June 2025 Paper 2 Q6
6 The diagram shows part of the graph of \(\mathrm{f}(x) = \operatorname{cosec} 2x\).
(a) State which of the following is the equation of the curve \(y = \dfrac{1}{\mathrm{f}(x)}\).
\(y = \cos 2x \qquad y = \operatorname{cosec}(-2x) \qquad y = -\operatorname{cosec} 2x \qquad y = \sin 2x\) [1]
\(y = \cos 2x \qquad y = \operatorname{cosec}(-2x) \qquad y = -\operatorname{cosec} 2x \qquad y = \sin 2x\) [1]
(b) State the exact equations of the asymptotes of \(y = \operatorname{cosec} 2x\) for \(0 \leqslant x \leqslant \pi\). [1]
| Scheme | Marks | AO |
|---|---|---|
| \(y = \sin 2x\) or \(\dfrac{1}{\mathrm{f}(x)} = \sin 2x\) | B1 | 1.2 |
| [1] |
Notes
B1: cao
| Scheme | Marks | AO |
|---|---|---|
| \(x = 0,\ x = \dfrac{\pi}{2},\ x = \pi,\) isw | B1 | 1.1 |
| [1] |
Notes
B1: all correct; ignore equations outside the range, B0 if extra equations in the range
B0 for \(x = 0, \frac{\pi}{2}, \pi\); B0 for \(y = \ldots\)