O-LevelMathematicsTrigonometry4024/21 · May/June 2017 · Q610 Marks
(a) [Figure with D, B, North arrow, A, C with distances 15, 12, 8] A, B, C and D are four towns. B is 12 km due north of A, C is 8 km due east of A and D is 15 km due west of B. (b) [Figure with T, S, North arrows] The diagram shows the position of a clock tower, T, and a statue, S, drawn to a scale of 1 cm to 75 m.
- (a)(i)Calculate the distance of B from C.[2]
- (a)(ii)Calculate the bearing of A from D.[3]
- (b)(i)Using measurements taken from the diagram, find the actual distance between T and S.[2]
- (b)(ii)A fountain, F, is situated 450m from T on a bearing of 210°. Draw and label F.[2]
- (b)(iii)Using measurements taken from the diagram, find the bearing of F from S.[1]
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 (May/June 2017). The mark or mark type is shown in brackets.
- [2] 14.4[2...]
- [1] M1 for 12² + 8²
- [3] 128.6° to 129°
- [1] M1 for tan θ = 12/15 or tan θ = 15/12
- [1] A1 for 38.6 to 38.7 or 51.3 to 51.4
- After A0, SC1 for 90 + tan⁻¹(15/12) evaluated or 180 – tan⁻¹(12/15) evaluated
- [2] 472 to 488
- [1] B1 for 6.3 to 6.5 seen
- [2] F correctly placed
- [1] M1 for either TF = 6 cm plotted or correct angle
- [1] 242° to 248°
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