The AMC past-papers library

Nothing prepares you for an AMC paper like an earlier AMC paper. Many years of past problems and solutions are freely available, and working through them is the most reliable way to raise a score. The papers below are the genuine articles — the same questions students sat in previous seasons — each paired with the official answer key so you can mark your own work.

Why past papers work

The AMC tests a stable set of ideas in a consistent style year after year. Counting and probability, number theory, geometry and clever algebra recur across the papers, dressed up in new situations. Sit enough of them and you stop meeting unfamiliar problem types — you start recognising old friends in new clothes, which is exactly the pattern recognition the contest rewards. Past papers also calibrate your pace: 25 questions in 40 or 75 minutes only feels comfortable once you have done it for real several times.

How to use them

Treat each paper as the exam, not a worksheet. The method is simple and it works:

• Sit the whole paper under real timed conditions. Set a clock for the exact limit, no calculator, no notes, no pausing. Finish the paper in one sitting exactly as you would on exam day.
• Mark it against the answer key before you look anything up, so you know your honest score.
• Then study the solution to every problem — not only the ones you missed. The official solutions often show a faster or cleverer route than the one you found, and those techniques are what carry over to the next paper.

A handful of papers worked this way, with the solutions studied properly, will teach you more than any amount of passive reading. Build up from the level below your target contest, then move to recent papers as the exam approaches.

Browse papers by competition

Pick your contest below. Each collection gathers that competition’s past problems and official solutions in one place.