Modelling with Functions (Cambridge International A-Level Mathematics)

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 use mathematical models?

• 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

Exam Hint

• 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