Higher June 2019 Paper 2 Q18

18 The diagram shows a solid cuboid.

Diagram NOT accurately drawn

The total surface area of the cuboid is \(A\) cm²

Find the maximum value of \(A\).

(5)

Mark scheme

Scheme	Marks
\(x^2\) oe or \(x(12 - 3x)\) oe	M1
\(x^2 + x^2 + 48x - 12x^2\) (\(= 48x - 10x^2\))	M1
\(\text{``}{48 - 20x}\text{''} = 0\) or \(\text{``}{-10}\text{''}[(x - \text{``}{2.4}\text{''})^2 - \text{``}{2.4}\text{''}^2]\) oe	M1
(\(x = 2.4\)) 48 × ‘2.4’ – 10 × ‘2.4’² or ‘−10’ × − ‘2.4’² or ‘−10’ × − ‘5.76’	M1
57.6	A1
	(5)
	(5 marks)

M1: for finding an expression for the area of one face

M1: for a complete expression for \(A\) (6 sides) with brackets expanded

M1: for differentiating a correct expression for \(A\) (allow 1 error) and equating to zero
or
completing the square

M1: ft if previous M1 awarded
for isolating \(x\) and substituting into \(A\)
or
finding max value of \(A\) from completing the square

A1: accept 58 from correct working