O-LevelMathematicsVectors and transformations4024/11 · Oct/Nov 2023 · Q235 Marks
In the diagram, OABC is a parallelogram. OA = a and OC = c. X is the midpoint of AC. Y is the point on AB where AY : YB = 2 : 1. Express, as simply as possible, in terms of a and c [Figure Parallelogram]
- (a)AC[1]
- (b)the position vector of X[2]
- (c)YX.[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 2023). The mark or mark type is shown in brackets.
- [1] (a) c - a
- [2] (b) 1/2 a + 1/2 c oe simplified vector
- [2] M1 for a correct route along the lines of the diagram or B1FT for AX = 1/2 (c - a) or CX = 1/2 (a - c)
- [2] (c) 1/6 a - 1/3 c oe simplified vector
- [2] M1 for a correct route for YX along the lines of the diagram but can include correct OX or B1 for AY = 2/3 c or BY = -1/3 c
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