Numeracy Intermediate June 2024 Unit 2 Q2
2. 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 | Marks | 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’ ÷ \(\dfrac{133}{60}\) 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 | Marks | Comments |
|---|---|---|
| 55 × 40 × 23 | M1 | |
| 50 600 (cm\(^{3}\)) 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 cm\(^{3}\), e.g.
|
| Scheme | Marks | 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 |
Corrected by Westie's Workshop
- The board's mark scheme printed “their c’ ≠ ‘their b’”. Changed to “‘their c’ ≠ ‘their b’” because the opening quotation mark is missing.
Original: see the board's mark scheme PDF (link above).