page 05 MARKS 7. (a) Solve the differential equation 5 2 6 x dy y e dx   given that when x = 0, y = −1. Express y in terms of x. (b) The solution of the differential equation in (a) is also a solution of 3 2 2 3 2 5 , x d y d y ke k dx dx   . Find the value of k. 8. The fourth and seventh terms of a geometric sequence are 9 and 243 respectively. (a) Find the: (i) common ratio (ii) first term. (b) Show that 2 1 3n n n S S  where n S represents the sum of the first n terms of this geometric sequence. 9. Express 57210 in base 9. 10. A curve is defined by 2 5x y x  ,where x > 0. Find dy dx in terms of x. [Turn over 4 2 1 1 2 2 5