How the diagnostic works
It is an adaptive competition-math test: every question is chosen based on how you answered the last one, so it pinpoints your level fast — without wasting your time on problems that are far too easy or far too hard.
The short version
Tell us your background
Pick your highest contest experience — from "never taken one" up to USAMO/Olympiad. This sets a smart starting difficulty so you are not stuck answering questions far from your level.
Answer adaptive questions
After each answer, the test re-estimates your level and serves the most informative next problem — harder when you are right, easier when you are wrong, while balancing all four subjects.
Get your skill-tree report
When the estimate is confident enough, it stops and builds your report: an overall tier, a per-subject breakdown, a skill map, and a recommended next focus.
What it measures
Four domains, one tier
Questions are drawn from the four pillars of competition math. Your performance is summarized as a single overall tier, plus a separate read on each subject.
The tier ladder
- Tier I Foundation
- Tier II AMC 8 Proficient
- Tier III AMC 10/12 Developing
- Tier IV AMC 10/12 Competitive
- Tier V AIME Qualifier
- Tier VI AIME Advanced
- Tier VII Olympiad
- Tier VIII Elite Olympiad
Tiers run from foundational skills up to elite Olympiad. Most students land somewhere in the middle — the point is to find your edge, not to rank you.
Your report
Overall tier & confidence range
Your estimated level, plus a 95% range so you can see how precise that estimate is.
Subject breakdown
How you did in each of the four domains, with accuracy and a note when a subject had only a few questions.
Skill map
A tree of specific skills the diagnostic touched, color-coded by the evidence it gathered for each.
Recommended next focus
One concrete skill to work on next, chosen from where your results suggest the most upside.
For the curious
Under the hood
You do not need any of this to take the diagnostic — but if you like knowing how the machinery works, here it is.
Item Response Theory (IRT) +
Every question is calibrated with parameters describing its difficulty, how sharply it separates strong from weak solvers (discrimination), and the chances of guessing or slipping. From these, the test models the probability that a student at a given ability level answers correctly.
Your ability is represented by a single number, theta (θ). Higher theta means a higher estimated competition-math level, and theta is what maps onto your tier.
How the next question is chosen +
After each answer, we update a probability distribution over your ability (a Bayesian posterior, computed on a grid). The next item picked is the one expected to be most informative about your true level — for the first few "cold-start" questions this uses expected information across the whole distribution, then switches to maximizing information right at your current estimate.
A content-balancing layer keeps the four subjects represented and avoids serving the same domain too many times in a row, so your report is not lopsided toward whatever you happened to see first.
When — and why — it stops +
The diagnostic asks at least 15 questions and at most 25. It stops early once two things are true: the estimate is precise enough (the standard error of your ability has dropped below a set threshold) and every subject has met a minimum number of questions.
That is why two people can finish after a different number of questions — the test stops as soon as it is confident, rather than making everyone answer a fixed list.
Questions
Do I need an account?
No. The diagnostic is free and anonymous. Your progress and result are stored in your browser, so you can return to an in-progress session on the same device.
How long does it take?
Usually about 30-60 minutes. The diagnostic asks between 15 and 25 questions and stops early once it has a confident estimate of your level.
What if I have never done a competition before?
That is fine — choose "I haven't taken one / not sure" at the start. The test simply begins at an easier point and adapts upward as you answer.
Can I retake it?
Yes. You can take the diagnostic as many times as you like. Each run starts a fresh session and produces a new, updated report.
Is my tier a permanent judgement of my ability?
No. This is a beta snapshot of your current competition-math level based on one session. Treat domain estimates with few questions as directional, not final.