Foundation November 2019 Paper 2 Q21
21.
(a) 
Shireen has a new shed.
The walls of the shed are vertical.
The shed stands on horizontal ground.
The uniform cross-section has one line of symmetry.
The diagram below shows some of the measurements of the cross-section.
Diagram not drawn to scale
Calculate the size of the angle between the roof of the shed and the horizontal. [4]
(b) 
Petra has a mathematically similar shed.
Diagram not drawn to scale
Calculate the two missing measurements on the diagram above.
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| Sight of appropriate measurements 0.8 (m) and 1.2 (m) | B1 | |
| Full method to find the correct angle, e.g. tan \(x\) = (0.8 / 1.2) | M1 | FT ‘their 2.5 – 1.7’ and ‘their 2.4 ÷ 2’ |
| (\(x\) =) \(\tan^{-1}\) (0.8/1.2) | m1 | |
| 33.69...(°) or 33.7(°) or 34(°) | A1 | If no marks, then award SC1 for an answer of 56(.3°) (or equivalent unrounded irrespective of any labelling on the diagram) |
| Scheme | Marks | Comments |
|---|---|---|
| 2.4 × 2.04 ÷ 1.7 or 2.5 × 2.04 ÷ 1.7 | M1 | |
| 2.88 (m) or 2.9 (m) | A1 | |
| 3 (m) | A1 | |
| (7) |