Higher June 2018 Paper 1R Q18
18 Here is a quadrilateral \(PQRS\).
Diagram NOT accurately drawn
Angle \(SRQ\) is acute.
Work out the size of angle \(SQR\).
Give your answer correct to 1 decimal place.
(6)
| Scheme | Marks |
|---|---|
| \(SQ^2 = 8^2 + 12^2 - 2 \times 8 \times 12 \times \cos 120^\circ\) | M1 |
| \((SQ) = \sqrt{304}\) | M1 |
| \(\dfrac{\sin R}{\text{``}{\sqrt{304}}\text{''}} = \dfrac{\sin 27^\circ}{9}\) | M1 |
| \(R = \sin^{-1}\left(\dfrac{\sin 27^\circ \times \text{``}{\sqrt{304}}\text{''}}{9}\right)\) | M1 |
| 61.58 | A1 |
| 91.4 | B1 |
| (6) | |
| (6 marks) |
Notes
M1: If this mark is awarded then ft on the remaining M marks
M1: for correct order of operations e.g. 64 + 144 + 96 or 304 or 17.4…. or \(4\sqrt{19}\)
M1: can be implied by 61.5833...
A1: for 61.58 - 61.6
B1: ft dep M3
180 – “61.6” – 27