page 04 MARKS Total marks — 65 Attempt ALL questions 1. Express   x x x x    2 2 3 3 5 5 in partial fractions. 2. Find the exact value of 3 0 4 2 1dx x   . 3. Use the Euclidean algorithm to find integers a and b such that 634 87 1 a b  . 4. Use integration by parts to find    1 2 2 2 7 x x dx    . 5. Matrix A is given by 1 3 1 2 3 , 18 7 A k k            where . k  Find the values of k so that the matrix A is singular. 6. The first three terms of a sequence are defined algebraically by 5, 3 2, 5 1 x x x    , where x. (a) Show that these three terms form the start of an arithmetic sequence. (b) Find a simplified expression for the 15th term of this sequence. (c) Given that the sum of the first 20 terms of this sequence is 1130, find the value of x. 3 2 3 3 3 2 2 2