Modelling with Functions (CIE A Level Maths: Pure 1)

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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

 

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

 

 

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

Examiner Tip

  • Reciprocal graphs generally have two parts/curves
    • Only one – usually the positive – may be relevant to the model
    • Think about why x/t/θ can only take positive values?

Worked example

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

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Lucy

Author: Lucy

Expertise: Head of STEM

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels. Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all. Lucy has created revision content for a variety of domestic and international Exam Boards including Edexcel, AQA, OCR, CIE and IB.