page 07 MARKS 9. (a) Write down and simplify the general term in the binomial expansion of , where d is a constant. (b) Given that the coefficient of is −70 000, find the value of d. 10. A curve is defined implicitly by the equation . (a) Find an expression for in terms of x and y. (b) There are two points where the tangent to the curve has equation x = k, . Find the values of k. 11. Let n be a positive integer. (a) Find a counterexample to show that the following statement is false. is always a prime number. (b) (i) Write down the contrapositive of: If is even then n is odd. (ii) Use the contrapositive to prove that if is even then n is odd. 12. Express 23111 in base 7. [Turn over 3 2 3 2 1 1 3 3