2007 MJC Prelim Paper 1 Questions

2007 MJC Prelim Paper 1 Questions - 2 1 An arithmetic...

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MJC/2007 JC2 Preliminary Examination/9740/01 [Turn over 2 1 An arithmetic progression G has first term a and a non-zero common difference d . Given that the sum of the first 10 terms in G is twice the 22 nd term of the series and the 6 th term is 37, find the values of a and d . [3] A new series H is formed by selecting every third term of G . Find the sum of the first 50 terms of H . [3] 2 Express 2 1 f( ) ( 1) ( 2) x xx  in partial fractions. Hence find the expansion of x , in ascending powers of x , up to and including the term in 3 x , where 1 x . [6] Show that the coefficient of the term in 2 n x in the expansion of x , where n is a positive integer, is 2 1 4 2 2 3 3 6 n n     . [2] 3 A child was blowing bubbles and noticed that if he blows too hard, the bubble would burst immediately but if he were to blow gently, the bubble increases in size till its optimal volume and detaches itself off the blowing stick. At time t minutes, the radius of the bubble blown is r cm, assuming that all bubbles blown are spherical in shape. If the child blows gently at a rate of   3 r  cm 3 min –1 , where is a constant, show that 23 d 4 d r rr t  . [3] Given that the initial volume of a bubble is negligible and the optimal volume of a bubble is 6 cm 3 , find the time taken for a bubble to detach itself off the blowing stick.
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2007 MJC Prelim Paper 1 Questions - 2 1 An arithmetic...

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