Real situations rarely hand you exactly the numbers a model needs. This section teaches you to sort the information first, then build and test the model.
It builds on defining variables and assumptions and sits inside SPM Mathematics.
How is this different from a normal modelling chapter?
A normal chapter starts with clean data and asks you to fit a model. Here the difficulty comes before the equation, and the lessons follow that order.
The first lesson sorts the quantities that matter from those that do not. The second compares two options and finds where they swap. The third checks how far a model can be trusted. The fourth handles a question that allows two readings.
One fare question, three kinds of imperfection
A ride-hailing trip costs a base fare plus a charge per kilometre. The question gives the distance, the driver’s name, the car colour and the number of passengers. It does not give the rate per kilometre.
Extra information: the driver’s name and car colour change nothing. Missing information: the rate per kilometre is needed, so you state an assumption or ask for it. Ambiguous information: if the question says “about 12 km”, you decide whether to use 12.
Each problem has a first move. The lessons below teach that move one at a time.
Who should start where?
Begin with deciding which quantities are necessary before calculating a fare if you tend to use every number in a question. Go to comparing a fixed fee and a usage fee if you are choosing between two plans.
If your model works but its prediction feels odd, read testing whether a model still works outside the supplied data range. When a question allows two reasonable readings, read explaining two defensible models.
The algebra step repair trainer helps with the algebra once the model is set. For lessons with a teacher, see online one-to-one Mathematics tuition.