Higher June 2018 Paper 1 Q30
30 Show that the value of \(\quad \cos 30^\circ \times \tan 60^\circ + \sin 30^\circ \quad\) is an integer. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{\sqrt{3}}{2} \times \sqrt{3} + \dfrac{1}{2}\) \(= \dfrac{3}{2} + \dfrac{1}{2}\) \(= 2\) | B3 | B2 \(\dfrac{\sqrt{3}}{2} \times \sqrt{3} + \dfrac{1}{2}\) B1 \(\cos 30^\circ = \dfrac{\sqrt{3}}{2}\) or \(\tan 60^\circ = \sqrt{3}\) or \(\sin 30^\circ = \dfrac{1}{2}\) |
Additional guidance
For B3 all steps must be shown
Allow \(\dfrac{\sqrt{3}}{2} \times \sqrt{3} + \dfrac{1}{2}\) given as \(\dfrac{\sqrt{3}}{2} \times \sqrt{3}\), followed by their \(\dfrac{3}{2} + \dfrac{1}{2}\)
Allow equivalent expressions for all trig values
eg
\(\cos 30^\circ = \sqrt{\dfrac{3}{4}} \quad \sin 30^\circ = \dfrac{\sqrt{1}}{2} \quad \tan 60^\circ = \dfrac{\sqrt{3}}{\sqrt{1}}\)
For B1 allow the trig value(s) given in a table unless contradicted in working