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O-LevelAdditional MathematicsVectors in two dimensions4037/22 · Oct/Nov 2012 · Q98 Marks

A plane, whose speed in still air is 420kmh⁻¹, travels directly from A to B, a distance of 1000km. The bearing of B from A is 230° and there is a wind of 80kmh⁻¹ from the east.

  1. (i)Find the bearing on which the plane was steered.[4]
  2. (ii)Find the time taken for the journey.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.

  1. [B1] Correct triangle
  2. [M1] Use of sine or cosine rule in any triangle with some of 80,420, their v and an angle.
  3. [A1] α = 7.03 or 7
  4. [A1] Bearing 223 (230 – α)
  5. [M1] Use of sine or cosine rule in any triangle with 80 or 420 or both.
  6. [A1] v = 478
  7. [M1] Use time = 1000/v
  8. [A1] 2.09 hours or 2 hours 5minutes

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About this question

Topic
Vectors in two dimensions, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2012 Paper 2 Variant 2, question 9.

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