page 03 MARKS Total marks — 65 Attempt ALL questions 1. Triangle ABC has vertices A(−1, −1), B(2, −4) and C(7, 3). C A y x B O (a) Find the equation of the altitude through C. (b) Find the equation of the median through B. (c) Determine the coordinates of the point of intersection of the altitude through C and the median through B. 2. The equation   2 2 8 4 0 x x p     has two real and distinct roots. Determine the range of values for p. 3. (a) Express sin cos 4 5 x x  in the form   sin k x a  where 0 k  and π 0 2 a   . (b) Hence solve sin cos 4 5 5.5 x x   for π 0 2 x   . [Turn over 3 3 2 3 4 3