2D Area & Perimeter: Eduqas GCSE Higher June 2023 Paper 2 Q10

Higher June 2023 Paper 2 Q10

10. In this question, all lengths are in metres.
The diagram shows Terry’s garden.

Diagram not drawn to scale

The patio is a square and the lawn is a rectangle.
The area of the lawn is 172·8 m².

Use an algebraic method to find the area of Terry’s patio. [5]

Mark scheme

Scheme	Marks	Comments
\((5x \times 4x)(x + 4x) = 172.8\) or better	M2	M1 for \(5xy(x + y) = 172.8\) Allow M1 for one of the following: \(x + y \times 5xy = 172.8\) \(5xy \times x + y = 172.8\) \(20x^2 \times 5x\)
\(20x^2 \times 5x = 172.8\) or better	M1	FT ‘their derived \((5x \times 4x)(x + 4x)\)’
\(x = 1.2\)	A1	CAO
(Area patio =) 23.04 (m²)	B1	FT (4 \(\times\) ‘their 1.2’)² provided at least 2 marks previously awarded

Scheme	Marks	Comments
\(\left(5 \times \dfrac{y}{4} \times y\right)\left(\dfrac{y}{4} + y\right) = 172.8\) or better	M2	M1 for \(5xy(x + y) = 172.8\) Allow M1 for one of the following: \(x + y \times 5xy = 172.8\) \(5xy \times x + y = 172.8\) \(\dfrac{5y^2}{4}\) x \(\left(\dfrac{y}{4} + y\right)\)
\(\dfrac{5}{4}y^2 \times \dfrac{5}{4}y = 172.8\)	M1	FT ‘their derived \(\left(5 \times \dfrac{y}{4} \times y\right)\left(\dfrac{y}{4} + y\right)\)’
\(y = 4.8\)	A1	CAO
(Area patio =) 23.04 (m²)	B1	FT (‘their 4.8’)² provided at least 2 marks previously awarded

(5)