O-LevelMathematicsVectors and transformations4024/21 · Oct/Nov 2014 · Q912 Marks

The diagram shows triangle A and octagon B.

(a)Find the gradient of the line of symmetry of triangle A.[1]
(b)Triangle A is mapped onto triangle C by a reflection in the line y = x . Draw and label triangle C.[2]
(c)Write down the equation of the line of symmetry of octagon B that is parallel to the y-axis.[1]
(d)State the order of rotational symmetry of octagon B.[1]
(e)Octagon B is mapped onto octagon D by an enlargement, scale factor 2 and centre (-3, -3). Draw and label octagon D.[2]
(f)(i)A mat is made from six identical octagons, each similar to octagon B, and two squar in the sketch below. The lengths of the short sides of the octagons are each 15cm. Calculate the area of one of these octagons.[2]
(f)(ii)Find the length of a diagonal of one of the squares.[1]
(f)(iii)Calculate the total area of the mat.[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 2014). The mark or mark type is shown in brackets.

[1] 1
[2] correct triangle
[2] B1 for two vertices correct or for an incorrect reflection
[1] x = -2.5
[1] 4
[2] Correct octagon
[2] M1 for 6 correct vertices or octagon scale factor 2 incorrectly placed
[2] 1575
[2] B1 for any correct relevant area st 2025 or 1125 or 112.5 soi or M1 for a complete, consistent, metho
[1] 30
[2ft] 10350
[2ft] ft their 900 + 6 × their 1575
[2ft] B1 for 450 seen or M1 for complete, consistent, method

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