O-LevelAdditional MathematicsVectors in two dimensions4037/21 · Oct/Nov 2010 · Q97 Marks

A plane, whose speed in still air is 250 kmh⁻¹, flies directly from A to B, where B is 500 km from A on a bearing of 060°. There is a constant wind of 80 kmh⁻¹ blowing from the south. Find, to the nearest minute, the time taken for the flight.

(a)A plane, whose speed in still air is 250 kmh⁻¹, flies directly from A to B, where B is 500 km from A on a bearing of 060°. There is a constant wind of 80 kmh⁻¹ blowing from the south. Find, to the nearest minute, the time taken for the flight.[7]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.

[M1] sin α / 80 = sin 60 / 250
[A1] α = 16.1
[A1√] β = 104
[DM1] v² = 80² + 250² – 2 × 80 × 250 × cos β or v / sin β = 250 / sin 60 = 80 / sin α
[A1] v = 280(.2...)
[DM1] t = 500 / v
[A1] 1 hour 47 minutes or 107 mins

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Topic: Vectors in two dimensions, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2010 Paper 2 Variant 1, question 9.

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