1MA0 Higher June 2013 Paper 1 Q17
17 Sumeet has a pond in the shape of a prism.
Diagram NOT accurately drawn
The pond is completely full of water.
Sumeet wants to empty the pond so he can clean it.
Sumeet uses a pump to empty the pond.
The volume of water in the pond decreases at a constant rate.
The level of the water in the pond goes down by 20 cm in the first 30 minutes.
Work out how much more time Sumeet has to wait for the pump to empty the pond completely. (6)
| Answer | Mark | Notes |
|---|---|---|
| 1 hour 45 mins | 6 | M1 for method to find volume of pond, eg \(\frac{1}{2}(1.3 + 0.5) \times 2 \times 1\) (= 1.8) M1 for method to find the volume of water emptied in 30 minutes, eg \(1 \times 2 \times 0.2\) (= 0.4), \(100 \times 200 \times 20\) (= 400000) A1 for correct rate, eg 0.8 m³/hr, 0.4 m³ in 30 minutes M1 for correct method to find total time taken to empty the pond, eg \(\text{``}1.8\text{''} \div \text{``}0.8\text{''}\) M1 for method to find extra time, eg 2 hrs 15 minutes − 30 minutes A1 for 1.75 hours, \(1\frac{3}{4}\) hours, 1 hour 45 mins or 105 mins OR M1 for method to find volume of water emptied in 30 minutes, eg. \(1 \times 2 \times 0.2\) (= 0.4), \(100 \times 200 \times 20\) (= 400000) M1 for method to work out rate of water loss eg. \(\text{``}0.4\text{''} \times 2\) A1 for correct rate, eg 0.8 m³/hr M1 for correct method to work out remaining volume of water eg. \(\frac{1}{2}(1.1 + 0.3) \times 2 \times 1\) (= 1.4) M1 for method to work out time, eg \(\text{``}1.4\text{''} \div \text{``}0.8\text{''}\) A1 for 1.75 hours, \(1\frac{3}{4}\) hours, 1 hour 45 mins or 105 mins NB working could be in 3D or in 2D and in metres or cm throughout |