Modelling with Functions (Edexcel A Level Maths: Pure): Flashcards

A mathematical model simplifies a real-world situation so that it can be described with mathematics and used to make predictions.

Examples are the path of a stone thrown from a cliff, or the number of toys a factory can produce in a day.

Use the function to make predictions, by substituting values into it or solving equations from it.

Sketching its graph then shows the overall behaviour: where it peaks, where it reaches zero, and how quickly it changes.

A model is refined when further information becomes available, or when it is compared with real-world data.

Allowing for the mass of the stone, or for thirty minutes of daily downtime at the factory, are refinements of exactly that kind.

False.

A model is a simplification, judged by whether its predictions are useful rather than by how completely it describes reality.

A model that matched every detail would be as complicated as the situation itself.

It shows the shape of the relationship at a glance, including any maximum or minimum and where the model reaches zero.

Those features usually correspond to something meaningful in the situation being modelled.