O-LevelMathematicsTrigonometry4024/21 · May/June 2014 · Q912 Marks
[Figure 9] The diagram shows a field on horizontal ground. The side AB is next to a straight road XY. AB = 130m, BC = 164m and ABC = 115°.
- (a)Calculate AC.[3]
- (b)Work out the area of the field.[2]
- (c)The field is to be sown with grass seed. Each square metre of the field is sown with 3.25 g of seed. The seed is only sold in 5 kg bags. How many bags of grass seed must be bought?[2]
- (d)A bird is hovering directly above B. The angle of elevation of the bird from A is 18.5°. Calculate the height of the bird above B.[2]
- (e)Calculate the shortest distance from C to the road XY.[3]
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 2014). The mark or mark type is shown in brackets.
- [3] M1 for 130^2 +164^2 +or−[2]×130×164× cos 115
- [3] And M1 for AC^2 =130^2 +164^2 - 2×130×164× cos115
- [2] M1 for 1/2 × 130 × 164 × sin115
- [2] M1 for their 9660×3.25/5000 or 6(.2) or 6.3
- [2] M1 for 130 tan 18.5
- [3] B1 for 65° or 25° seen
- [3] M1 for 164 × sin '65' or 164 × cos '25' soi
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