Applied maths and modelling · Accessible · Dissertation or artefact

How fast does a cup of tea cool?: a maths EPQ idea

Why it works as an EPQ

A cheap, safe experiment produces your own data to test a model that is on the A Level course.

Scope and difficulty

Accessible. Accessible. Add a better model (for example with evaporation) only if time allows.

The maths

Builds on these A Level topics: Exponentials and logarithms · Differentiation · Integration.

You would learn:

• Solving first-order differential equations
• Fitting by linearising with logarithms
• Residual analysis

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Derive the exponential model from the differential equation.
2. Record temperature every minute in different cups, with and without a lid.
3. Estimate the constant by plotting ln(T − room temperature) against time.
4. Evaluate where the model fails and why.

Pitfalls

• Hot liquids: follow your school's safety advice.
• Changing more than one thing between runs.

Where to start reading

• Search for: Newton's law of cooling experiment evaporation
• Search for: linearising exponential data logarithms

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

Making something? Read the artefact guide first: an artefact still needs a research-based written report.

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Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.