Modelling assumptions

Objective. State, test and refine mathematical assumptions.

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Learn: the key idea

Modelling assumptions are simplifications made so a real-world situation can be described using mathematics, and good mathematicians always state them clearly before calculating. Common assumptions include constant speed, negligible air resistance, a person treated as a point mass, or uniform rates of change, since without such simplifications the problem becomes too complex to solve with standard formulae. After calculating, you should test whether the assumption is reasonable and discuss how the real answer might differ, such as noting actual speed would vary due to traffic, making the true journey time longer than the modelled estimate.

Worked example

A model assumes a car travels at a constant 60 mph to estimate the journey time for 90 miles. State the assumption and find the modelled time.

1 $State the assumption: speed is constant at 60 mph throughout$
2 $Apply time = distance \div speed = 90 \div 60$
3 $Simplify 90/60 to 1.5 hours$
4 $Note the real time may differ if speed actually varies$

Answer: 1.5 hours

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Common mistake. A common mistake is calculating an answer without stating the assumptions used, e.g. finding a travel time using distance ÷ speed without noting that speed is assumed constant, which hides where the model could be wrong.

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