Numeracy Higher June 2025 Unit 2 Q11
11. Pupils in Ysgol Ddwysaint have designed a new bike shelter.
It is made of 3 clear plastic sheets.
The two ends of the shelter are equal in size.
The back and roof of the shelter are made from one curved rectangular sheet that connects the two end sheets.
The bike shelter is 6 m long.
Diagram not drawn to scale
One of the end sheets is shown below.
\(AC\) is an arc of a circle with centre \(O\) and radius 2·5 m.
\(BC\) = 1·4 m and \(A\hat{O}C\) = 75º.
Diagram not drawn to scale
Calculate the total area of plastic used to make the bike shelter. [6]
| Scheme | Mark | Comments |
|---|---|---|
| (Area of curved rectangular sheet =) \(\dfrac{75}{360}\)×2×\(\pi\)×2.5×6 | M1 | Accept values of \(\pi\) from 3.14 to 3.142 |
| = 19.6 to 19.64 | A1 | Or 25\(\pi\)/4 or equivalent Note: an answer of 19.6(…) from \(\pi\)×2.5\(^2\) is awarded M0A0 If no marks awarded, SC1 for any one of the following:
|
| (Area of an end sheet =) \(\dfrac{75}{360}\) × \(\pi\) × 2.5\(^2\) − \(\dfrac{1}{2}\) × 2.5 × (2.5 – 1.4) × sin75 or equivalent (= 4.08 to 4.1) (= 1.32 to 1.33) | M2 | May be embedded within the calculation for both ends M1 for any one of the following:
|
| = 2.75 to 2.8 (m\(^2\)) | A1 | CAO May be implied by (2 × (2.75 to 2.8) =) 5.5 to 5.6 |
| (Total area = 19.634… + 2 × 2.762… =) 25.1 to 25.24 (m\(^2\)) | B1 | Allow an answer of 25 (m\(^2\)) provided from correct working FT ‘their 19.6 to 19.64’ + 2 × ‘their 2.75 to 2.8’ provided at least 2 method marks previously awarded |