Modelling with Functions (OCR A Level Maths: Pure)

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Paul

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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

Notes what_model_is, A Level & AS Level Pure Maths Revision Notes

 

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

 Notes model_lin_qu, A Level & AS Level Pure Maths Revision Notes

 

Notes model_lin_soltn, A Level & AS Level Pure Maths Revision Notes

Examiner Tip

  • 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

Example soltn, A Level & AS Level Pure Maths Revision Notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.