Higher November 2018 Paper 6 Q18
18
(a) Sketch the graph of \(y = \cos x + 1\) for \(0° \leqslant x \leqslant 720°\).
[3]
(b) Explain why the equation \(\cos x + 1 = 2.7\) has no solutions. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Cosine-shaped curve with maximum 2 at x = 0°, 360° and 720° and minimum 0 at x = 180° and 540° | 3 | B1 for general shape B1 for max at +2, minimum at 0 B1 for max at x = 0, 360, 720 | Starting at max above the x axis, and completing at least one full cycle For full marks, it must be a curve and have correct curvature |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| The maximum value of \(\cos x + 1\) is 2 and 2.7 is greater than 2 oe | 1 | More ‘work’ may be correctly done before an equivalent conclusion, e.g. \(\cos x = 1.7\), and max value of \(\cos x\) is 1 and 1.7 is greater than 1. | |