O-LevelMathematicsVectors and transformations4024/12 · Oct/Nov 2022 · Q265 Marks
OAC is a triangle and B is a point on AC such that AB : BC = 3 : 2. OA = a and OB = b. [Figure of OAC triangle with vectors a and b] NOT TO SCALE
- (a)Find OC in terms of a and b, giving your answer in its simplest form.[3]
- (b)D is a point on OC such that OD = b - 2/5 a. Show that OABD is a trapezium.[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 2022). The mark or mark type is shown in brackets.
- [3] 5/3 b - 2/3 a final answer
- B2 for AC = 5/3 (b-a) or 5/3 b - 5/3 a
- or BC = 2/3 (b-a) or 2/3 b - 2/3 a
- or M1 for a correct vector route for OC or [AB =] b-a
- If 0 scored, SC1 for answer -5/3 b + 2/3 a oe
- [M1] DB = 2/5 a or BD = -2/5 a
- [A1] DB is a multiple of OA, hence parallel oe
- Or BD = 2/5 AO, hence parallel
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