Higher November 2021 Paper 2 Q18
18 Here is a graph of \(y = \sin x^\circ\) for \(0 \leqslant x \leqslant 360\)
(a) Using this graph, find estimates of all four solutions of
\(\sin x^\circ = 0.6\) for \(0 \leqslant x \leqslant 720\) (2)
\(\sin x^\circ = 0.6\) for \(0 \leqslant x \leqslant 720\) (2)
The graph of \(y = \sin x^\circ\) is reflected in the \(x\)-axis.
(b) Write down an equation of the reflected graph. (1)
Here is a graph of \(y = \mathrm{f}(x)\)
(c) On the grid, draw the graph of \(y = \mathrm{f}(x - 2)\) (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 37, 143, 397, 503 | M1 | for any two correct angles within the ranges below or for a correct method to find a solution beyond 360, eg. “angle read from 0 to 360” + 360 |
| A1 | for all 4 angles in the range, 35 to 40, 140 to 145, 395 to 400 and 500 to 505 |
Additional guidance
Accept given as coordinates for M1 only
| Answer | Mark | Mark scheme |
|---|---|---|
| \(y = -\sin x^\circ\) | B1 | for any acceptable equations, eg. \(y = -\sin x^\circ\) or \(y = \sin(-x^\circ)\) or \(-y = \sin x^\circ\) or \(y = \cos(x^\circ + 360n + 90)\) or for any positive integer \(n\), \(y = \sin(x^\circ - (2n - 1)180)\) or \(y = \cos(x^\circ + 360n)\) |
Additional guidance
Quoted are just the more likely solutions but check all attempts
Condone missing degrees sign
| Answer | Mark | Mark scheme |
|---|---|---|
| graph | C1 | for correct graph shown translated 2 in the positive \(x\)-direction |
