OT3: Mathematical modelling: Translate a situation in context into a mathematical model, making simplifying assumptions.

The idea

This skill involves taking a real-world scenario and representing it mathematically, while consciously deciding which features to ignore or simplify. You must identify the key variables, choose appropriate mathematical structures (such as equations, graphs or algorithms), and state assumptions that make the problem tractable. For example, modelling the cooling of a cup of tea might assume a constant room temperature and ignore heat loss through the cup's sides, leading to Newton's law of cooling. The assumptions must be justified in context and their likely effect on the model's accuracy considered. Assessment focuses on your ability to abstract essential features, define variables clearly, and communicate the modelling process logically, not on producing a single 'correct' model.

What earns the marks

• Identifies relevant variables and parameters from the context, distinguishing between those that can be measured and those that must be estimated.
• States simplifying assumptions explicitly, such as ignoring air resistance or treating a population as continuous, and explains why each assumption is reasonable.
• Selects a suitable mathematical form (e.g. linear, exponential, trigonometric) that captures the essential behaviour of the situation.
• Defines notation clearly and consistently, including units where appropriate, so that the model can be understood and used by others.
• Considers limitations of the model and how assumptions might affect predictions, showing awareness that models are approximations.

Common mistakes and how to put them right

• Failing to state any assumptions.

  Put it right: Begin by listing at least two assumptions and justify them in context.

• Using variables without defining them or mixing units.

  Put it right: Define every symbol and include units in a key or within the model description.

• Overcomplicating the model by including too many factors.

  Put it right: Start with a simple model, then discuss how it could be refined if needed.

Exam tips

• Read the context carefully and underline the quantities that change; these are likely to become your variables.
• Write a clear 'Assumptions' section before deriving any equations; this demonstrates modelling awareness and can gain credit even if later algebra is imperfect.
• Check that your model can produce sensible outputs for extreme inputs (e.g. zero or very large values) as a quick validity test.