Additional Mathematics 0606: FUNCTIONS, MODOLUS Topical Past Paper Questions

Two of the graphs A, B, C and D have equations of the form $ y = (x - 1)(x - p)(x - q) $ where p and q are constants such that $ q \geqslant p $ and q > 1. Find the two correct graphs, giving the values of p and q for each. [2] A B C D Graph ..... $p = \ldots\ldots\ldots\ldots$ $…

(a) (i) Write $ x^{2}-x-6 $ in the form $ (x+a)^{2}+b $ where a and b are constants. [2] (ii) Hence write down the coordinates of the stationary point on the curve $ y = x^{2} - x - 6 $. [2] (b) On the axes, draw the graph of $ y = |x^2 - x - 6| $ for $ -4 \leq x \leq 4 $. [3]

(a) Solve the equation $ 2|8-4x|+5=25 $. [3] (b) Solve the inequality $ 16x - 5x^{2} - 3 < \frac{57 - 9x}{6} $. [4]