O-LevelMathematicsVectors and transformations4024/21 · May/June 2014 · Q1012 Marks

(a) p = (1 -3) q = (-2 0) (b) The diagram shows triangles A and B. [Figure 10.1]

(a)(i)Find |p|.[1]
(a)(ii)On the unit grid below, draw and label the vector p - q. [Grid][2]
(a)(iii)The vector r is shown on the unit grid below. It is given that r = ap + bq. Find the values of a and b.[2]
(b)(i)Describe fully the single transformation that maps triangle A onto triangle B.[3]
(b)(ii)(a)The transformation represented by the matrix (1 0; 0 2) maps triangle A onto triangle C. Find the coordinates of the vertices of triangle C.[2]
(b)(ii)(b)Describe fully the single transformation that maps triangle A onto triangle C.[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 (May/June 2014). The mark or mark type is shown in brackets.

[1] 3.16 to 3.163 or √10
[2] B1 for two correct movement without arrow Or one correct movement with arrow
[2] B1 for each
[2] Or SC1 a = -2 and b = -3
[3] B1 Enlargement
[3] B1 Scale factor -2
[3] B1 Centre (3, 1)
[3] BO for question if second transformation mentioned
[2] B1 for 2 correct
[2] B1 Stretch
[2] B1 Factor 2 x-axis invariant

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