ruseyr12_2u_trial_2011 - S t d dS d S dS T T T T T q dd u d...

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Question 1 - Start a new sheet of paper Marks a) Solve 0 18 3 2 g32 g16 g16 x x 1 b) Convert 9 7 g83 radians to degrees 1 c) Write down a primitive of x 3 sec 2 1 d) Solve 7 1 2 g32 g16 x 2 e) Write 3 17 2 g16 with a rational denominator 1 f) Given f ( x ) = x 3 1 x < 3 1 ) 3 ( 2 g14 g16 x 3 g116 x , evaluate ) 1 ( ) 4 ( 2 g16 g16 f f 2 g) Find the non-zero values of x for which the geometric series ..... 18 6 2 2 g16 g14 g16 x x has a limiting sum 2 h) i) Write down the equation of the locus of a point P that is 3 units from the point A (2,-4) 1 ii) How many times does this locus cut the x axis ? 1 Question 2 - Start a new sheet of paper Marks a) Differentiate the following with respect to x : i) 3 ln 2 g14 x 2 ii) 3 2 ) 7 2 ( g14 x 1 iii) x x cos 2 2 b) The equation of a parabola is given by 12 4 8 2 g14 g14 g32 x x y i) Find the coordinates of the vertex 2 ii) Write down the focal length of the parabola 1 iii) Sketch the parabola, clearly showing the focus and directrix 2 c) Solve the equation 4 sec 2 g32 x for g83 2 0 g100 g100 x 2
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Question 3 - Start a new sheet of paper Marks a) Given that 838 . 1 5 log g32 k and 792 . 0 2 log g32 k , find the values of i) 50 log k ii) ) 4 0 ( log g152 k iii) k 10 log 4 b) An unbiased spinner, as shown, is equally likely to stop at any one of the letters A , E , I , O or U I E A U O i) If the spinner is spun twice, find the probability that it stops on the same letter both times. 1 ii) How many times must the spinner be spun for it to be 99% certain that the spinner will have stopped on E at least once? 2 c) i) Sketch the graph of x y 2 sin 3 g32 for g83 2 0 g100 g100 x (Your diagram should take up at least one quarter of a page.) 2 ii) Draw the line 2 x y g32 on the same diagram, noting particularly the point on the line where g83 2 g32 x 1 iii) Hence determine the total number of solutions there are to the equation 0 2 sin 6 g32 g16 x x for all x 2 ( NB You are not required to solve the equation but you should include a short explanation of your answer)
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Question 4 - Start a new sheet of paper Marks a) The gradient of a curve is given by 4 3 2 g16 g32 x dx dy i) Find 2 2 dx y d 1 ii) Find those values of x for which the curve is both increasing and concave downwards. Show your reasoning.
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