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O-LevelAdditional MathematicsVectors in two dimensions4037/12 · May/June 2021 · Q35 Marks

The diagram shows the quadrilateral OABC such that OA = a, OB = b and OC = c. The lines OB and AC intersect at the point P, such that AP : PC = 3:2. [Figure 3.1]

  1. (a)Find OP in terms of a and c.[3]
  2. (b)Given also that OP : PB = 2 : 3, show that 2b = 3c+2a.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

  1. [1] B1 AC = c – a
  2. [1] M1 Maybe implied, for correct use of ratio OP=a+3/5(their AC) or c–2/5(their AC)
  3. [1] A1 Allow unsimplified
  4. [1] B1 OP = 2/5 b oe
  5. [1] B1 Dep on previous B mark for equating vectors and rearrangement to obtain AG
  6. [1] (B1) Need a clear indication of the method used, in the form of a correct unsimplified statement.
  7. [1] (B1) Dep for simplification to obtain AG

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About this question

Topic
Vectors in two dimensions, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2021 Paper 1 Variant 2, question 3.

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