Higher June 2022 Paper 1 Q28
28 Work out the value of \(\quad (\cos 30^\circ \times \sin 45^\circ \times \tan 60^\circ)^2\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((\cos 30 =)\ \dfrac{\sqrt{3}}{2}\) or \((\sin 45 =)\ \dfrac{\sqrt{2}}{2}\) or \(\dfrac{1}{\sqrt{2}}\) or \((\tan 60 =)\ \sqrt{3}\) | M1 | oe correct trig function may be implied by position in multiplication string may be seen in a table |
| \(\left(\dfrac{\sqrt{3}}{2} \times \dfrac{\sqrt{2}}{2} \times \sqrt{3}\right)^2\) or \(\left(\dfrac{\sqrt{3}}{2}\right)^2 \times \left(\dfrac{\sqrt{2}}{2}\right)^2 \times \left(\sqrt{3}\right)^2\) | M1dep | oe with all values correct |
| or \(\dfrac{3\sqrt{2}}{4}\) or \(\dfrac{3}{2\sqrt{2}}\) or \(\dfrac{\sqrt{18}}{4}\) | oe single term not squared | |
| \(\left(\dfrac{3\sqrt{2}}{4}\right)^2\) or \(\left(\dfrac{3}{2\sqrt{2}}\right)^2\) or \(\left(\dfrac{\sqrt{18}}{4}\right)^2\) | M1dep | oe with all values correct oe single term squared |
| or \(\dfrac{3}{4} \times \dfrac{1}{2} \times 3\) | oe multiplication string without surds | |
| or \(\dfrac{\sqrt{324}}{16}\) | oe single fraction with one surd | |
| \(\dfrac{9}{8}\) or \(1\dfrac{1}{8}\) or 1.125 | A1 | oe fraction, mixed number or decimal |
Additional guidance
| Ignore an incorrect attempt to simplify or convert a correct answer eg \(\dfrac{9}{8} = 1.8\) | M1M1M1A1 |