Units & Time: WJEC GCSE Numeracy Foundation June 2018 Unit 2 Q2

Numeracy Foundation June 2018 Unit 2 Q2

WJECFoundationCurrent spec5 marksUnits & Time

2. The Celtic Trail is part of the UK National Cycle Network.

Map of south Wales showing the Celtic Trail through Fishguard, Broad Haven, Laugharne, Kidwelly, Mumbles, Pontypridd and Chepstow

(a)

Arfon plans a cycle tour on the Celtic Trail from Fishguard to Chepstow.
The route is split into stages.

Stage	Starting from	Going to	Distance (miles)
1	Fishguard	Broad Haven	36
2	Broad Haven	Laugharne	46
3	Laugharne	Kidwelly	32
4	Kidwelly	Mumbles	29
5	Mumbles	Pontypridd	40
6	Pontypridd	Chepstow	44

(i) What is the total distance that Arfon plans to cycle? [1]

(ii)

Arfon plans to take 3 days for his cycle tour.
He cannot cycle further than 85 miles in one day.

Complete the table to show how Arfon could plan his route from Fishguard to Chepstow. [2]

Day	Starting from	Going to
1	Fishguard
2
3		Chepstow

(b)

Bryn plans to cycle a total of 425 miles from Fishguard to London.
He uses Arfon’s plan from (a)(ii) for the first three days of his cycle ride.
Bryn also cannot cycle more than 85 miles in one day.

Explain why Bryn cannot complete his cycle ride from Fishguard to London in 5 days.

You must show all your working. [2]

Mark scheme (a)

Scheme

Marks

Comments

(a)(i) 227 (miles)

(a)(ii)

Day	Starting from	Going to	Distance (miles)
1	Fishguard	Laugharne	82
2	Laugharne	Mumbles	61
3	Mumbles	Chepstow	84

B1 for incorrect place names with correct totals 82, 61 and 84 in correct order.
Or
B1 for incorrect place names with totals that sum to ‘their 227’.
Or
B1 for correct place names with one or more incorrect totals or totals omitted.
Or
B1 for one or more correct rows.
Or
B1 for Broad Haven to Kidwelly 78 (miles) or for Kidwelly to Pontypridd 69 (miles)

Mark scheme (b)

Scheme	Marks	Comments
A valid explanation involving appropriate calculation(s) e.g. ‘425 ÷ 5 = 85 so he would have to ride 85 miles every day but his first three days are all less than 85 so the last two days would be more than 85’. ‘227 + 85 + 85 = 397 which is not enough to get him to London.’ ‘(425 – 227) ÷ 2 = 99. So, the last two days will need an average of 99 miles per day’. ‘425 – 227 – 85 = 113 so the 5^th day will need 113 miles’. ‘425 – 227 – 85 – 85 = 28 so there will be 28 miles left after 5 days. 425 ÷ 5 = 85 so each day needs 85 miles on average but three days had less than 85 miles ‘85 × 5 = 425. If each day was 85 miles he would travel 425 miles but the first three days are less than 85 miles.	E2	FT ‘their 227’ Award E1 for sight of an appropriate calculation(s) that could lead to a correct explanation e.g. 227 + 85 + 85 or 397, Or (425 – 227) ÷ 2 or 198 ÷ 2 or 99 Or 425 – 227 – 85 or 113 Or 425 – 227 – 85 – 85 or 28 Or 425 ÷ 5 Or 425 ÷ 85 Or 85 × 5 E1 NOT awarded for 85 or 425 alone Or E1 for an appropriate explanation without supporting calculation e.g. ‘It will take him 6 days for the whole journey to London.’ Or ‘It will take him one extra day.’ Or ‘When he arrives at Chepstow he will have 198 miles to go to London and this is not enough with 85 miles each day Do not accept a response containing only a repeat of the facts of the question FT ‘their 227’ provided their answer is consistent with the ride NOT being possible and 170<’their 227’<255.