O-LevelMathematicsMensuration4024/22 · Oct/Nov 2014 · Q510 Marks
[Figure 5.1] The diagram shows the perimeter of a 400 m running track. It consists of a rectangle measuring 100m by d metres and two semicircles of diameter d metres. The length of each semicircular arc is 100m. [Figure 5.2] S is the starting point and finishing point for the 400m race for a runner in the inside lane. A runner in an outer lane is always 3 m from the inner perimeter. The runner in the outer lane starts at A, runs 400m and finishes at T. TS = 3 m.
- (a)Calculate d.[2]
- (b)Calculate the total area of the region inside the running track.[3]
- (c)(i)Calculate the length of the arc TA.[3]
- (c)(ii)O is the centre of a semi-circular part of the track. Calculate AỘT.[2]
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 (Oct/Nov 2014). The mark or mark type is shown in brackets.
- [2] 63.7 or 63.6 (m)
- [2] M1 for π×d/2 = 100
- [3] 9540 to 9560
- [3] M1 for πr² soi and M1 for their circular area + 100 × their (a)
- [3] 18.7 to 19.0 (m)
- [3] M1 for 2πR And M1 for their 2πR – 200 or πR – 100
- [2] 30.8 to 31.1
- [2] M1 for θ/360 × 2πR oe
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