O-LevelMathematicsVectors and transformations4024/22 · Oct/Nov 2021 · Q78 Marks
P is the point (-5, 2), Q is the point (3, 7) and QR = (-4 / 6). OACB is a quadrilateral and N is a point on AB. OA = a and OB = b. OA = 2BC and BN : NA = 1 : 3. [Figure showing a quadrilateral OACB and points N on AB. Vectors OA=a, OB=b. NOT TO SCALE]
- (a)(i)Find the coordinates of the midpoint of PQ.[1]
- (a)(ii)Find the coordinates of point R.[1]
- (a)(iii)Find |QR|.[2]
- (b)(i)Find, in terms of a and b, in its simplest form AB,[1]
- (b)(ii)NC.[3]
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 2021). The mark or mark type is shown in brackets.
- [1]
- [1]
- [2] M1 for (-4)² + 6² oe
- [1]
- [3] M1 for correct vector route along the lines of the diagram B1 for BC = a/2 soi or for NB = 1/4 their (b-a) soi or NA = 3/4 their (a-b) soi
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