Compound Measures: WJEC GCSE Numeracy Intermediate November 2018 Unit 2 Q6

Numeracy Intermediate November 2018 Unit 2 Q6

WJECIntermediateCurrent spec11 marksCompound Measures Units & Time

6. 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]

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.

How much petrol does the lawn mower use for every 100 metres that Emyr walks?
Give your answer in litres. [3]

“The petrol for my lawn mower costs me approximately 60p per pint.”

Is Emyr correct?
You must show all your working. [3]

Yes ☐ No ☐

(d) Emyr’s friend claims that she walks \(1\frac{7}{8}\) miles when she cuts her lawn.
Approximately how far is this in metres?
Circle your answer. [1]

780 metres 1200 metres 2400 metres 3000 metres 3400 metres

Mark scheme (a)

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, award 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

Corrected by Westie's Workshop

The board's mark scheme printed “If no marks, awarded SC1”. Changed to “If no marks, award SC1” because every other special-case instruction in the scheme reads “If no marks, award SC1”.

Original: see the board's mark scheme PDF (link above).

Mark scheme (b)

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	M1	FT ‘their 25 × 300’
0.06 (litres)	A1

Alternative

6(b) Alternative method:

Scheme	Marks	Comments
4.5 ÷ 25 (= 0.18)	M1
× 100 ÷ 300	m1	Allow use of 33.3(...) × 9 for 300
0.06 (litres)	A1	FT allowed use of 33.3(...) × 9 for 300 leading to an answer of 0.06(... litres)

Mark scheme (c)

Scheme	Marks	Comments
Any of the following conversions 1 litre ≈ 1.75 pints 1 pint ≈ 568 ml 1 gallon = 8 pints AND 1 gallon ≈ 4.5(46...) litres OR 1 litre ≈ 0.22 gallon	B1	Also accept the following throughout: 1 litre ≈ 1.76 pints 1 pint ≈ 567 ml 1 pint ≈ 569 ml 1 pint ≈ 570 ml 1 gallon = 8 pints AND 1 litre ≈ 0.219 gallon
Any of the following methods 1(.)3(0) ÷ 1.75 1(.)3(0) × 568 ÷ 1000 \(\dfrac{1(.)3(0) \div 0.22}{8}\) \(\dfrac{1(.)3(0) \times 4.5(46\ldots)}{8}\)	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

6(c) Alternative method 1:

Scheme	Marks	Comments
1 litre ≈ 1.75 pints OR 1 pint ≈ 568 ml	B1	Also accept the following throughout: 1 litre ≈ 1.76 pints 1 pint ≈ 567 ml 1 pint ≈ 569 ml 1 pint ≈ 570 ml
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

6(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