Numeracy Foundation June 2024 Unit 2 Q7
7. Idris flies from Cardiff to Faro, in Portugal.
The actual flying time is 133 minutes.
The plane flies at an average speed of 8 miles per minute.
Calculate the flying distance between Cardiff and Faro.
Give your answer in miles. [2]
Calculate the plane’s average speed in miles per hour. [2]
Idris takes a cabin bag on board his flight.
His bag measures 55 cm by 40 cm by 23 cm.
The label on his cabin bag says,
| Bag capacity is greater than 48 litres. |
Is this label correct?
Yes ☐ No ☐
You must show all your working and give a reason for your answer. [3]
Idris looks out of the aeroplane window.
He notices a village below.
Idris takes a photograph of the village to try to work out where he is.
From the photograph, he draws a sketch including some parallel streets.
His sketch is shown below.
Diagram not drawn to scale
Find the size of each of the angles \(a\), \(b\), \(c\) and \(d\). [4]
\(a\) = ………… ° \(b\) = ………… ° \(c\) = ………… ° \(d\) = ………… °
| Scheme | Mark | Comments |
|---|---|---|
| (i) 133 × 8 | M1 | |
| 1064 (miles) | A1 | Mark final answer. Allow 1064 km |
| (ii) 8 × 60 | M1 | FT from (a)(i) 60 × ‘their 1064’ ÷ 133 or ‘their 1064’ ÷ \(\frac{133}{60}\) or ‘their 1064’ ÷ 2.2(166…) |
| 480 (mph) | A1 | Allow A1 for 479 (mph) < answer ≤ 483.64 (mph) from 1064 ÷ 2.2(1666…) rounded or truncated to at least 1 d.p. or similar for a correctly evaluated ‘their 1064’ ÷ 2.2(166..) |
| Scheme | Mark | Comments |
|---|---|---|
| 55 × 40 × 23 | M1 | |
| 50 600 (cm3) or 50 600 ml or 50.6 litres | A1 | |
Unambiguously implies ‘Yes’ with one of the following:
| E1 | FT from M1 A0 provided appropriate conclusion and conversion is shown Allow ‘Yes’ with clear use of 1 litre = 1000 cm3, e.g.
|
| Scheme | Mark | Comments |
|---|---|---|
| a = 43(°) | B1 | |
| b = 137(°) | B1 | FT b = 180 - ‘their a’, provided ‘their b’ > 90 and ‘their b’ ≠ 112 |
| c = 112(°) | B1 | FT 360 – (68 + ‘their a’ + ‘their b’), provided:
|
| d = 112(°) | B1 | FT d = ‘their c’, provided 90 < ‘their c’ < 180 |