Sketch the graph of $f$ indicating clearly any intercepts with the axes and the coordinates of any local maximum or minimum points.

State the range of $f$.

Solve the inequality $\left| {3x\arccos (x)} \right| > 1$.

correct shape passing through the origin and correct domain     A1

Note: Endpoint coordinates are not required. The domain can be indicated by $- 1$ and 1 marked on the axis.

$(0.652,{\text{ }}1.68)$    A1

two correct intercepts (coordinates not required)     A1

Note: A graph passing through the origin is sufficient for $(0,{\text{ }}0)$.

[3 marks]

$[-9.42,{\text{ }}1.68]{\text{ }}({\text{or }} - 3\pi ,{\text{ }}1.68])$    A1A1

Note: Award A1A0 for open or semi-open intervals with correct endpoints. Award A1A0 for closed intervals with one correct endpoint.

[2 marks]

attempting to solve either $\left| {3x\arccos (x)} \right| > 1$ (or equivalent) or $\left| {3x\arccos (x)} \right| = 1$ (or equivalent) (eg. graphically)     (M1)

$x =  - 0.189,{\text{ }}0.254,{\text{ }}0.937$    (A1)

$- 1 \leqslant x <  - 0.189{\text{ or }}0.254 < x < 0.937$    A1A1

Note: Award A0 for $x <  - 0.189$.

[4 marks]