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# Which of the following curves could be the graph of 5

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20. Which of the following curves could be the graph of 5 log y x = ? a) b) c d) E2 21. The expression 55 3 P is equal to: a 55 54 53 i i b) 55! c) 55! 3! d) 55 52 P E2 22. The number of ways to arrange 8 chairs of different colours in a circle is: d 7! y x y x y x y x

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Pre-Calculus Mathematics: Marking Guide (January 2009) 35 G5 23. The school’s Math Club consists of 4 boys and 6 girls. If the names of 3 club members are drawn at random, the probability they are all girls is: b 6 3 10 3 C C 3 6 10 E2 24. The letters of the word EXCELLENCE can be arranged in: b 10! ways 4!2!2! G3 25. Two events that cannot occur at the same time are: a) conditional b) dependent c) independent d mutually exclusive
36 Pre-Calculus Mathematics: Marking Guide (January 2009) Part 2: Short-Answer Questions Award half marks for incorrect answers that have resulted from arithmetic or notation errors as indicated in the marking guidelines. Do not award any other half marks unless indicated in this marking guide.

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Pre-Calculus Mathematics: Marking Guide (January 2009) 37 Question 26 A1 1 mark Find the measure of Y . Solution 11 55 π ° 36 or Note(s): give ½ mark for 4 45 or 80 4 9 π π = = D D deduct ½ mark for missing degree symbol Question 27 A2 1 mark If 1 , 2 y is a point on the unit circle, what is a possible value of y ? Solution Question 28 A3 1 mark Find the exact value of 11 cos 4 π . Solution 2 1 2 2 or Note(s): award no marks for 2 1 or 2 2 T Y R π 4 80 ° 3 3 2 2 or
38 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 29 B2 1 mark One point on the graph of ( ) y f x = is ( ) 4, 8 . Give the coordinates of a point that must be on the graph of 1 4 y f x = . Solution ( ) 16, 8 Question 30 A3 1 mark If sec 2 θ = , what is a possible value of θ ? Solution 5 7 or or or ... 3 60 or 300 or 420 or ... θ θ π π π = 3 3 = ° ° ° or Note(s): give ½ mark for 1 cos 2 θ = Question 31 B3 1 mark Write an equation for the line formed by reflecting the graph of 4 1 y x = over the x -axis. Solution ( ) 4 1 4 1 4 1 y x y x y x = − = − + = or or

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Pre-Calculus Mathematics: Marking Guide (January 2009) 39 Question 32 F3 1 mark Find the centre of the circle with the equation ( ) 2 2 2 9 x y + = . Solution ( ) 2, 0 Question 33 D3 1 mark Find the exact value of log 7 5 5 . Solution 7 Question 34 D5 1 mark Write log 6 log a a x as a single logarithm. Solution 6 log a x
40 Pre-Calculus Mathematics: Marking Guide (January 2009) Question 35 H1 1 mark The 5th term of a geometric sequence is 18 and the 6th term is 12. What is the common ratio? Solution 12 2 18 3 or Question 36 E1 1 mark In Grade 12 there are 4 mathematics courses, 5 science courses, and 2 English courses.

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

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