O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2022 · Q311 Marks

A cuboid has height h cm and a square base of edge x cm. The volume of the cuboid is 60 cm³. [Figure with cuboid labeled h and x]

(a)Show that the surface area, A cm², of the cuboid is given by A = 2x² + 240/x .[2]
(b)Complete the table for A = 2x² + 240/x. x: 1, 2, 3, 4, 5, 6, 7, 8. A: 242, 128, 98, 92, (blank), (blank), 132, 158.[2]
(c)On the grid, draw the graph of A = 2x² + 240/x for 1 ≤ x ≤ 8. [Figure with graph grid][3]
(d)Find the minimum possible surface area of the cuboid.[1]
(e)The cuboid has a surface area of 120 cm². The height of the cuboid is greater than the length of the edge of its base. Find the dimensions of the cuboid.[3]

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 2022). The mark or mark type is shown in brackets.

[2] M1 for h = 60/x² seen or xh = 60/x seen A1 for [A=]2x² + 4x(60/x²) → 2x² + 240/x A0 if any errors or A0 if any errors
[2] B1 for each
[3] B2FT for 7 or 8 points correctly plotted or B1FT for 5 or 6 points correctly plotted
[1] FT their minimum point provided < 92
[3] M1 for a correct reading of their graph at A = 120 M1 for 60/(their2.2)² or (120 - 2 × (their2.2)²)/(4 × their 2.2)

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.