MARKS Page three Attempt ALL questions Total marks – 60 1. Vectors u = 8i + 2j − k and v = −3i + tj − 6k are perpendicular. Determine the value of t. 2. Find the equation of the tangent to the curve y = 2x3 + 3 at the point where x = −2. 3. Show that (x + 3) is a factor of x3 − 3x2 − 10x + 24 and hence factorise x3 − 3x2 – 10x + 24 fully. 4. The diagram shows part of the graph of the function y = p cos qx + r. y 4 x −2 π 2 Write down the values of p, q and r. 5. A function g is defined on , the set of real numbers, by g(x) = 6 − 2x. (a) Determine an expression for g−1(x). (b) Write down an expression for g(g−1(x)). 6. Evaluate log612 + 1 3 log627. 7. A function f is defined on a suitable domain by f (x) = 2 3 – x x x x ⎛ ⎞⎟ ⎜ ⎟ ⎜ ⎟⎟ ⎜⎝ ⎠ . Find f ′(4). [Turn over 2 4 4 3 2 1 3 4 O