Higher January 2021 Paper 1 Q3
3 The diagram shows a container for water in the shape of a prism.
Diagram NOT accurately drawn
The rectangular base of the prism, shown shaded in the diagram, is horizontal.
The container is completely full of water.
Tuah is going to use a pump to empty the water from the container so that the volume of water in the container decreases at a constant rate.
The pump starts to empty water from the container at 10 30 and at 12 00 the water level in the container has dropped by 20 cm.
Find the time at which all the water has been pumped out of the container.
(4)
| Scheme | Marks |
|---|---|
| e.g. 30 × 20 × 125 (= 75 000) or 85 × 40 × 125 (= 425 000) or \((60 \times 30 + (85 - 30) \times 40) \times 125\) (= 500 000) oe | M1 |
“75 000” ÷ 1.5 (= 50 000) or “75 000” ÷ 90 (= 833.3... or \(\dfrac{2500}{3}\)) or “425000” ÷ “75000” (= 5.66... or \(\dfrac{17}{3}\)) or “500000” ÷ “75000” (= 6.66... or \(\dfrac{20}{3}\)) | M1 |
| “425 000” ÷ “50 000” (= 8.5) or “425 000” ÷ (“833.3...” × 60) oe (= 8.5) or “5.66…” × 1.5 (= 8.5) or “6.66…” × 1.5 (= 10) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 20 30 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a method to find the volume of water already pumped out or the volume of water left or the total volume of the container
M1: M2 for \(\dfrac{\text{“}425000\text{”}}{\text{“}75000\text{”}} \times 1.5\) oe (= 8.5)
or \(\dfrac{\text{“}500000\text{”}}{\text{“}75000\text{”}} \times 1.5\) oe (= 10)
A1: Allow 8 30 (pm)