(a)     Sketch the curve \(f(x) = \left| {1 + 3\sin (2x)} \right|{\text{, for }}0 \leqslant x \leqslant \pi \) . Write down on the graph the values of the x and y intercepts.

(b)     By adding one suitable line to your sketch, find the number of solutions to the equation \(\pi f(x) = 4(\pi  - x)\) .

(a)    

     A1A1A1A1

Note: Award A1 for y-intercept

A1A1 for x-intercepts

A1 for shape

(b)     correct line     A1

5 solutions     A1

[6 marks]

Part (a) was well executed by the majority of candidates. Most candidates had the correct graph with the correct x and y intercepts. For part (b), some candidates had the straight line intersect the x-axis at 3 rather than at \(\pi \) , and hence did not observe that there were 5 points of intersection.