Drawing & Using Graphs: WJEC GCSE Numeracy Higher June 2018 Unit 2 Q7

Numeracy Higher June 2018 Unit 2 Q7

WJECHigherCurrent spec9 marksDrawing & Using Graphs Units & Time

7. Gwen fills a 10-litre bucket with water from a tap.
She turns the tap until it is fully open. The bucket fills up with water, and when Gwen thinks it is close to being full, she slowly closes the tap.
The bucket is full after 20 seconds.

The graph below shows the volume of water in the bucket during the 20 seconds.

Graph of volume of water (litres, 0 to 10) against time t (seconds, 0 to 20): nearly flat to 5 s, rising steeply in a straight line to about 8·5 litres at about 9 s, then curving and levelling off to 10 litres at 20 s

(a) After how many seconds did Gwen start to close the tap? [1]

(b) Estimate at what rate water is entering the bucket at time \(t\) = 10 seconds.
Give your answer in litres per second. [3]

(i) Express 2 litres per second in gallons per minute.
You must show all your working. [3]

Remember
1 gallon = 8 pints

(ii) Can a fully open tap fill a 90-gallon tank in under \(3\tfrac{1}{2}\) minutes?
You must show all your working. [2]

Scheme	Marks	Comments
A time between 9 and 9·5 seconds inclusive	B1

Mark scheme (b)

Scheme	Marks	Comments
Tangent drawn at 10 seconds Idea of increase in y ÷ increase in x	M1 M1	Attempt to draw a tangent at time 10 seconds Needs to come from a tangent to the curved part of the graph Ignore signs for M1 only
Correctly evaluated gradient for their tangent	A1	Dependent on M1M1 awarded

Mark scheme (c)

Scheme	Marks	Comments
(i) 2 × 1·75 × 60 ÷ 8	M2	May be seen in stages M1 for the correct use of 2 with any 2 operations
= 26·25 (gallons/min)	A1	FT only from M2 Accept 26 (gallons/min) from correct working Alternative method: M2 for \(\dfrac{2 \times 60}{4{\cdot}5(46)}\) May be seen in stages M1 for correct use of 2 with 4·5(46) A1 for 26(·…) FT only from M2 Accept 26 (gallons/min) from correct working Note: Accept an answer of 27 (gallons/min) from use of 4·5
(ii) 90 ÷ 26·25	M1	FT ‘their derived 26·25’
= 3·4(2857…) (min) AND e.g. ‘Yes’	A1	Alternative methods: M1 for 26·25 × 3·5 FT ‘their derived 26·25’ A1 for 91(·875) (gallons) AND e.g. ‘Yes’ OR M1 for 90 ÷ 3·5 A1 for 25·7(142…) or 26 (gallons/min) AND e.g. ‘Yes’ FT ‘their derived 26·25’