Higher November 2022 Paper 1 Q23
23 \(4 \times \sin 30^\circ \times \tan 30^\circ \times \cos 30^\circ = \sin y\)
Work out one possible value of \(y\).
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \((\sin 30 =)\ \dfrac{1}{2}\) or \((\tan 30 =)\ \dfrac{1}{\sqrt{3}}\) or \(\dfrac{\sqrt{3}}{3}\) or \((\cos 30 =)\ \dfrac{\sqrt{3}}{2}\) | M1 | oe may be implied by \((4 \times \sin 30 =)\ 2\) may be implied by correct position in a multiplication string |
| \(4 \times \dfrac{1}{2} \times \dfrac{1}{\sqrt{3}} \times \dfrac{\sqrt{3}}{2}\) | M1dep | oe with all trig values correct condone any order unless error seen |
| 1 with all three values seen | A1 | implied by 90 with all three values seen |
| 90 with M1M1A1 scored | A1 | accept any angle of the form \(90 + 360n\), where \(n\) is an integer |
| Alternative method 2 | ||
| \(4 \times \sin 30^\circ \times \dfrac{\sin 30^\circ}{\cos 30^\circ} \times \cos 30^\circ\) | M1 | |
| \(4 \times \dfrac{1}{2} \times \dfrac{1/2}{\sqrt{3}/2} \times \dfrac{\sqrt{3}}{2}\) | M1dep | oe eg \(4 \times \left(\dfrac{1}{2}\right)^2\) |
| 1 with \(\dfrac{\sin 30^\circ}{\cos 30^\circ}\) and \(\dfrac{1}{2}\) and \(\dfrac{\sqrt{3}}{2}\) seen | A1 | if \(\cos 30^\circ\) is cancelled out only \(\dfrac{1}{2}\) need be seen |
| 90 with M1M1A1 scored | A1 | accept any angle of the form \(90 + 360n\), where \(n\) is an integer |
Additional guidance
Condone a square root sign on 1 up to M1M1