page 03 MARKS Attempt ALL questions Total marks — 70 1. The diagram shows the curve with equation y x x = + − 2 3 2 . y y = 3 + 2 x − x2 x O 3 −1 Calculate the shaded area. 2. Vectors u and v are defined by − ⎛ ⎞ ⎜ ⎟ = ⎜ ⎟ ⎜ ⎟ − ⎝ ⎠ 1 4 3 u and − ⎛ ⎞ ⎜ ⎟ = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ 7 8 5 v . (a) Find u.v. (b) Calculate the acute angle between u and v. 3. A function, f , is defined on the set of real numbers by ( ) f x x x = − − 3 7 6 . Determine whether f  is increasing or decreasing when x = 2 . 4. Express 2 3 6 7 x x − − + in the form ( ) a x b c + + 2 . [Turn over 4 1 4 3 3