O-LevelMathematicsTrigonometry4024/22 · Oct/Nov 2019 · Q710 Marks
A field is in the shape of a quadrilateral PQRS. A path crosses the field from P to R. PQ = 280 m, RS = 146 m and PR = 325 m. S is on a bearing of 042° from P, PŜR = 108° and RPQ = 38°.
- (a)Calculate the bearing of R from P.[4]
- (b)(i)Show that QR = 202m, correct to the nearest metre.[3]
- (b)(ii)Mia walks at a constant speed of 5.5 km/h. Calculate the time it takes her to walk from Q to R. Give your answer in minutes and seconds, correct to the nearest second.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [4] [0]67.3 or [0]67.29...
- [4] B3 for [∠SPR =] 25.3 or 25.29...
- [4] or M2 for [sin SPR =] (146 sin 108)/325
- [4] or M1 for 146/sin SPR = 325/sin 108 oe
- [4] AND M1 for their SPR+42
- [3] [QR^2 =] 280^2+325^2-2×280×325×cos38
- [3] M1
- [3] = 201.5... [= 202]
- [3] A2 A1 for [QR^2 =] 40 607.[...]
- [3] 2 minutes 12 seconds
- [3] M2 for (202/(1000×5.5))×60[×60] oe
- [3] or M1 for figs 202 / figs 5.5
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