Numeracy Higher June 2019 Unit 1 Q5
5. You are given that:
1 gigalitre = 1 000 000 m3
1 megalitre = 1 million litres
Lake Vyrnwy is a reservoir in mid Wales.
(a) Lake Vyrnwy can release between 25 and 45 megalitres of water per day from the dam.
The lake also supplies water through underground pipes to another reservoir at a rate of 230 000 m3 per day.
(i) How many litres are there in 25 megalitres?
Circle your answer. [1]
Circle your answer. [1]
\(25 \times 10^{8}\) \(25 \times 10^{-6}\) \(25 \times 10^{7}\) \(2{\cdot}5 \times 10^{6}\) \(2{\cdot}5 \times 10^{7}\)
(ii) Which is the best estimate for the volume of water passing through the underground pipes per hour?
Circle your answer. [1]
Circle your answer. [1]
8500 m3 9600 m3 10 040 m3 10 400 m3 11 000 m3
(b) Lake Vyrnwy has a surface area of approximately 4 540 000 m2.
Lake Vyrnwy contains 59·7 gigalitres of water.
Lake Vyrnwy contains 59·7 gigalitres of water.
Calculate an estimate of the average depth of the lake.
Give your answer in metres. [3]
Estimate of average depth is …………………… m
(i)
(ii)
| Scheme | Marks | Comments |
|---|---|---|
| \(2.5 \times 10^{7}\) | B1 |
(ii)
| Scheme | Marks | Comments |
|---|---|---|
| 9600 m3 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| (Volume seen or implied) 59 700 000 (m3) or 60 000 000 (m3) OR (Surface area seen or implied, used as) 4.5(4) or 5 | B1 | Accept using index notation or standard form, e.g. 59.7 × 106, 5.97 × 107, 60 × 106, 6 × 107 Accept exact or correctly rounded volume written in m3, i.e. do not accept, e.g. 59 000 000 Ignore any units given |
Average depth calculation, e.g.
| M1 | FT e.g. 'their volume' ÷ 4 540 000 Accept written as a fraction Accept exact or rounded values provided estimates are reasonable Watch for compensating errors, which is M0 and A0 |
| Answer in the range 12 (m) to 13.5 (m) | A1 | CAO, answer must be in this range, no FT |