O-LevelMathematicsVectors and transformations4024/12 · May/June 2022 · Q254 Marks
OABC and OPQR are parallelograms. A is a point on OP and C is a point on OR. OA = a and OC = c. OA : OP = 1 : 4 and OC : CR = 2 : 3. [Figure showing two parallelograms OABC and OPQR, with A on OP and C on OR. Vectors a and c are shown.]
- (a)Find OR in terms of c.[1]
- (b)Find CQ, as simply as possible, in terms of a and c.[2]
- (c)Find the ratio area OABC : area OPQR.[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 2022). The mark or mark type is shown in brackets.
- [1] (a) 5/2 c oe final answer
- [2] (b) 4a + 3c/2 or 4a + 1.5c oe final answer B1 for final answer 4a + kc oe or ka+1.5c oe, k≠0 or AP = 3a soi or M1 for a correct route along the lines of the diagram using the given vertex letters
- [1] (c) 1 : 10 oe
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