What is the fewest number of exam sessions my school needs?

AI HLAA HLAI SL Solid Also in: Pure maths

Research question

Modelling subjects as vertices joined when a student takes both, what is the chromatic number of my school's exam graph, and how close does a greedy colouring algorithm get?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Exam officers solve a graph-colouring problem every season. Using your school's subject combinations (anonymised) makes a classic piece of discrete mathematics practical.

The mathematics you'll need

Graphs and graph colouring (explain)
Greedy algorithms and ordering
Lower bounds from cliques
Comparing with the real timetable

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Anonymised subject-combination counts from your school's options (with permission) or your own class.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Build the conflict graph.
Find a lower bound using the largest clique.
Apply the greedy algorithm with different orders.
Compare with the actual exam timetable.
Reflect on other constraints (rooms, time of day).

Pitfalls that cost marks

Any identifiable student data.
Only one vertex order for the greedy method.
Confusing the chromatic number with the maximum degree.

Showing personal engagement

Use your own school's options.
Discuss with the exams officer.
Design a fairer timetable for students with many exams.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Weight edges by the number of students affected and minimise back-to-back exams.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).