(a) \(\mathrm{h}(x) = \sqrt[3]{x} \qquad\) for all values of \(x\)
On the grid, draw the graph of the inverse function \(\;y = \mathrm{h}^{-1}(x) \quad\) for \(\;-2 \leqslant x \leqslant 2\) [2 marks]
(b) For all values of \(x\)
\(\mathrm{f}(x) = \sin x\)
\(\mathrm{g}(x) = x + 90\)
On the grid, draw the graph of the composite function \(\;y = \mathrm{fg}(x) \quad\) for \(\;0^\circ \leqslant x \leqslant 360^\circ\) [2 marks]
Mark scheme (a)
Answer
Mark
Comments
Fully correct graph passing through \((-2, -8)\ (-1, -1)\ (0, 0)\ (1, 1)\) and (2, 8)
B2
B1 \(x^3\) or \(y^3 = x\) or at least 4 points from \((-2, -8)\ (-1, -1)\ (0, 0)\ (1, 1)\) and \((2, 8)\) plotted or seen in a table Tolerance of \(\pm 1\) small square Points can be implied by graph passing through them
Additional guidance
Tolerance of \(\pm 1\) small square means it is on the edges of or within the shaded area
Ignore graph drawn outside of \(\;-2 \leqslant x \leqslant 2\)
B1 \(\sin (x + 90)\) or \(\cos x\) or at least 4 points from \((0, 1)\ (90, 0)\ (180, -1)\ (270, 0)\) and \((360, 1)\) plotted or seen in a table Mark intention
Additional guidance
Ignore graph drawn outside of \(\;0^\circ \leqslant x \leqslant 360^\circ\)
