O-LevelMathematicsVectors and transformations4024/11 · May/June 2017 · Q235 Marks
[Figure 23.1 - A parallelogram OPRQ. Vector OP is p and vector OQ is q. S is a point on PR such that PS : SR = 1 : 3.] OPRQ is a parallelogram and S is a point on PR such that PS : SR = 1 : 3. OP = p and OQ = q.
- (a)(i)Express PQ in terms of p and/or q.[1]
- (a)(ii)Express QS, as simply as possible, in terms of p and/or q.[1]
- (b)(i)T is a point on QS extended such that QT = 4/3 QS . Express PT, as simply as possible, in terms of p and/or q.[2]
- (b)(ii)What can you conclude about the points O, P and T?[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 (May/June 2017). The mark or mark type is shown in brackets.
- [1] q - p
- [1] p - 3/4 q or (4p-3q)/4
- [2] PT = 1/3 p M1 for PT = PS + 1/3 QS soi or PT = PQ + QT soi
- [1] O, P and T are collinear oe e.g. T is on OP produced
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