OT3: Mathematical modelling: Use a mathematical model with suitable inputs to engage with and explore situations (for a given model or a model constructed or selected by the student).

The idea

Once a model exists, you must apply it by choosing appropriate input values, performing calculations or simulations, and interpreting the outputs in the original context. This involves selecting realistic inputs, using the model to generate predictions or explore 'what if' scenarios, and reflecting on whether the results are sensible. The model may be given, constructed by you, or selected by you from a range of candidates; in the selected case, justify why your chosen model suits the situation. For instance, given a model for the height of a projectile, you might input different launch angles to find the maximum range, then discuss whether air resistance would alter the conclusion. Assessment rewards methodical use of the model, correct substitution and evaluation, and critical interpretation of results, including recognising when outputs are unrealistic due to model limitations.

What earns the marks

• Selects input values that are meaningful and within the domain of the model, explaining why those values are chosen.
• Substitutes inputs correctly into the model, carrying out calculations accurately and showing sufficient working.
• Interprets outputs in the context of the original situation, including units and practical meaning.
• Explores the effect of varying inputs, such as by considering a range of values or extreme cases, to understand the model's behaviour.
• Critically evaluates the model's predictions, noting where results may be unreliable or where assumptions break down.
• When selecting a model from candidates, justifies the choice by comparing assumptions and suitability for the situation.

Common mistakes and how to put them right

• Choosing inputs that are outside the model's valid domain (e.g. negative time) without comment.

  Put it right: Check the domain and discuss why certain inputs are inappropriate.

• Ignoring units when substituting or interpreting results, leading to answers that are dimensionally inconsistent.

  Put it right: Carry units through calculations and state the units of the final answer.

• Accepting model outputs without question, even when they are clearly unrealistic (e.g. a population exceeding the total land area).

  Put it right: Compare outputs with real-world knowledge and comment on discrepancies.

• Selecting a model without justifying why it fits the situation.

  Put it right: Compare the model's assumptions with the context and explain your choice.

Exam tips

• When given a model, identify its variables and parameters first, then decide which to vary and which to hold constant.
• Show all substitution steps clearly; this helps you avoid arithmetic errors and allows method marks to be awarded.
• After calculating, write a sentence interpreting the result in context, e.g. 'This means the ball reaches a maximum height of 12 metres after 1.5 seconds.'.
• If you select the model yourself, state your selection criteria and justify the choice briefly before using it.