Numeracy Foundation June 2024 Unit 2 Q10
10. The Severn Bridge was built in 1966 to allow vehicles to travel between England and Wales.
The bridge has a width of 23 m and a total length of 1600 m.
The section of the bridge between the two towers is 988 m long.
The tarmac road surface is 0·035 m thick.
The cables from the towers to support the road are made from 18 000 miles of wire.
(a)
What fraction of the total length of the bridge is the section between the two towers?
Give your fraction in its simplest form. [2]
(b)
Calculate the length of the wire used to make the cables in kilometres. [2]
(c)
The cost of tarmac is £250 per m3.
Calculate the cost of the volume of the tarmac needed to resurface the total length of the Severn Bridge. [3]
| Scheme | Mark | Comments |
|---|---|---|
| \(\dfrac{247}{400}\) | B2 | Mark final answer B1 for sight of \(\dfrac{988}{1600}\) or \(\dfrac{494}{800}\) If no marks, award SC1 for a final answer of \(\dfrac{153}{400}\) |
| Scheme | Mark | Comments |
|---|---|---|
| 18000 × 8 ÷ 5 or 18000 × 1.6 or equivalent | M1 | Accept use of × 1.6 to × 1.613 or ÷ 0.62 to ÷ 0.625 |
| 28 800 (km) | A1 | Also accept answers in the range 28960 (km) to 28980 (km) |
| Scheme | Mark | Comments |
|---|---|---|
| (Cost of tarmac) 1600 × 23 × 0.035 × 250 | M2 | M1 for a product including any 3 of these 4 values Allow M1 for
|
| (£) 322 000 | A1 | CAO If no marks, award SC1 for an unsupported answer with leading digits 322 and all other digits zero e.g. 32 200 or 3 220 000 If no marks, award either
|