O-LevelMathematicsTrigonometry4024/21 · May/June 2022 · Q910 Marks
The diagram shows the positions of three towns, A, B and C. B is on a bearing of 072° from A. C is on a bearing of 150° from A. AB = 300 km and AC = 280 km. [Figure showing towns A, B, C with bearings and lengths]
- (a)Find the bearing of A from C.[1]
- (b)Calculate BC.[4]
- (c)Town D is 145 km from town B. Angle ADB is 120°. Find the two possible bearings of D from A. You may add lines to this sketch to help you. [Figure showing towns A, B with North line and AB=300][5]
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 2022). The mark or mark type is shown in brackets.
- [1] 330°
- [4] 365 or 365.3...
- B1 for [BAC =] 78
- M2 for √(300² + 280² - 2×300×280costheir78) or B2 for 133000 or 133400 to 133500
- or M1 for 300²+2802-2×300×280costheir78
- [5] [0]47.3 or [0]47.25 to [0]47.26 and [0]96.7 or [0]96.74 to [0]96.75
- B4 for [0]47 and [0]97 nfww or [0]47.3 or [0]47.25 to [0]47.26 or [0]96.7 or [0]96.74 to [0]96.75
- or B3 for [DAB =] 24.7 or 24.74 to 24.75
- or M2 for sin A = (145 sin 120) / 300
- or M1 for 145/sin A = 300/sin 120
- After 0 scored SC1 for sketch with 120 and 145 in correct place or 72 + their DAB or 72 – their DAB
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