# The function y g x has a domain of 6 3 the domain of

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16. The function ( ) y g x = has a domain of [ ] 6, 3 . The domain of the graph of ( ) y g ax = is [ ] 2, 1 . The value of a is: a) 1 3 b) 1 2 c) 2 d) 3

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Page 30 Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 17. On the unit circle as shown, the x -coordinate at point P is 1 3 . Find sin θ . 18. A point on the graph of ( ) ( ) is 2, 3 y f x = . A point that must be on the graph of ( ) 1 y f x = is: 19. If 2 log 6 x y = , the value of log x y is: y x 1 , 3 P y θ
Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 Page 31 20. Simplify ( ) ( ) 2 ! 1 ! n n + a) ( )( )( ) 1 1 1 n n n + b) ( )( )( ) 2 1 n n n + + c) ( )( ) 2 1 n n + + d) ( ) 2 n + 21. The value of 40 10 C is equivalent to: 22. Kyle has 15 marbles of the same size in his pocket. Four are white, five are red, and the rest are blue. If he arranges the marbles in a row on his desk, how many permutations can he possibly make?

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Page 32 Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 23. The graph of ( ) ( ) 2 1 3 2 x y = − + is a parabola that: 24. Light bulbs are produced in two factories: A and B. The probability that a light bulb is produced in factory A is 0.6. The probability that a light bulb produced in factory B is defective is 0.2. What is the probability that a light bulb is from factory B and is defective? a) 0.48 b) 0.32 c) 0.12 d) 0.08 25. The first term of ( ) 0 0.9 n n = is:
Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 Page 33 Question No. 26 Outcome: A3 State the exact value of 7 cos 4 π . Answer Note(s): give 0 marks for 2 1 2 2 or Question No. 27 Outcome: A4 On the interval [ ] 0 , 360 ° ° , one solution of the equation 4 tan is 127 3 θ θ = − = ° . Find the other solution. Answer 2 1 2 2 or 307 127 180 or θ θ = ° = ° + ° Part 2—Short-Answer Questions

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Page 34 Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 Question No. 28 Outcome: A5 Solve the equation sin 1 θ = on the interval [ ] 0, 2 π . Answer Question No. 29 Outcome: B7 State the y value of a maximum point on the graph of ( ) 3cos 2 1 y x = + . Answer y = 4 2 θ π =
Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 Page 35 Question No. 30 Outcome: B5 The function ( ) y f x = is sketched below: Answer Sketch the graph of ( ) y f x = . Question No. 31 Outcome: B4 The function ( ) y f x = is sketched below: Answer Sketch the graph of ( ) 1 y f x = . 1 mark ½ mark for each branch y x ( ) y f x = y x y x ( ) y f x = y x

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Page 36 Marking Guide—Pre-Calculus Mathematics (40S)—June 2007 Question No. 32 Outcome: C2 Find the exact value of ( ) ( ) ( ) ( ) tan 20 tan 25 1 tan 20 tan 25 ° + ° ° ° .
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