Higher November 2021 Paper 2 Q4
4.
(a) The diagram shows the side view of a design for a ramp to a building.
Use calculations to show that the design should be approved. [3]
Diagram not drawn to scale
For the design to be approved, the angle of rise must not be more than 4·8°.Use calculations to show that the design should be approved. [3]
(b)
It was not approved and needs to be completely removed.
The ramp is a triangular prism and is 2·5 m wide.
How many cubic metres of concrete will need to be removed?
You must show all your working. [5]
Diagram not drawn to scale
The diagram shows a concrete ramp to a different building.It was not approved and needs to be completely removed.
The ramp is a triangular prism and is 2·5 m wide.
How many cubic metres of concrete will need to be removed?
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| \(\sin^{-1}\left(\dfrac{0.5}{6}\right)\) | M2 | M1 for \(\sin(\ ) = \dfrac{0.5}{6}\) |
| 4.7(8…) | A1 | Unsupported 4.7(8…) is awarded no marks |
| Scheme | Marks | Comments |
|---|---|---|
| \(\sqrt{1.8^2 - 0.6^2}\) (= 1.69705….) | M2 | M1 for \(1.8^2 - 0.6^2\) or \(x^2 + 0.6^2 = 1.8^2\) |
| \(\dfrac{\sqrt{1.8^2 - 0.6^2} \times 0.6}{2}\) | M1 | Allow FT from use of \(\sqrt{1.8^2 + 0.6^2}\) ( = 1.897….) |
| \(\times\ 2.5\) | m1 | |
| 1.27(…) or 1.28 or 1.3 (m\(^3\)) | A1 | CAO |