O-LevelMathematicsVectors and transformations4024/22 · Oct/Nov 2016 · Q1012 Marks
ACB and OCD are straight lines. AC : CB = 1:2. OA = 3a and OB = 6b. [Figure showing a quadrilateral with vectors OA=3a, OB=6b, and points C, D, with lines ACB and OCD]
- (a)(i)Express AB in terms of a and b.[1]
- (a)(ii)Express AC in terms of a and b.[1]
- (a)(iii)BD = 5a-b. Showing your working clearly, find OC : CD .[4]
- (b)(i)Describe fully the single transformation that maps triangle A onto triangle B. [Figure showing triangle A and triangle B on a grid][2]
- (b)(ii)(a)Triangle A is mapped onto triangle C by the shear H in which the y-axis is invariant, and H(2, 1) = (2, 3). On the grid, draw and label triangle C.[2]
- (b)(ii)(b)State the shear factor of H.[1]
- (b)(ii)(c)Find the matrix that represents H.[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 (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [1] 6b – 3a oe isw
- [1ft] 2b – a oe isw
- [4] 2:3 cao NB www
- [1] M1+M1 for two of OC = OA+ AC, CD = CB + BD, OD = OB + BD
- [1] A1 for OC = 2a + 2b ft or CD = 3a + 3b ft or OD = 5a + 5b
- [2] Reflection y = -x oe
- [1] B1 for either
- [2] Triangle C with vertices (2, 3),(2, 2), (5, 5)
- [1] B1 for two vertices correct or
- [1] M1 for a correct construction line involving H(2, 1) or H(2, 0)
- [1] 1
- [1ft] (1 0 / 1 1)
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