Numeracy Foundation June 2023 Unit 2 Q1
1. A group of 9 friends from Cardiff raised money for charity.
They took part in the Welsh Three Peaks challenge.
They had to climb the mountains Snowdon, Cader Idris and Pen y Fan in less than 24 hours.
The table below shows the road distances between the places listed above.
| Cardiff | |||
| 160 miles | Snowdon | ||
| 127 miles | 69 miles | Cader Idris | |
| 42 miles | 125 miles | 92 miles | Pen y Fan |
What is the distance between Cardiff and Cader Idris? [1]
Circle your answer.
92 miles 127 miles 42 miles 69 miles 125 miles
The friends travelled by minibus from:
- Cardiff to Snowdon
- Snowdon to Cader Idris
- Cader Idris to Pen y Fan
- Pen y Fan to Cardiff.
Calculate the total distance the friends travelled by minibus. [3]
In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Here are the team’s start times and finish times for the three mountains they climbed.
| Mountain | Started climbing | Finished climbing |
|---|---|---|
| Snowdon | 04:00 | 08:30 |
| Cader Idris | 11:00 | 16:20 |
| Pen y Fan | 18:50 | 21:05 |
Find the total time the team spent climbing the three mountains.
Give your answer in hours and minutes.
You must show all your working. [5 + 2 OCW]
The friends walked a total distance of 31·05 km when climbing the three mountains.
They walked 14·6 km when climbing Snowdon.
They walked 10 050 m when climbing Cader Idris.
Find the distance they walked when climbing Pen y Fan.
Write your answer in kilometres.
You must show all your working. [3]
The distance walked when climbing Pen y Fan was …………… km
The friends raised the following amounts of money for charity.
£540 £1452 £53 £28 £280 £350 £300 £500 £340
Mr Morris says,
“I think the mean amount of money raised per person is greater than £400.”
Show that Mr Morris is correct.
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 127 miles | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| Identification of the 4 correct distances needed: 160, 69, 92, 42 | B1 | May be seen in the bullet list or in the table (only 4 values to be explicitly identified for B1) May be implied in later working e.g. a total of 726 implies adding the 4 correct values twice. |
| 160 + 69 + 92 + 42 | M1 | FT the sum of 4 distances provided at least 3 correct For example: Award B0M1A1 for: 160 + 125 + 92 + 42 = 419 |
| 363 (miles) | A1 | If no marks awarded, award SC1 for:
|
| Scheme | Marks | Comments |
|---|---|---|
| (Snowdon = ) 4 (hours) 30 (mins) or 4 ½ (hours) or 270 (minutes) | B1 | Allow incorrect notation but penalise in OCW Allow 4:30 or 4.3(0) |
| (Cader Idris = ) 5 (hours) 20 (mins) or 320 (minutes) | B1 | Allow 5:20 or 5.2(0) |
| (Pen y Fan = ) 2 (hours) 15 (mins) or 135 (minutes) | B1 | Allow 2:15 or 2.15 |
| (Total time =) 4 (hours) 30 (mins)+5 (hours) 20 (mins)+2 (hours) 15 (mins) or equivalent | M1 | Award M1 for adding ‘their’ 3 times even if there is a mix of units and/or notation. FT ‘their 4 (hours) 30 (mins) ‘ + ‘their 5 (hours) 20 (mins)’ + ‘their 2 (hours) 15 (mins)’ or equivalent |
| (Total time =) 12 (hours) 5 (mins) | A1 | FT ‘their total time’ correctly evaluated and converted into hours and minutes Award A1 for 12:05 or 12.05 but A0 for 12:5 or 12.5 Award A0 for an answer of 11 (hours) 65 (mins) Note: 4 hours 30mins + 5 hours 20 mins + 2 hours 55 mins = 12 hours 5 mins is awarded B1B1B0M1A0 |
| Scheme | Marks | Comments |
|---|---|---|
| Organisation and communication | OC1 | For OC1, candidates will be expected to: • present their response in a structured way • explain to the reader what they are doing at each step of their response • lay out their explanations and working in a way that is clear and logical • write a conclusion that draws together their results and explains what their answer means |
| Writing | W1 | For W1, candidates will be expected to: • show all their working • make few, if any, errors in spelling, punctuation and grammar • use correct mathematical form in their working • use appropriate terminology, units, etc. |
| Scheme | Marks | Comments |
|---|---|---|
| Sight of 10·05 (km) | B1 | May be implied in later working |
| 31·05 – 14·6 – 10·05 or 31.05 – (14.6 + 10.05) or 31.05 – 24.65 | M1 | FT ‘their 10·05’ for M1 including 10 050 |
| 6·4 (km) | A1 | FT 31·05 – 14·6 – ‘their 10.05’ correctly evaluated and given in km. For A1, do not FT use of 10050(m) or a value that leads to a negative answer Note- use of 10.5 instead of 10.05: 31.05 – (14.6 + 10.5) or 31.05 – 25.1 = 5.95 is awarded B0M1A1 |
Alternative
Alternative method: (printed in italics in the mark scheme)
| Scheme | Marks | Comments |
|---|---|---|
| Sight of 31 050 (m) AND 14 600 (m) | B1 | May be implied in later working |
| 31 050 – 14 600 – 10 050 or equivalent | M1 | FT ‘their 31 050’ and ‘their 14 600’ for M1 including 31·05 and 14·6 |
| 6·4 (km) | A1 | FT ‘their 31 050’ and ‘their 14 600’ correctly evaluated AND the answer given in km |
| Scheme | Marks | Comments |
|---|---|---|
| 540+1452+53+28+280+350+300+500+340 (=(£)3843) | M1 | Attempt to add all the values. Allow a total in the range of 3303 to 4383 as evidence of adding Allow one omission or one repeated value |
| ÷ 9 | m1 | FT ‘their 3843’ Award M1 m1 A0 for 540+1452+53+28+280+350+300+500+340 ÷ 9 (=3540.77…) |
| (£)427 (this is more than £400) | A1 | CAO |
Alternative
Alternative method: (printed in italics in the mark scheme)
| Scheme | Marks | Comments |
|---|---|---|
| 540+1452+53+28+280+350+300+500+340 (=(£)3843) | M1 | Attempt to add all the values. Allow a total in the range of 3303 and 4383 as evidence of adding Allow one omission or one repeated value |
| 400 × 9 (= £)3600) | M1 | |
| (£)3843 is more than (£)3600 | A1 | CAO |