Numeracy Intermediate June 2018 Unit 1 Q7
7. Macy and Gareth are planning a bike ride.
They have a map with a scale of 1:50 000.
Gareth suggests a route that measures a total of 48 cm on the map.
Macy says she could cycle up to 13 miles.
Will Macy be able to cycle the route Gareth is suggesting?
You must show all your working and give a reason for your answer. [5]
| Scheme | Marks | Comments | ||||
|---|---|---|---|---|---|---|
| 1cm : 50 000cm means 1cm is 500 m or 0.5(0) km OR Sight of (48 × 50 000 =) 2 400 000 | B1 | Units given must be correct or measures clearly used correctly FT incorrect map scale conversion with place value error B0, with FT for possible B1, M1, A0, E1, except no FT with use of 50 000 | ||||
| (48cm route is 0.5×48 =) 24 (km), OR 1cm is 5/16 mile | B1 | If map scale conversion is correct then this B1 implies the previous B1 If units are given they must be correct | ||||
| Route is 5 × 24 ÷ 8 or 48 × 5 ÷ 16 or 24 ÷ 1.6 | M1 | FT ‘their 24’ or ‘their 48 × 0.5’ | ||||
| (=) 15 miles | A1 | CAO. Units must be given or implied correctly by comparison with 13 (miles). Alternative M and A marks
| ||||
| Reasonable conclusion, e.g. ‘Yes, Macy could push herself to cycle a bit further’, ‘No, Macy only wants to cycle 13 miles’, ‘Don’t know, could depend on the hills’, “no, it is 2 miles longer than Macy can ride’ | E1 | Depends on at least 2 marks previously awarded including M1 and FT reasonable for ‘their number of miles/km’ |