Higher November 2024 Paper 2 Q11
11. A ship sails 11 km due south from port A.
It then travels 17 km due east and arrives at port B.
Diagram not drawn to scale
Calculate the bearing of port B from port A. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Finding the angle at Port A) \((x =)\ \tan^{-1}\left(\frac{17}{11}\right)\) | M2 | M1 for \(\tan(x) = \frac{17}{11}\) |
| \((x =)\ 57.09\ldots(^\circ)\) or \(57.1(^\circ)\) or \(57(^\circ)\) | A1 | |
| (Bearing) \(((180 - 57.09)\) or \((90 + 32.9))\) \(122.905\ldots(^\circ)\) or \(122.9(^\circ)\) or \(123(^\circ)\) | B1 | FT ‘their 57.09…’ provided M1 awarded |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Finding the angle at Port B) \((x =)\ \tan^{-1}\left(\frac{11}{17}\right)\) | M2 | M1 for \(\tan(x) = \frac{11}{17}\) |
| \((x =)\ 32.90\ldots(^\circ)\) or \(32.9(^\circ)\) or \(33(^\circ)\) | A1 | |
| (Bearing) \(((180 - 57.09)\) or \((90 + 32.9))\) \(122.905\ldots(^\circ)\) or \(122.9(^\circ)\) or \(123(^\circ)\) | B1 | FT ‘their 32.90…’ provided M1 awarded |
| (4) |