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O-LevelAdditional MathematicsVectors in two dimensions4037/12 · May/June 2017 · Q34 Marks

Vectors i and j are unit vectors parallel to the x-axis and y-axis respectively.

  1. (a)The vector v has a magnitude of 3√5 units and has the same direction as i– 2j. Find v giving your answer in the form ai + bj, where a and b are integers.[2]
  2. (b)The velocity vector w makes an angle of 30° with the positive x-axis and is such that |w|= 2. Find w giving your answer in the form √c i + dj, where c and d are integers.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. [M1] attempt to find the magnitude of (i – 2j) and use
  2. [A1] for 3i-6j only
  3. [M1] attempt to use trigonometry correctly to obtain components
  4. [A1] for √3i + j

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About this question

Topic
Vectors in two dimensions, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source
O-Level Additional Mathematics, May/June 2017 Paper 1 Variant 2, question 3.

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