following equations has no solution for ? θ 15. The domain of the function ( ) 1 sin y x = is: a) , 2 2 π π b) [ ] 0, π c) [ ] 1, 1 d) ( ) , −∞ ∞
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  • Spring '12
  • A.Young
  • ........., New Testament chapters, Guide—Pre-Calculus Mathematics

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