page 04 MARKS Total marks — 35 Attempt ALL questions 1. (a) Given 2 1 3 4 x y x    , find dy dx . Simplify your answer. (b) Given ( ) cosec5 f x x  , find  f x  . 2. Use Gaussian elimination to solve the following system of equations: 2 4 2 3 3 7 4 9 x y z x y z x y z          3. Given that 1 5 3 z i   and 2 6 2 z i   , express 1 2 z z in the form a ib  where a and b are real numbers. 4. A curve is defined by the equation 3 4 2 1 y y xy   . (a) Use implicit differentiation to find an expression for dy dx . (b) Find the gradient of the tangent to the curve when 1 y . (c) Show that the curve has no stationary point. 5. (a) Find, and simplify, the Maclaurin expansion for 4x e , up to and including the term in 3 x . (b) Hence find the first four terms of the Maclaurin expansion of 4 3 2 x x e  . 3 2 4 2 3 1 2 2 2