Higher June 2025 Paper 2 Q21
21. A boat makes the following journey from Port A to Port C.
- It sails 30 km on a bearing of \(108^\circ\) from Port A to Port B.
- It then sails 42 km on a bearing of \(065^\circ\) from Port B to Port C.
Diagram not drawn to scale
On its return journey, the boat travels directly from Port C to Port A.
This journey takes 1 hour and 45 minutes.
Calculate the average speed of the boat on its return journey. [6]
| Scheme | Marks | Comments | ||||||
|---|---|---|---|---|---|---|---|---|
| Answer line takes precedence | ||||||||
| (Angle ABC = \(65 + 180 - 108\) =) \(137^\circ\) | B1 | |||||||
| (AC =) \(\sqrt{30^2 + 42^2 - 2\times30\times42\times\cos(137)}\) | M2 | FT ‘their stated or derived 137’ provided it is obtuse. M1 for (AC2 =) \(30^2 + 42^2 - 2\times30\times42\times\cos(137)\) | ||||||
| = 67.(13…) (km) | A1 | CAO | ||||||
| \(67.(13\ldots) \div 1.75\) or \(67(.13\ldots) \div 105 \times 60\) | M1 | FT ‘their 67.(13.. )’ provided at least M1 awarded. | ||||||
| = 38.3(6…) or 38.4 (km/h) | A1 | FT Allow answers in the range 38.28 to 38.4 or 38 from correct working. Mark final answer
| ||||||
| (6) |