O-LevelMathematicsVectors and transformations4024/21 · Oct/Nov 2015 · Q68 Marks
The diagram shows the vectors PQ and QR . PQ = (5 / 2) and QR = (a / b) Find a and b.
- (a)(i)The diagram shows the vectors PQ and QR . PQ = (5 / 2) and QR = (a / b) Find a and b.[2]
- (a)(ii)Calculate |PQ|.[2]
- (b)(i)OACB is a parallelogram. OA = a, OB = b and D is the point such that 2OB = BD. E is the midpoint of CD. Express CÉ, as simply as possible, in terms of a and b.[1]
- (b)(ii)Express OE, as simply as possible, in terms of a and b.[1]
- (b)(iii)F is a point on BC such that OF = kOE. Find BF: FC.[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 2015). The mark or mark type is shown in brackets.
- [2] a = 1, b = -3
- B1 for one correct
- [2] 5.38 to 5.39 or √29
- M1 for √5² + 2²
- [1] 1/2 b - 1/2 a or 1/2 (2b-a) final answer
- [1] 2b + 1/2 a or 1/2 (a+4b) final answer
- [2dep] λ: 3λ
- B1dep for b + 1/4 a seen
- or n(b + 1/4 a) seen
- or k = 1/2 or OF = 1/2 OE oe
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