Higher November 2020 Paper 5 Q13
13
(a) Sketch the graph of \(y = \sin x\) for \(0^\circ \leqslant x \leqslant 360^\circ\).
(b) The graph of \(y = \cos(x - 30)\) for \(0^\circ \leqslant x \leqslant 360^\circ\) crosses the \(x\)-axis in two places.
Write down the values of \(x\) where this occurs. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Correct sketch with max at (90, 1) and min at (270, –1) and crossing \(x\)-axis at 0, 180 and 360 | 2 | M1 for correct shape starting at (0, 0) but inaccurate at roots and max/min. Needs at least one cycle, but may have more than one. | Mark intention |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 120 | 1 | ||
| 300 | 1 | FT their 120 + 180 | For FT both must be in range 0 to 360 |