O-LevelMathematicsTrigonometry4024/22 · May/June 2023 · Q912 Marks
[Figure 9.1] A, B and C are points on horizontal ground. The bearing of B from A is 072°. The bearing of C from A is 205°. AB = 170m and AC = 95 m. (c) [Figure 9.2] The point D lies on the horizontal ground, due south of A and due east of C.
- (a)Calculate BC.[4]
- (b)Find the bearing of A from C.[2]
- (c)(i)Show that AD = 86.1m, correct to 1 decimal place.[2]
- (c)(ii)A point X is at the top of a vertical mast at A. The angle of elevation of X from B is 7°. Calculate the angle of elevation of X from D.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [4] B1 for angle BAC = 133
- M2 for √(170² + 95² – 2×170×95cos(their133)) oe
- OR M1 for 170² + 95² -2×170×95cos(their133) oe
- A1 for 60000 or 59950 to 59960
- 245 nfww or 244.8 to 244.9
- [2] B1 for angle CAS = 25 or angle ACN = 25 or angle NAC= 155
- or M1 for 205 – 180
- [0]25
- [M1] cos(their25) = AD/95 or sin(90 – their25) = AD/95 oe
- [A1] 86.09[9...] or 86.10
- [4] M2 for AX = 170tan7 oe
- or M1 for tan7 = AX/170
- M1 for tan [...] = theirAX/86.1 oe
- 13.6 or 13.62 to 13.63 nfww
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