Higher November 2019 Paper 1 Q29
29 Show that the value of \(\quad 5\sin 30^\circ \times \cos 30^\circ \times 8\tan 30^\circ \quad\) is an integer. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \((\sin 30^\circ =)\ \dfrac{1}{2}\) or \((\cos 30^\circ =)\ \dfrac{\sqrt{3}}{2}\) or \((\tan 30^\circ =)\ \dfrac{1}{\sqrt{3}}\) or \(\dfrac{\sqrt{3}}{3}\) or \(\left(\dfrac{1/2}{\sqrt{3}/2}\right)\) | M1 | may be seen beside question |
| \(5\left(\dfrac{1}{2}\right) \times \dfrac{\sqrt{3}}{2} \times 8\left(\dfrac{1}{\sqrt{3}}\right)\) or \(5\left(\dfrac{1}{2}\right) \times \dfrac{\sqrt{3}}{2} \times 8\left(\dfrac{1/2}{\sqrt{3}/2}\right)\) or \(\dfrac{5}{2} \times \dfrac{\sqrt{3}}{2} \times \dfrac{8\sqrt{3}}{3}\) | M1dep | oe multiplication string with all correct values |
| \(\dfrac{40\sqrt{3}}{4\sqrt{3}}\) or \(\dfrac{40\sqrt{3}\sqrt{3}}{12}\) | M1dep | oe single fraction with roots rationalised or able to be cancelled |
| 10 from correct working | A1 | |
| Alternative method 2: substituting \(\dfrac{\sin}{\cos}\) for tan and cancelling | ||
| \(5\sin 30^\circ \times \cos 30^\circ \times 8\dfrac{\sin 30^\circ}{\cos 30^\circ}\) | M1 | |
| \(40\sin^2 30^\circ\) | M1dep | oe cancels \(\cos 30^\circ\) |
| \(40\left(\dfrac{1}{2}\right)^2\) | M1dep | oe |
| 10 from correct working | A1 | |