Numeracy Intermediate June 2024 Unit 2 Q5
5. 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.
What fraction of the total length of the bridge is the section between the two towers?
Give your fraction in its simplest form. [2]
Calculate the length of the wire used to make the cables in kilometres. [2]
The cost of tarmac is £250 per m\(^{3}\).
Calculate the cost of the volume of tarmac needed to resurface the total length of the Severn Bridge. [3]
Some of the tolls charged for a car to enter Wales are given in the table below.
| Year | 2004 | 2009 | 2014 | 2019 |
| Toll for a car | £4.60 | £5.40 | £6.40 | FREE |
In which of the following 5-year periods was there the greatest percentage increase in the toll?
2004 to 20092009 to 20142014 to 2019
State the percentage increase for this 5-year period.
You must show all your working. [4]
The greatest percentage increase in the toll was in the period …………… to …………… .
The percentage increase was ……………
| Scheme | Marks | 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 | Marks | 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 | Marks | 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
|
| Scheme | Marks | Comments |
|---|---|---|
| Ignore any working for ‘2014 to 2019’ Accept working in £ or p consistently | ||
| (2009 to 2014) (100 ×) \(\dfrac{6.40-5.40}{5.40}\) or \(\dfrac{1}{5.40}\) or \(\dfrac{6.40}{5.40}\) (- 1) | M1 | |
| (2004 to 2009) (100 ×) \(\dfrac{5.40-4.60}{4.60}\) or \(\dfrac{0.80}{4.60}\) or \(\dfrac{5.40}{4.60}\) (- 1) | M1 | |
| Choice of ‘2009 to 2014’ AND 18.5(.... %) or 19(%) AND sight of 17(.39...%) or 17.3 (%) or 17.4 (%) or 1.17(...) or 117.(…) or 0.17(...) (for 2004 to 2009) | A2 | Answer space takes precedence Allow percentage increase given as 18(%) Award M mark as well as A mark for a correct percentage from a ‘reverse percentage method’ A1 for sight of any of the following:
If M1 A1 awarded for 2004 to 2009, also award M1 for (2009 to 2014) 1.1739 × 5.40 = (£)6.339 (< 6.40) If M1 A1 awarded for 2009 to 2014, also award M1 for (2004 to 2009) 1.185... × 4.60 = 5.451(8…) (>5.40), with A1 for 18.5…(%) given on the answer line |
Corrected by Westie's Workshop
- The board's mark scheme printed “for (2009 2014)”. Changed to “for (2009 to 2014)” because the word “to” is missing (the rest of the scheme writes “2009 to 2014”).
- The board's mark scheme printed “for (2004 2009)”. Changed to “for (2004 to 2009)” because the word “to” is missing (the rest of the scheme writes “2004 to 2009”).
Original: see the board's mark scheme PDF (link above).