O-LevelMathematicsGeometry4024/21 · May/June 2019 · Q511 Marks

ABCD is a parallelogram. AD = 6cm, AB = 8 cm and BD = 11 cm.

(a)ABCD is a parallelogram. AD = 6cm, AB = 8 cm and BD = 11 cm.
(a)(i)Using a ruler and compasses only, construct an accurate drawing of ABCD. AD has been drawn for you.[3]
(a)(ii)Measure DÂB.[1]
(a)(iii)E is the point on BD such that AE is the shortest distance from A to BD. Draw and measure AE.[1]
(b)PQRS is a trapezium with PQ parallel to SR and SPQ = 90°. SQ = 15 cm, QR = 11 cm and PŜQ = 58°.
(b)(i)Calculate PS.[2]
(b)(ii)Calculate the obtuse angle SRQ.[4]

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Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[3] Correct parallelogram with construction arcs at B and C B2 for correct parallelogram without arcs or B1 for two of AB = 8 or DC = 8 or BD = 11 or BC = 6
[1] 101 to 105 FT their triangle ABD
[1] 4[.0] to 4.4 with AE drawn FT their AE from correct parallelogram
[2] 7.95 or 7.948 to 7.949 M1 for cos 58 = PS/15 oe
[4] 133.7 or 133.72 to 133.73 B1 for 32 and M2 for sin R = (15 sin their 32)/11 or M1 for 15/(sin R) = 11/(sin their 32) oe

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