Graphs - WJECFurther examples for Intermediate and Higher tier

Graphs can be used to present data clearly and as a tool to aid calculations in the form of conversion graphs and travel graphs. Sometimes graphs can be used to misrepresent data.

Part of Maths Numeracy (WJEC)Algebra

Further examples for Intermediate and Higher tier

1. Use the table below to draw a conversion graph for litres and gallons. Plot 0 to 20 gallons on the \({x}\) axis and 0 to 100 litres on the \({y}\) axis.

A 2 column comparison table labelled 'gallons' and 'litres'. 0 gallons equals 0 litres, 10 gallons equals 45.5 litres, and 20 gallons equals 91 litres

2. Using the conversion 1 mile = 1.6 km, draw a conversion graph for miles and km. Plot 0 to 50 miles on the \({x}\) axis and 0 to 80 km on the \({y}\) axis.

3. A British motorist takes her car to France for the weekend. She covers a distance of 400 km and uses 27 litres of fuel and wants to know if this is in keeping with her normal fuel consumption of 45 ± 5 MPG (miles per gallon). Use your conversion graphs to convert km to miles and litres to gallons and then calculate her fuel consumption while in France. Is it in her normal range?

4. A French motorist travels the other way and while in Britain he covers 450 miles and uses 9 gallons of diesel. He wants to know if his fuel consumption is within its normal range of 20 ± 2 km/litre. Use your conversion graphs to convert miles to km and gallons to litres and then calculate his fuel consumption while in France. Is it in his normal range?

Solution

Example graphs:

2 conversion graphs. Graph 1 is gallons to litres, and graph 2 is miles to kilometres

Calculations

British motorist: 400 km = 250 miles, 27 litres = 6 gallons.

Fuel consumption in MPG = 250 ÷ 6 = 41.67 MPG (to two decimal places).

Yes, this is within the usual range.

French motorist: 450 miles = 720 km, 9 gallons = 41 litres.

Fuel consumption in MPG = 720 ÷ 41 = 17.56 km/litre (to two decimal places).

No, this is not within the usual range. It is lower.