O-LevelMathematicsMensuration4024/23 · May/June 2025 · Q1810 Marks

The diagram shows a cuboid. The length of the cuboid is x cm. The height of the cuboid is 3 times its length. The width of the cuboid is 4 cm less than its length.

(a)Write down expressions, in terms of x, for the height of the cuboid and the width of the cuboid.[2]
(b)The surface area of the cuboid is 200cm². Form an equation in x and show that it simplifies to 7x²-16x-100 = 0.[4]
(c)Solve the equation 7x²-16x-100 = 0. You must show all your working and give your answers correct to 2 decimal places.[3]
(d)Find the height of the cuboid.[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[2] [height = ] 3x
[width = ] x - 4
B1 for each
[4] 2x(3x) + 2x(x – 4) + 2(3x)(x – 4)
Or 2 (x(3x) + x(x – 4) + 3x(x – 4))
M2 FT their algebraic expressions in x for height and width
B1FT for two different areas seen e.g. two of x(3x), x(x – 4), (3x)(x – 4) or better
M1dep Dep on M2 earned
Set equal to 200 and expansion of their algebraic brackets
A1 with no errors or omissions
[3] 5.09 and -2.81
B2 for √(-16)²-4×7×-100 or for -(-16)±√k / 2x7 OR 8/7 ± √(100/7 + (8/7)²) oe
B1 for each
[1] 15.27 to 15.3
FT 3 × their positive root from (c)

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