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O-LevelMathematicsVectors and transformations4024/12 · Oct/Nov 2024 · Q264 Marks

In the diagram, OA = a, OB = 2b and AB : BC = 1 : 3 . OBD is a straight line. [Figure showing a triangle OAC with B on OC and D on OB extended, vectors a and 2b shown, NOT TO SCALE]

  1. (a)Express AB in terms of a and b.[1]
  2. (b)Show that OC = 8b-3a.[2]
  3. (c)AD=kOC. Find the value of k.[1]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [1] 2b – a final answer
  2. [2] [OC =] a + 4(2b - a) oe
  3. [2] or [OC =] 2b + 3(2b - a) oe
  4. [2] with correct working leading to [OC =] 8b - 3a
  5. [2] M1 for AC = 4(2b – a) or BC = 3(2b – a)
  6. [2] or AC = 4(their(2b – a))
  7. [2] or BC = 3(their(2b – a))
  8. [2] or for a correct route for OC seen e.g. [OC =] OA + AC oe
  9. [2] or [OC =] OB + BC oe
  10. [1] 1/3

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About this question

Topic
Vectors and transformations, O-Level Mathematics (syllabus 4024). Structured question, 4 marks.
Source
O-Level Mathematics, Oct/Nov 2024 Paper 1 Variant 2, question 26.

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