Problem Solving and Modelling
Core concepts
Apply mathematics to unfamiliar contexts: translate a word problem into equations, select appropriate models, and interpret results in context. Understand assumptions behind models, units, and the meaning of parameters. Practise checking reasonableness of answers.
Traps
- Ignoring units or mixing them within a calculation.
- Overlooking domain restrictions imposed by the real-world context.
- Presenting a numerical answer without interpreting it in context.
- Failing to state assumptions when building a model.
Worked example
A population grows according to P(t)=P0 e^(kt). Given P(0)=200 and P(5)=400, then e^(5k)=2, so k=ln2/5, and P(t)=200 e^((ln2/5)t). This predicts doubling every 5 time units.
Rule of thumb
Always restate the answer in the language of the problem, with units, and check whether it is physically reasonable.