Sharpen the underlying maths — free
Whatever your exploration uses — calculus, regression, probability, matrices — the practice portal has graded question sets to make that mathematics fluent before you write with it.
Open the practice portal →The exploration is 20% of your final grade, and most of that 20% is decided before you write a single word — by the topic. Here is a five-question filter that separates topics with a Band 7 ceiling from topics that can never get there, no matter how well they're written up.
Every spring I read draft explorations, and the pattern is brutal in its consistency: the write-up quality varies by a mark or two, but the topic choice varies by six. A student who picks a dead-end topic and writes beautifully will lose to a student who picks a living, breathing topic and writes adequately — because three of the five criteria are substantially determined by what you chose to explore, not how you wrote it up.
The exploration is marked out of 20 across five criteria. Read what each one actually pays for — the descriptors reward different things than students assume:
Rewards: a coherent arc — aim stated early, every section advancing that aim, conclusion answering the opening question. Quietly punishes: scope creep. Explorations that "do three things" rarely feel organised. The topic implication: a question you can state in one sentence produces a structure examiners can follow.
Rewards: correct notation, defined variables, labelled graphs, equations that are part of sentences. Quietly punishes: screenshot-itis — pasted calculator output and unlabelled Excel charts. Topic implication: choose something whose mathematics you can typeset and explain, not something where the software does the talking.
Rewards: evidence of independent thinking: your own data, your own question, a route the textbook didn't hand you. Quietly punishes: the 400th Monty Hall exploration — engagement can't be performed ("I have always been fascinated by…") on a topic with a well-worn path. This criterion is decided almost entirely at topic selection.
Rewards: critical reflection woven through: testing assumptions, questioning the model where it breaks, comparing approaches, limitations with consequences. Quietly punishes: a one-paragraph "limitations" section bolted on the end. Topic implication: you need a topic where something can go wrong or surprise you — a comparison, a model–data mismatch, a decision.
Rewards: mathematics commensurate with the level of the course, used with precision and (at HL) with sophistication. Quietly punishes: both directions of mismatch — GCSE-level percentages can't reach the top band, and half-understood graduate material collapses under its own notation. Topic implication: the maths should sit at the edge of your syllabus, not beyond it.
Run any candidate topic through these five questions. Each maps directly onto the criteria above; a "no" tells you which criterion has just had its ceiling lowered.
These topics are not banned, and a brilliant student can occasionally resurrect one. But each has been done so many thousands of times that criterion C starts in a hole, and examiners can recite the structure from memory: the Monty Hall problem, the golden ratio in faces/architecture, the birthday paradox, basic SIR modelling of COVID (with borrowed parameters and no fitting), penalty-kick optimal angles (without your own data), and cryptography surveys that explain RSA without exploring anything. The pattern in all six: famous puzzle, known answer, no personal data, nothing at stake. They fail questions 3, 4 and 5 of the filter simultaneously.
Don't take these as topics to copy — take them as shapes to imitate: one question, real material, syllabus-edge maths, uncertain outcome. Adapt the subject matter to your own life.
| Interest | Seed question | Core mathematics |
|---|---|---|
| Sport | Does a drag-adjusted projectile model predict my own basketball free throws better than the vacuum model? | Calculus, parametric motion, residual analysis |
| Music | How many Fourier terms does a recorded violin note need before my ear can't distinguish the reconstruction? | Trigonometric series, modelling (strong AA HL fit) |
| Games | What's the expected long-run distribution of board positions in Monopoly, and does it match 200 of my own dice rolls? | Markov chains, matrices (strong AI fit) |
| Economics | At what price does my school canteen maximise revenue for its most-bought item, given demand I survey myself? | Regression, optimisation, elasticity |
| Biology | Does logistic or exponential growth better fit my own yeast-culture measurements — and where does each break? | Differential equations / regression, model comparison |
| Space | How much velocity change does a Hohmann transfer to Mars require, and how sensitive is it to launch-window timing? | Circular motion, energy, optimisation |
| Design | What tin proportions minimise material for a fixed volume — and why do real supermarket tins deviate from the optimum? | Optimisation with constraints, then model-vs-reality reflection |
| Statistics | Is home advantage in my football league real? Hypothesis testing on five seasons of results. | Distributions, significance testing (AI SL-friendly) |
| Art | Can a piecewise Bézier model reproduce a calligraphy stroke, and how does control-point count trade against accuracy? | Parametric curves, error metrics |
| Personal finance | Under what return assumptions does investing monthly beat my country's actual house-deposit savings schemes? | Sequences & series, compound interest, sensitivity |
| Running | Does a critical-speed model predict my 5k time from my training data better than Riegel's formula? | Modelling, linearisation, regression |
| Networks | What's the shortest sensible route for my paper round, and how close does a greedy algorithm get to optimal? | Graph theory, algorithms (AI HL fit) |
Analysis & Approaches explorations score best when there's something to derive — calculus, series, proof-adjacent reasoning. Applications & Interpretation explorations score best when there's something to model and validate — data, technology, statistical inference. The same theme can usually be tilted either way: the violin note above is a derivation story for AA (build the series) and a modelling story for AI (fit, measure error, validate). Tilt your topic toward your course's centre of gravity, because criterion E reads "commensurate with the course" — not "impressive in general".
Choose the topic at the end of IB year one — late enough to have met the syllabus-edge maths, early enough that data collection isn't rushed. Budget the work in thirds: a third on the mathematics, a third on writing, and a third — the third nobody budgets — on the iteration loop after your teacher's single permitted round of written feedback. And the page guidance (12–20 pages): treat the upper bound as a hard editor. Explorations rarely fail for being too short; they routinely fail criterion A for being bloated.
Whatever your exploration uses — calculus, regression, probability, matrices — the practice portal has graded question sets to make that mathematics fluent before you write with it.
Open the practice portal →Bring your candidate topic to a free assessment session — we'll run it through the filter together and leave you with a one-page exploration plan.
Book the free assessment