Mathematical Modelling · Guided Practice
Introduction to Modelling
5 questions with answers. Try each one before revealing the answer.
1
A council wants to model the total number of wheelie bins it will empty in a town during one year.
State three sensible assumptions it would need to make.
State three sensible assumptions it would need to make.
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Answer
e.g.
Every household has exactly one bin.
Every bin is emptied once a fortnight.
No collections are missed for holidays or bad weather.
The number of households does not change during the year.
Every household has exactly one bin.
Every bin is emptied once a fortnight.
No collections are missed for holidays or bad weather.
The number of households does not change during the year.
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2
A café owner wants to model the total number of cups of coffee sold in a typical week.
State three sensible assumptions they would need to make.
State three sensible assumptions they would need to make.
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Answer
e.g.
The café opens the same number of hours every day.
The same average number of customers arrives each day.
Every customer buys exactly one cup.
Trade does not change with the weather or the time of year.
The café opens the same number of hours every day.
The same average number of customers arrives each day.
Every customer buys exactly one cup.
Trade does not change with the weather or the time of year.
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3
A cyclist wants to model the total distance they will cycle commuting to work in one year.
State three sensible assumptions they would need to make.
State three sensible assumptions they would need to make.
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Answer
e.g.
They cycle to work and back on every working day.
They take the same route each time.
They work a fixed number of days per year.
They never travel by another means of transport.
They cycle to work and back on every working day.
They take the same route each time.
They work a fixed number of days per year.
They never travel by another means of transport.
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4
A school wants to model the electricity used by its classroom lights over one year.
State three sensible assumptions it would need to make.
State three sensible assumptions it would need to make.
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Answer
e.g.
Every classroom has the same number of lights.
The lights are on for the same number of hours each school day.
All lights use the same power.
The lights are switched off during holidays.
Every classroom has the same number of lights.
The lights are on for the same number of hours each school day.
All lights use the same power.
The lights are switched off during holidays.
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5
Explain what is meant by a mathematical model.
State one reason why a model may not give an exact answer.
State one reason why a model may not give an exact answer.
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Answer
A mathematical model is a description of a real situation using mathematics, used to make predictions.
It cannot be exact because it relies on assumptions that simplify the real situation, and real data varies.
It cannot be exact because it relies on assumptions that simplify the real situation, and real data varies.
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