O-LevelAdditional MathematicsVectors in two dimensions4037/21 · May/June 2011 · Q98 Marks

A coastguard station receives a distress call from a ship which is travelling at 15 kmh⁻¹ on a bearing of 150°. A lifeboat leaves the coastguard station at 1500 hours; at this time the ship is at a distance of 30 km on a bearing of 270°. The lifeboat travels in a straight line at constant speed and reaches the ship at 1540 hours.

Mark scheme

Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.

[1] (i) Diagram with 60° (or similar vector resolution)
[1] (i) 10 (km distance by ship) or 45 (km distance for alternative method)
[1] (i) Uses cosine rule
[1] (i) D² = 10² + 30² – 2 × 10 × 30 × cos60 or V² = 15² + 45² – 2 × 15 × 45 × cos60
[1] (i) 39.7 or 39.8 or 15√7
[1] (ii) sinα/10 = sin60/(10√7) (or sinβ/30 = sin60/(10√7) and use β)
[1] (ii) α = 19.1 or β = 101
[1] (ii) 251

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Topic: Vectors in two dimensions, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, May/June 2011 Paper 2 Variant 1, question 9.

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