O-LevelMathematicsVectors and transformations4024/12 · Oct/Nov 2017 · Q276 Marks
In the diagram, OP = (-3, 4) and PQ = (2, 0).
- (a)Find |OP|+|PQ|.[3]
- (b)(i)T is the point where PT = kPQ. (i) Express OT as a column vector in terms of k.[1]
- (b)(ii)M is the point such that O, T and M lie on a straight line and OM = (24, 16). Find the value of k.[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 2017). The mark or mark type is shown in brackets.
- [3] 27(a) 7
- M1 for |OP| = √(-3)² + (4)²
- B1 for |PQ| = 2
- [1] 27(b)(i) ((-3+2k) (4)) oe
- [2] 27(b)(ii) 4½ oe
- B1 for expressing OM as a multiple (by 4) of OT
- or B1 for T is (6, 4); or for OT = ((6) (4))
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