page 04 MARKS Total marks — 65 Attempt ALL questions 1. The function f  is defined by  sin 1 2 3 f x x   . Find  ' f x . 2. Find 2 3 10 x dx x   . 3. Matrix A is defined by 2 2 4 1 0 1 0 2 x A x              , where x. (a) Find a simplified expression for the determinant of A. (b) Hence, determine whether A−1 exists for all values of x. 4. Calculate the gradient of the tangent to the curve with equation sin 2 2 2 3 x y y x   at the point (0, 0). 5. (a) Write down and simplify the general term in the binomial expansion of 8 2 2 3x x        . (b) Hence, or otherwise, determine the coefficient of x−1. 6. (a) Use the Euclidean algorithm to find d, the greatest common divisor of 703 and 399. (b) Find integers a and b such that d = 703a + 399b. (c) Hence find integers p and q such that 76 = 703p + 399q. 2 2 2 1 3 3 2 1 2 1