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O-LevelMathematicsVectors and transformations4024/11 · Oct/Nov 2014 · Q238 Marks

The vector f and the point A are shown on the grid. On the grid, mark and label the point B when AB = f+g, (where f = (3/2) and g = (4/1))

  1. (a)(i)The vector f and the point A are shown on the grid. On the grid, mark and label the point B when AB = f+g, (where f = (3/2) and g = (4/1))[1]
  2. (a)(ii)the point C when AC =-2h, (where h = (-1/2))[1]
  3. (a)(iii)the point D when AD = 2f- 3g.[1]
  4. (b)(i)In the diagram, OP = p and OQ = q. R is the point on PQ such that PR:RQ=1:2. Express PQ, as simply as possible, in terms of p and q.[1]
  5. (b)(ii)Express OR, as simply as possible, in terms of p and q.[1]
  6. (b)(iii)T is a point such that TR = 2OP. Express OT, as simply as possible, in terms of p and q.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

  1. [1] (a)(i) the point B marked correctly
  2. [1] (a)(ii) the point C marked correctly
  3. [1] (a)(iii) the point D marked correctly
  4. If [0] scored in (a), in (aiii) award B1 for the vector (-6/1) soi.
  5. [1] (b)(i) q - p
  6. [1] (b)(ii) (2/3)p + (1/3)q
  7. [2] (b)(iii) (1/3)q - (4/3)p, or FT their(ii) – 2p
  8. M1 for OT = OR + RT Or for OT = OP + PR + RT Or for OT = OQ + QR + RT Or equivalents in terms of p and q.

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About this question

Topic
Vectors and transformations, O-Level Mathematics (syllabus 4024). Structured question, 8 marks.
Source
O-Level Mathematics, Oct/Nov 2014 Paper 1 Variant 1, question 23.

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