IB Mathematics Internal Assessment
Growth of bacteria, how a drug leaves the body, heart rate and fitness, the spread of an illness. Biology and health give you real quantities that change in interesting ways, which is exactly what mathematics is for. They also tempt students into reporting a science result with a graph attached. Here is how to make the mathematics the main event.
If you study biology or hope to go into medicine, the engagement is genuine and the context is easy to explain. The risk is that the interesting part of the work belongs to biology, and the mathematics turns into a short step in the middle: plug the data into a calculator, read off a number, move on.
Ask yourself: which decisions in this exploration are mathematical ones? If a biology teacher could have made all of them, the Use of Mathematics has a ceiling, however good the science is.
A handful of people, one scatter graph, one coefficient. The technique is routine, the sample is too small to support the claim, and there is nothing to surprise you. It also reads as a school science practical.
Everybody does it, and the fit is usually good for a few hours and then fails. If you stop at the good part, you have curve fitting. The marks are in the failure: why growth slows, and what changes in your model when you account for it.
Take a standard compartment model from a website, change the parameters to match a disease and plot the curves. You have shown you can follow instructions. Nothing about the structure is a choice you made or can defend.
Download a spreadsheet, press the regression button, interpret the output. The software has done the mathematics. Without your own decisions about cleaning, choosing and testing, the work is hard to credit to you.
Medicine or caffeine concentration over time can be modelled with exponential decay, then made more realistic with repeated doses. You decide what "safe" or "effective" means, work out when a second dose should be taken, and test the model against whatever data you can gather. Suits AA and AI students who like calculus or sequences.
Start with simple growth, show where it fails against real measurements, then move to a model with a limit, such as logistic growth. Justify each step from the data rather than from a textbook. Keep the biology to one paragraph and spend the pages on why the model changed.
Choose a few groups, such as people who are healthy, infected and recovered, and write the rules for how people move between them. Solve small cases by hand, then use technology for longer runs. The value is in how the answer changes when you alter one assumption, and in saying honestly what the model leaves out. HL students can use differential equations; SL students can use step-by-step calculations.
Medical claims rest on comparing groups. Collect your own data on something harmless, such as reaction times before and after a task, and decide whether a difference is bigger than random variation. A hypothesis test can fit well here, but only if you can explain why it suits your data and what its assumptions are.
A test that is mostly accurate can still give a misleading answer when the condition is rare. Work through conditional probability with realistic values, show how the answer shifts as the rarity changes, and say what that means for how a result should be read. This is compact, rigorous and rarely done well.
Take "how much of a painkiller is in the body over a day" as a starting idea. Calculated once, it is a short exercise. To turn it into an exploration, keep pushing.
None of that needs advanced mathematics. It needs a question you can defend and an honest look at your own result.
Health data about real people needs care. Talk to your teacher or coordinator before you start. Keep anything you gather anonymous, ask for clear agreement from every participant, and avoid measuring anything that could embarrass or harm someone. Do not collect medical information about anyone. Reaction times, or a resting pulse after a set task, are far safer than anything clinical. Publicly available datasets are fine, but say where they came from and how you cleaned them.
Reflection comes naturally when a model meets real measurements, because they will rarely agree. Record those moments properly, with what you expected, what you found and what you changed. They are worth more than a tidier graph.
Got a health or biology idea and not sure it can score?
Send me the question and what you plan to do with the mathematics. I read real submitted explorations every year, and I will tell you honestly whether it has enough to do, while there is still time to change direction.
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Written by a serving IB Diploma and Career-related Programme Coordinator and Head of Mathematics, who reads internal assessments across every subject group every year. If you then want the whole draft reviewed properly against all five criteria, that is the paid one, and it is refunded if it does not name at least three specific things to fix.
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