Line Graphs


Introduction


Scales are related to ratios

Scales are used on maps, drawings etc., as well as for scale models.


There are two ways the scale could be stated


  As a straightforward relation between the dimensions on the map/drawing etc. and the real-life dimensions.

e.g.    2 cm to 1 km



  more mathematically, as a ratio

e.g.    1 : 50 000

     This particular ratio is the same as '2 cm to 1 km' because

2 cm x 50 000
= 100 000 cm
= 1 kilometer







The Bounty
Length 366 mm,   Scale 1:87

Ark Royal

Length 406 mm,   Scale 1:600


Concorde

Length 425 mm,   Scale 1:144

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Quick Quiz     What is the true length of distances depicted by the following lengths and scales ?


  1. 1.   3 cm on a scale of 1:44
  2. 2.   5 cm on a scale of 1:72
  3. 3.   12.5 cm on a scale of 2cm to 1 km.
  4. 4.   12 mm on a scale of 1:600
  5. 5.   1.2 m on a scale of 1:7

Quick Quiz     What is the length which would represent the following true lengths using the scales given ?


  1. 1.   25 m on a scale of 1:44
  2. 2.   235 m on a scale of 1:72
  3. 3.   13.5 km on a scale of 2cm to 1 km
  4. 4.   12 m on a scale of 1 mm to 5 m
  5. 5.   1400 m on a scale of 1:7

Quick Quiz     Represent the following scales in terms of the scale convention 1:number, as in 1:44, for example.


  1. 1.  2 cm to 1 km
  2. 2.   4 cm to 1 km
  3. 3.  4.5 cm to 10 km.
  4. 4.   1 mm to 2.5 m
  5. 5.   1 m to 2.5 km
  6. 6.   1 cm to 0.5 km

Quick Quiz     Calculate the true lengths represented by these models




  1. Boeing 777

    210 mm long at a scale of 1:300



  2. Volkswagen Beetle

    120 mm long at a scale of 1:32



  3. Tiger Tank

    82 mm long at a scale of 1:72



  4. Graf Zeppelin

    352 mm at a scale of 1:720

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Past Exam Questions


Some friends are planning a camping holiday in May. The table shows information on the prices of some of the campsites available


There are 4 people in the group and they are taking 2 tents for 3 nights in May. They calculate that Roversí Rest is the cheapest for them and Vibram Farm would be the most expensive.

1. How much would they save by going to Roversí Rest rather than Vibram Farm?

  • A    £6.50
  • B    £8.50
  • C    £19.50
  • D    £25.50

2. There is a brilliant surfing beach 25 kilometres from Roversí Rest but no one can remember its name. One of the friends has a map with a scale of 2cm to 5km and he measures the distance from Roversí Rest on the map to 4 local beaches. Which one is the surfing beach?

  • A    Blackrock Sands 2 cm
  • B    Gull Cove 5 cm
  • C    St Peter's Bay 7 cm
  • D    Whitesands 10 cm

3. Their car uses 1 litre of petrol to travel 14.8 kilometres. The campsite is 88 kilometres away from their home town. They estimate how much fuel they will need for the trip there and back. Which of these 4 attempts gives the closest estimate of the fuel required?

  • A    90 ÷ 15 = 6 litres
  • B    90 ÷ 10 = 9 litres
  • C    180 ÷ 15 = 12 litres
  • D    180 ÷ 10 = 18 litres

4. One of the items on their list of supplies is 6 yoghurts. The supermarket has several special offers. Which would work out cheapest?

  • A    Original price 26p: buy one, get a second half-price
  • B    Original price 26p: buy two, get the third free
  • C    Original price 27p: one third off
  • D    Original price 28p: 25% off





An architect is making a scale model of a new house from a drawing. One of the dimensions on the drawing shows that the height of the real house is 12.5 metres. What scale does the architect need to work to, if the height of the model house has to be 2.5 centimetres?

  • A     1 : 5
  • B     1 : 50
  • C     1 : 100
  • D     1 : 500






Stage 3

Holly is looking at a scale model of the Sports Hall where she works. The model is a cuboid and is 1 metre long, 50 centimetres wide and 200 millimetres high.



a)   What are the dimensions of the Sports Hall in meters, if the scale of the model is 1:50?

b)  It costs 0.03p per cubic metre each hour to heat the Hall. The Hall is open every day and heated for 8 hours each day. How much would it cost to heat the Hall for one week?

c)   Holly orders new badminton nets for the 4 badminton courts. Each court requires 8 meters of netting, which costs £2.67 per meter plus VAT at 17.5%. What is the cost of replacing all the netting?






Stage 3

This scale drawing shows the front view of a garage.

a)   What is the actual length of the sloping edge of the roof (on the original diagram the length was 3.5 cm?

b)  Work out the actual area of the garage door (on the original diagram the length and width were both 2.5 cm.

c)   The garage roof is a rectangle 6 m long. Draw a scale diagram of the garage roof, to a scale of 1:80.



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