O-LevelMathematicsMensuration4024/21 · Oct/Nov 2023 · Q914 Marks

The diagram shows a triangular prism. AB = 6cm, angle BAC = 55° and the length of the prism is 20 cm. The area of triangle ABC is 34.4 cm².

(a)(i)Calculate the volume of the prism. Give the units of your answer.[2]
(a)(ii)Show that AC = 14.0cm, correct to 3 significant figures.[3]
(a)(iii)Calculate the surface area of the prism.[5]
(b)The diagram shows a cuboid with a square base. The height of the cuboid is 8 cm. The volume of the cuboid is 98 cm³. Calculate PQ.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[2] (a)(i) 688 cm³
[2] (a)(i) B1 for 688
[2] (a)(i) B1 for cm³
[3] (a)(ii) 13.998[...] or 14.00 A1
[3] (a)(ii) M2 M1 for 1/2 x 6 x AC x sin 55 = 34.4
[5] (a)(iii) 702 or 701.6 to 701.8
[5] (a)(iii) B2 for [BC² =] 135.4 to 135.6... soi
[5] (a)(iii) or M2 for sqrt(6^2 + 14^2 - 2x6x14cos55) or M1 for 6^2 + 14^2 - 2x6x14cos55
[5] (a)(iii) AND M2 for 2x34.4+6x20+14x20+their BCx20 oe or M1 for sum of areas of 4 faces from the M2 calculation
[4] (b) 9.41 or 9.407...
[4] (b) M1 for area of base = 98/8 soi
[4] (b) M2 for sqrt(their 12.25+their12.25+8^2) oe or M1 for sqrt(their 12.25+their12.25) oe or sqrt(their12.25+8^2) oe

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