O-LevelMathematicsTrigonometry4024/21 · Oct/Nov 2016 · Q712 Marks
The diagram shows the positions of four islands at A, B, C and D. A is due north of B. DÂC = 48°, CÂB = 55° and BĈA = 51°. AC = 19 km and AD = 27 km. [Figure 7.1]
- (a)Calculate the bearing of D from A.[1]
- (b)Calculate the bearing of A from C.[1]
- (c)Calculate the distance between A and B.[3]
- (d)Calculate the distance between D and C.[3]
- (e)A boat leaves D and sails, at a constant speed, in a straight line to A. It takes 3 hours and 36 minutes to sail from D to A. X is the point on DA that is closest to C. Calculate the time, correct to the nearest minute, the boat takes to travel from D to X.[4]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [1] (a) 283°
- [1] (b) 055°
- [3] (c) [AB = ] 15.4 or 15.36[...] B1 for ABC = 74° M1 for AB / sin 51 = 19 / sin ABC
- [3] (d) [DC = ] 20.08 to 20.1 M2 for [DC² =] 19² + 27² – 2 × 19 × 27 × cos 48 or M1 for cosine formula with one error
- [4] (e) Correct working leading to 114 minutes or 1 hour 54 minutes M1 for AX = 19 × cos 48 or for CX = 19 × sin 48 M1 for DX = 27 – their AX Or for DX = √(their DC² – their CX²) M1 for Time = 216 × (their DX / 27) oe
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