Higher June 2018 Paper 2 Q8
8. Aled decides to pour milk from a full carton into an empty bottle.
The measurements for the carton and the bottle are shown below.
Diagrams not drawn to scale
(a) Is it possible to pour all the milk from the full carton into the bottle?
You must show all your working and give a reason for your answer. [5]
You must show all your working and give a reason for your answer. [5]
Yes ☐ No ☐
(b)
(i) When evaluating your result in part (a), what assumption did you make? [1]
(ii) If your assumption were not true, what impact would this have on your answer? [1]
| Scheme | Marks | Comments |
|---|---|---|
| (Volume of the carton) \(6\times6\times20\) | M1 | |
| 720 (cm3) | A1 | Allow if a drop extra is included, up to a maximum of 10cm3 |
| (Volume in the bottle) \(\pi\times3.5^2\times18.5\) | M1 | |
| 711.6 to 712.1(cm3) | A1 | |
| Conclusion stating or implying ‘No’, with a reason, e.g. ‘No as 720 >712’ OR ‘Yes’, with a reason, e.g. ‘Yes, as the milk will fill up past the height of 18.5cm (beyond the cylindrical part of the bottle)’ | E1 | FT for ‘their volume of the carton’ and ‘their height in the milk bottle’ provided at least M1, M1 previously awarded Accept reasoning based on uncertainty |
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) Assumption stated, e.g. ‘the bottle is in the shape of a cylinder (with height 18.5cm)’, ‘the measurements given are the internal measurements’, ‘no milk in the top of the carton’, ‘no milk in the neck of the bottle’, ‘assumed filled to the top’ | E1 | Do not accept ‘measurements given were not accurate’ Accept ‘measurements were internal measurements’ |
| (b)(ii) Impact, e.g. ‘all the milk may not fit into the bottle’, ‘the milk might overflow in the bottle’, ‘the milk might fill the neck of the bottle’ | E1 | Allow ‘milk may or may not fit’ provided this could reasonably be an impact following ‘their assumption’ |
| (7) |