O-LevelMathematicsTrigonometry4024/22 · Oct/Nov 2023 · Q911 Marks

[Figure Diagram of Rectangular Field ABCD with North arrow at A]

(a)(i)ABCD is a rectangular field. C is due south of A. AB = 450 m and BC = 210 m. Martha walks at an average speed of 5.2 km/h. Calculate the time Martha takes to walk once around the perimeter of the field. Give your answer correct to the nearest minute.[3]
(a)(ii)Show that the bearing of D from A is 245°, correct to 3 significant figures.[3]
(b)PQR is a triangle and S is a point on PR. PS = 10.3 cm, QR = 12.6 cm, QPS = 42° and QRS = 35°. Calculate QS. [Figure Triangle PQR][5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[3] M2 for (2×450+2×210)/5.2 × 60/1000 oe
or M1 for (2×450+2×210)/5.2 oe isw
or for (450+210)÷5.2 × 60/1000
[3] M2 M1 for tan[DAC]=450/210 oe
or tan[CAB]=210/450 oe
A1 244.98...
[5] M2 for [PQ =] (12.6 sin 35) / sin 42
or [PR =] (12.6 sin 103) / sin 42
or M1 for sin 35/PQ = sin 42/12.6 oe
or M1 for sin 103/PR = sin 42/12.6 oe
M2 for any correct method using their PQ or their PR to find QS e.g. sqrt(PQ²+10.3²-2xPQ×10.3cos 42)
or M1 for any correct method for QS² e.g. PQ²+10.3²-2xPQ×10.3cos42

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