O-LevelMathematicsMensuration4024/21 · Oct/Nov 2016 · Q58 Marks
The diagram shows a semicircle with radii OP and OQ drawn. The circle, centre C, touches the radii at A and B and the semicircle at T. The radius of the circle is 1.8 cm. BĈA = 120°. [Figure 5.1]
- (a)Calculate the length of the minor arc AB.[2]
- (b)The shaded region lies between the circle and the radii OP and OQ. Calculate the perimeter of this shaded region.[3]
- (c)(i)Show that the radius of the semicircle is 5.4 cm.[2]
- (c)(ii)Calculate the length of BQ.[1]
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 2016). The mark or mark type is shown in brackets.
- [2] (a) 3.76 to 3.77... M1 for (120/360) × 2 × π × 1.8 oe
- [3ft] (b) 9.99 to 10.01 FT their (a) + 6.235[...] M2 for [OB = ] 1.8 tan 60 oe or M1 for tan 60 = [...] / 1.8 oe
- [2] (c)(i) Full calculation, including calculation for OC = 3.6 and radius = TC + OC M1 for cos 60 = 1.8 / OC oe or OC² = 1.8² + their OB²
- [1ft] (c)(ii) 2.28 FT 5.4 - their OB
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