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O-LevelAdditional MathematicsVectors in two dimensions4037/12 · May/June 2012 · Q1210 Marks

Answer only one of the following two alternatives. EITHER At 1200 hours, a ship has position vector (54i + 16j) km relative to a lighthouse, where i is a unit vector due East and j is a unit vector due North. The ship is travelling with a speed of 20km h⁻¹ in the direction 3i +4j.

  1. (i)Express OQ and PQ in terms of a and b.[2]
  2. (ii)Express QR in terms of λ, a and b.[2]
  3. (iii)Express QR in terms of μ, a and b.[3]
  4. (iv)Hence find the value of λ and of μ.[3]

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Mark scheme

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

  1. [B1] Allow unsimplified
  2. [B1] Follow through on their OQ, allow unsimplified
  3. [M1] M1 for λa – their OQ
  4. [A1] A1 - allow unsimplified
  5. [M1] M1 for attempt to obtain QR in terms of PQ
  6. [M1] M1 for attempt to simplifiy
  7. [A1] QR = (μ/(1-μ))( (2/3)a - (11/12)b )
  8. [M1] M1 for equating like vectors and attempt to solve
  9. [A1] A1 for each

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About this question

Topic
Vectors in two dimensions, O-Level Additional Mathematics (syllabus 4037). Structured question, 10 marks.
Source
O-Level Additional Mathematics, May/June 2012 Paper 1 Variant 2, question 12.

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