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MATHEMATICS (Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time) Section A Answer Question 1 (compulsory) and five other questions. Section B and Section C Answer two questions from either Section B or Section C. All working, including rough work, should be done on the same sheet as, and adjacent to, the rest of the answer. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables and graph papers are provided. Slide rule may be used. ..... SECTION A Question 1 [10 3] (iv) 1 2 3 1 1 x 1 4 5 6 2 0 3 2 5 3 Find the value of x if 2 2 Find the value of k so that the line 2 x y k 0 may touch the ellipse x 2 y 2 1 1 2 tan 1 tan 1 3 7 4 Prove that: 1 lim cot x x 0 x Using L Hospital s rule, evaluate: (v) Evaluate: (i) (ii) (iii) x tan 2 x dx 2 cos x dx (vi) Evaluate: (vii) For 5 observations of pairs of 0 x, y of variables x and y the following results are 2 2 obtained: x 15 , y 25 , x 55 , y 135 , xy 83 . Find: regression coefficients bxy byx and (viii) (ix) (x) . A bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random, what is the probability that both balls are red or both are black? z 2i z 3 If z x iy and , show that 6 x 4 y 5 0 Solve the differential equation: x y 1 dy 1 dx This Paper consists of 5 printed pages and 1 blank page. Sample paper Turn over
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