O-LevelMathematicsMensuration4024/22 · Oct/Nov 2014 · Q410 Marks

[Figure 4.1] The diagram shows a solid triangular prism. The dimensions are in metres. [Figure 4.2] The diagrams show the cross-sections of a ramp A and a triangular prism B. The triangular prism B can move up and down the ramp A. The ramp is inclined at 25° to the horizontal.

(a)(i)Calculate the volume of the prism.[2]
(a)(ii)Calculate the total surface area of the prism.[4]
(b)(i)When the prism has moved 2m up the ramp, it has risen h metres vertically. Calculate h.[2]
(b)(ii)As it moves, the uppermost face of the prism B remains horizontal. The length of the horizontal edge of the face is 0.6m. The length of the vertical edge of the prism is y metres. Calculate y.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

[2] 105
[2] B1 for (1/2) × 7 × 3 × 10 or M1 for Area of cross section × 10 soi
[4] 197.2 (m²)
[4] M1 for 3² + 7² and M1 for area of one triangular face and M1 for area of one rectangular face
[2] 0.845
[2] M1 for h/2 = sin 25 oe
[2] 0.280
[2] M1 for y/0.6 = tan[...] oe or SC1 for 25

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