O-LevelMathematicsVectors and transformations4024/12 · Oct/Nov 2023 · Q245 Marks
[Figure 24] OAB is a triangle. P lies on AB and AP : PB = 2:3. OA = 4a and OP = 3a+2b.
- (a)(i)Find, in terms of a and b, giving your answer in its simplest form AP[1]
- (a)(ii)Find, in terms of a and b, giving your answer in its simplest form OB.[3]
- (b)Q is a point on OA such that QP is parallel to OB. Find QP.[1]
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 2023). The mark or mark type is shown in brackets.
- [1] 2b – a final answer
- [3] (3/2)a + 5b final answer
- or (3a+10b)/2 final answer
- M1 for a correct vector route for OB along the lines of the diagram
- or [AB =] (5/2)AP or 2AB=5AP oe stated
- or [PB =] (3/2)AP or 2PB=3AP oe stated
- B1 FT for AB = (5/2) their (2b – a) oe
- or [PB =] (3/5) their (2b – a) oe
- [1] (3/5)a + 2b oe
- FT (2/5) × their OB or (2/5) × their OB
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