CIE A Level Maths: Pure 1复习笔记1.7.1 Modelling with Functions
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
Exam 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
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