page 04 MARKS Total marks – 100 Attempt ALL questions 1. (a) Given ( ) sin f x x − = 13 , find ( ) f x ′ . (b) Differentiate x e y x = + 5 7 1 . (c) For cos y x y x + = 2 6 , use implicit differentiation to find dy dx . 2. Use partial fractions to find x dx x x − − − ⌠⎮⌡ 2 3 7 2 15 . 3. (a) Write down and simplify the general term in the binomial expansion of x x ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ 9 2 5 2 . (b) Hence, or otherwise, find the term independent of x. 4. Given that z i = + 1 2 3 and , , z p i p = − ∈\ 2 6 find: (a) z z 1 2; (b) the value of p such that z z 1 2 is a real number. 5. Use the Euclidean algorithm to find integers a and b such that a b + = 306 119 17. 2 2 4 4 3 2 2 1 4