O-LevelMathematicsMensuration4024/22 · May/June 2022 · Q414 Marks

[Figure with a pentagon showing lengths 12, 15, 9, 4 and right angles] The diagram shows a pentagon. All the lengths are in centimetres.

(a)(i)Calculate the area of the pentagon.[2]
(a)(ii)Find the perimeter of the pentagon.[3]
(b)[Volume of a sphere = 4/3 πr³] A sphere has a volume of 2572 cm³. Find the radius of the sphere.[3]
(c)(i)[Figure with a cuboid showing dimensions 22.5, 6, 2] A cuboid has dimensions 2 cm by 6 cm by 22.5 cm. Calculate the surface area of the cuboid.[3]
(c)(ii)A cube of edge x cm has the same surface area as the cuboid. Form an equation in x and solve it to find the length of the edge of the cube. Show your working.[3]

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Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

[2] M1 for correct area of a relevant triangle or trapezium
[3] M2 for √((12-4)² + (15-9)²) soi OR M1 for √(8² + k²) oe or √(k² + 6²) oe M1 for 12+15+4+9+ theirh where theirh is from use of Pythagoras
[3] M2 for r³ = (2572×3)/(4×π) oe or M1 for (4/3)πr³ = 2572
[3] M2 for (2×6 + 2×22.5 + 6×22.5) [×2] oe or M1 for two different face areas seen
[3] M2 M1 for 6x² = their (c)(i) oe

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