O-LevelMathematicsGeometry4024/21 · May/June 2017 · Q1211 Marks

(a) [Figure: Triangle ABC] ABC is a triangle. B and D are points on opposite sides of the line AC. DA = 9 cm and CD = 7 cm. (b) [Figure: Quadrilateral PQRS] This is an accurate diagram of quadrilateral PQRS.

(a)(i)Accurately draw and label the point D.[2]
(a)(ii)Measure DÂB .[1]
(a)(iii)(a)Measure the shortest distance from B to AC.[1]
(a)(iii)(b)Work out the area of triangle ABC.[2]
(b)(i)Give a reason why it is not possible for P, Q, R and S to be points on the circumference of a circle.[1]
(b)(ii)(a)T is a point inside PQRS such that it is I more than 6 cm from R II nearer to R than P III nearer to PQ than QR. Construct and shade the region within which T lies.[4]
(b)(ii)(b)Find the maximum possible length of RT.[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[2] D correctly placed to the left of AC
[1] B1 for DA = 9 or CD = 7
[1] 44° to 48°
[1] FT
[1] 2.9 to 3.1
[2] 19.1 to 20.8
[1] B1 for 13.2 to 13.4 seen
[1] Opposite angles are both obtuse or both acute so their total is not 180 Or opposite angles are not supplementary
[4] Correct region shaded
[1] B1 for arc 6 cm from R
[1] B1 for angle bisector of Q
[1] B1 for perpendicular bisector of PR
After B2, SC1 for 'correct' region shaded provided only slight inaccuracy with the other line/curve
[1] 7.9 to 8.3
[1] FT

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