Applied maths and modelling · Accessible · Dissertation

Modelling the UK population: a maths EPQ idea

A title to start from

How well do exponential and logistic models predict the UK's population?

A starting point, not your title. Change the case, the data or the comparison until it is yours, then agree it with your supervisor. Check your title.

Why it works as an EPQ

Official data are free, the models are on or near the A Level course, and comparing their predictions gives a clear judgement.

Scope and difficulty

Accessible. Accessible. One country, two or three models, a fair test on data you hold back.

The maths

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

You would learn:

The logistic differential equation
Fitting models to data
Residuals and prediction error

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

One possible plan

Download population estimates from the Office for National Statistics.
Fit an exponential and a logistic model to the earlier years.
Test both on the later years you held back.
Discuss what the models leave out (migration, policy) and how far ahead they can be trusted.

Pitfalls

Testing a model on the same data used to fit it.
Over-reading a good fit as an explanation.

Where to start reading

Office for National Statistics population estimates
Search for: logistic growth model fitting

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

Next steps

Check your title Plan your timeline

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.

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