O-LevelMathematicsVectors and transformations4024/22 · Oct/Nov 2015 · Q1112 Marks

ABCDE is a pentagon. AFB, AHE and BGC are straight lines.

(a)(i)AE = (6, 1). Calculate |AE|.[1]
(a)(ii)H is the midpoint of AE, and FH = (2, -3.5). Find AF.[2]
(a)(iii)(a)G divides BC in the ratio 1 : 2. BG = (2.5, 0) and CD = (-1, -7). Find GD.[1]
(a)(iii)(b)Explain why GD is parallel to FH.[1]
(a)(iv)B is the point (3, 10). Find the coordinates of D.[1]
(b)(i)Flag A is mapped onto flag T by the translation (-3, -6). Draw, and label, flag T.[1]
(b)(ii)Describe fully the enlargement that will map flag A onto flag B.[2]
(b)(iii)Find the centre of the rotation that will map flag A onto flag C.[1]
(b)(iv)Rotate flag B through 45° anticlockwise about the origin. Label the image R.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

[1] 6.08
[2] M1 for AF = AH + HF oe or B1 for (1/2)(6, 1)
(4, 4)
[1] (3) = (2.5, 0) + (-1, -7)
(1.5, -7)
[1] dep
GD = 2 FH_stated or appropriate numerical vector statement
[1ft] (9.5, 3)
[1] Correct image
[2] B1 for either
Centre (4, 0) oe Scale factor ×2 oe
[1] (5, 2)
[2] B1 for either Stem of flag R on or parallel to y = – x or Hypotenuse of flag parallel to y-axis. SC1 for correct clockwise rotation
Correct image

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