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2007 MJC Prelim Paper 2 Questions

# 2007 MJC Prelim Paper 2 Questions - 2 Section A Pure...

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2 MJC/2007 JC2 Preliminary Examination/9740/02 [Turn Over Section A: Pure Mathematics [40 marks] 1 The function f is defined by 2 f : 2, 0 x x x x . (i) Find the range of f. [1] (ii) Sketch the graphs of f( ) y x and 1 f ( ) y x on the same diagram. Label clearly the coordinates of any intersection point(s). [3] The function g is defined by g: ln( ), 0 e x x x . (iii) Show that the composite function fg does not exist. [1] (iv) The function fg exists if the domain of g is restricted to e k x . Find K , the least value of k . [2] (v) Find the range of fg, where fg is defined on [ K , e]. [1] 2 Samuel owes the bank \$15000 for his university fees which he intends to pay by monthly instalments. He intends to pay \$300 in the middle of every month. Interest is added to the amount owed at the end of every month at a fixed rate of 0.5% of the outstanding amount, after making the payment in the middle of the month. (i) Show that the amount he owes at the end of the second month after the interest has been added is \$14545.87 . [1] (ii) Show that, at the end of the n th month, after the interest has been added, he will still owe the bank \$ 60300 45300 1.005 n . [4] (iii) Calculate how many more months he will take to repay his debt, compared to the case when no interest is imposed. [3]

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3 MJC/2007 JC2 Preliminary Examination/9740/02 [Turn Over 3 A curve is defined parametrically by 2 x , 2 ln 2 y , where 0 . Find d d y x , expressing your answer in terms of x . [2] (i) The tangent and normal to the curve at the point where 2 x meet the x -axis at P and Q respectively. Find the distance between P and Q in exact form. [4] (ii) Determine the rate of change of xy when 1 3 and x increases at a constant rate of 0.1 unit per second. [4] 4 A line l has equation 4 3 0 2 5 1 r , .
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