Numeracy Higher November 2017 Unit 2 Q6
6. The diagram below shows the locations of the ports of Lindat, Molk and Nuir.
Lindat is due south of Nuir, and Nuir is due west of Molk.
Diagram not drawn to scale
Agnetha lives in Molk.
She travels from Molk to Lindat by ship.
- Lindat is 24 km due south of Nuir.
- The ship sails directly to Lindat on a bearing of 211°.
- The ship has an average speed of 20 km/h.
- The ship leaves at 11:45 a.m.
Calculate Agnetha’s arrival time in Lindat. [7]
| Scheme | Marks | Comments |
|---|---|---|
| Sight of appropriate 31° or 59° in the diagram OR appropriate use of these angles in their calculations | B1 | |
| (Distance from Molk to Lindat =) \(\dfrac{24}{\sin 59(^\circ)}\) OR \(\dfrac{24}{\cos 31(^\circ)}\) | M2 | FT ‘their 31’ or ‘their 59’ provided the angle <90 for M2 or M1 only. A correct method for calculating the distance Molk to Nuir using trigonometry, followed by correct use of Pythagoras is awarded M2. M1 for sin 59(°) = 24/distance OR M1 for cos 31(°) = 24/distance |
| = 27·9(992…) or 28 (km) | A1 | CAO |
| (Time taken to sail from Molk to Lindat =) 27·9(992…) ÷ 20 | M1 | FT ‘their derived 27·9(992…)’ from the use of trigonometry. |
| = 1·4 (hours) (= 1h 24m) | A1 | On FT, accept an answer that has been rounded to 1dp, but it needs to be correct to 1dp for ‘their 27·9(9…)’. |
| (Arrival time =) 1:09pm or 13:09 | A1 | ISW. (Allow 13:09pm). FT ‘their 1·4 hours’ correctly converted provided of equivalent difficulty. On FT, their answer needs to be correct to the nearest minute for ‘their 1·4’ |