Modelling with Functions (AQA A Level Maths): Revision Note
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Modelling with Functions
What is a mathematical model?
A mathematical model simplifies a real-world situation so it can be described using mathematics which can then be used to make predictions
The path a stone will take if thrown from the top of a cliff
The number of toys a factory can produce in a day
Assumptions about the situation are made in order to simplify the mathematics
Air resistance on the stone can be ignored
The machines/people at the factory produce toys at a constant rate
Models can be refined (improved) if further information is available or the model is compared to real-world data
The mass of the stone needs to be considered
30-minutes downtime per day is allowed for machine repairs/maintenance
How do I solve modelling problems?
There will be no one-size-fits-all step-by-step guide to solving modelling questions
A combination of skills and problem-solving skills will be needed
Examiner Tips and Tricks
Read – and re-read – the question carefully.Try to “get involved” in the context of the question – however boring it may be!
Imagine what happens to a stone as you throw it from a cliff
What would it be like to manage a toy factory?
Draw a diagram – sketch a graph of the function being used as the model.
If you are completely stuck try “doing something” with the maths. For example, if there’s a quadratic function – sketch it, factorise it, solve it. Or if there’s a polynomial – use factor theorem and algebraic division to factorise it.
Worked Example
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