Numeracy Higher November 2018 Unit 2 Q2
2. Emyr has set his lawn mower to work at a constant speed of 2000 m per hour.
He walks a distance of 300 m when he cuts his lawn.
(a)
(i) Use this information to calculate how long Emyr takes to cut his lawn.
Give your answer in minutes. [2]
Give your answer in minutes. [2]
It takes Emyr …………… minutes.
(ii) What assumption have you made? [1]
(iii) What impact would this have on the time you calculated in answering (a)(i)? [1]
(b) Emyr cuts his lawn 25 times a year.
He uses 4·5 litres of petrol in his lawn mower each year.
He uses 4·5 litres of petrol in his lawn mower each year.
How much petrol does the lawn mower use for every 100 metres that Emyr walks?
Give your answer in litres. [3]
(c) Petrol costs £1.30 per litre.
Emyr says,
“The petrol for my lawn mower costs me approximately 60p per pint.”
Is Emyr correct?
You must show all your working. [3]
Yes ☐ No ☐
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(\dfrac{300}{2000}\) × 60 or 300 ÷ (2000 ÷ 60) or 60 ÷ (2000 ÷ 300) or equivalent | M1 | May be seen in stages |
| 9 (minutes) | A1 | ISW Allow 9.1 (minutes) from premature approximation If no marks, awarded SC1 for an answer or sight of 3/20 or 0.15 (ignore units) |
| (ii) Assumption, e.g. ‘he was walking in a straight line’, ‘no turning’, ‘he didn’t stop’, ‘lawn mower didn’t run out of petrol’, | E1 | Allow, e.g. ‘lawn mower goes the same distance as Emyr’, ‘didn’t push the mower faster than it was set’, ‘didn’t hold the lawn mower back’, ‘Emyr kept going at a constant / same speed’ Do not accept, e.g. ‘(lawn mower) kept going at a constant / same speed’ ‘flat terrain’, ‘Emyr can walk fast enough to keep up with the mower’ |
| (iii) Impact, e.g. ‘it could take longer to cut’, ‘more time needed’, 'the answer is shorter than it will be', | E1 | Strict FT from (a)(ii) Allow, e.g. 'longer (time)', ‘increased (time)’ Do not accept e.g. 'shorter (time)', ‘could have been shorter or longer time’, ‘time could have been affected / impacted’, ‘it could vary’ Do not accept contradictions |
| Scheme | Marks | Comments |
|---|---|---|
| (4.5 litres for 25 × 300=) 7500 (m) | B1 | Allow for (33.3... × 9 × 25 =) 7492.5 to 7500 (m) |
| (Cutting 100 metre uses)100 × 4.5 ÷ 7500 0.06 (litres) | M1 A1 | FT ‘their 25 × 300’ |
Alternative
2(b) Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| 4.5 ÷ 25 (= 0.18) × 100 ÷ 300 0.06 (litres) | M1 m1 A1 | Allow use of 33.3(...) × 9 for 300 FT allowed use of 33.3(...) × 9 for 300 leading to an answer of 0.06(... litres) |
| Scheme | Marks | Comments |
|---|---|---|
Any of the following conversions
| B1 | Also accept the following throughout:
|
Any of the following methods
| M1 | |
| Answer in the range (£)0.73 to (£)0.74(3) or 73 to 74(.3p) AND Conclusion ‘No’ | A1 | Accept £0.74(...)p Do not accept 0.73p, 0.74(...)p, £73 or £74 Do not accept ‘Yes’ unless statement saying e.g. ‘74p is fairly close to 60p’, i.e. a comparison stated |
Alternative
2(c) Alternative method 1:
| Scheme | Marks | Comments |
|---|---|---|
| 1 litre ≈ 1.75 pints OR 1 pint ≈ 568 ml | B1 | Also accept the following throughout:
|
| 60 × 1.75 OR 60 × 1000 ÷ 568 | M1 | |
| Answer in the range (£)1.05 or 105(p) to (£)1.06 or 106(p) AND conclusion 'No' | A1 | Accept £1.05p or £1.06p Do not accept £105 or £106 or 1.05p or 1.06p Do not accept ‘Yes’ unless statement saying e.g. ‘(£)1.05 is fairly close to (£)1.30’, i.e. a comparison stated |
Alternative
2(c) Alternative method 2:
| Scheme | Marks | Comments |
|---|---|---|
| 1 pint > 0.5 litre or 2 pints > 1 litre | B1 | May be expressed in words |
| (But) 60 < 130 ÷ 2 or 60 < 65 or 2 × 60 < 130 or equivalent in £s | M1 | Accept 60p < £1.30 ÷ 2 etc. with correct units included |
| Conclusion ‘No’ | A1 | Do not accept ‘Yes’ unless statement saying e.g. ‘60(p) is fairly close to 65(p)’, i.e. a comparison stated |