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Numeracy Higher June 2023 Unit 1 Q2

WJECHigherCurrent spec7 marksCompound MeasuresPrismsRatio & Basic Proportion

2.

(a)
Map with North arrow showing Llangollen, Pontcysyllte Aqueduct, Llantysilio, Acrefair, Froncysyllte, Chirk Castle, Glyn Ceiriog, Dolywern, Pontfadog, Llwynmawr and Bronygarth, with the A5 road

The direct straight-line distance between Llangollen and the Pontcysyllte Aqueduct is 5·6 km.
On the map this distance is 5·6 cm.
What is the scale of the map?
Circle your answer. [1]

1 : 10    1 : 1000    1 : 10 000    1 : 100 000    1 : 1 000 000

(b) The Pontcysyllte Aqueduct was built to carry the Llangollen canal over a valley.

The following facts about the section of the canal over the aqueduct were found on the internet.

  • It has a rectangular uniform cross-section.
  • It is 300 m in length.
  • It holds 1 500 000 litres of water.
  • It takes 2 hours to drain the water.
(i) The section of the canal over the aqueduct is to be drained.

Calculate the number of litres of water that drain from this section of the canal per minute.
You may assume that the water drains from the canal at a constant rate.
You must show all your working. [3]

(ii) Calculate the area of the canal’s uniform cross-section.
Give your answer in cm2. [3]
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