Resources
Olympiad Past Papers & Solutions Library
Maths, physics, chemistry, biology, computing and astronomy olympiad papers — with topic breakdowns, mark boundaries and step-by-step solutions written by mentors who have coached AIME, BMO, BPhO and IOI qualifiers.
Maths olympiads
AMC 8 Past Papers
Every AMC 8 paper with topic-tagged questions and worked solutions, plus the honour-roll score ranges and the route on to AMC 10.
- 40 minutes · 25 multiple-choice questions
- 41 years archived
AMC 10 Past Papers
Every AMC 10 A and B paper with topic-tagged questions and step-by-step solutions from mentors who have coached AIME and USA(J)MO qualifiers.
- 75 minutes · 25 multiple-choice questions
- 26 years archived
AMC 12 Past Papers
AMC 12 A and B past papers with worked solutions covering trigonometry, complex numbers, logarithms and advanced counting.
- 75 minutes · 25 multiple-choice questions
- 16 years archived
AIME Past Papers
AIME I and II past papers with full worked solutions — the bridge between AMC speed problems and USAMO proof writing.
- 3 hours · 15 questions, each with an integer answer from 000 to 999
- 16 years archived
UKMT JMC Past Papers
Free JMC past papers from 2011 to 2026 with direct PDF links to every question paper, solutions and extended solutions, plus Junior Kangaroo and JMO follow-on routes.
- 60 minutes · 25 multiple-choice questions
- 16 years archived
Junior Kangaroo Past Papers
Free Junior Kangaroo past papers from 2015 to 2026 with direct PDF links to every question paper and solutions booklet, plus the JMC invitation route and Merit boundaries.
- 60 minutes · 25 multiple-choice questions
- 11 years archived
UKMT IMC Past Papers
Free IMC past papers from 2015 to 2026 with direct PDF links to every question paper, solutions and extended solutions, plus Pink, Grey and Cayley/Hamilton/Maclaurin follow-on routes.
- 60 minutes · 25 multiple-choice questions
- 15 years archived
UKMT SMC Past Papers
Senior Mathematical Challenge past papers with full solutions, plus the Senior Kangaroo and BMO1 progression route.
- 90 minutes · 25 multiple-choice questions
- 12 years archived
BMO Round 1 Past Papers
BMO1 past papers and solutions with mentor-marked proof feedback — the first UK round where writing the argument matters as much as finding it.
- 3 hours 30 minutes · 6 problems requiring full written proofs
- 16 years archived
BMO Round 2 Past Papers
BMO2 past papers with solutions and IMO-squad-level proof coaching — four hard problems, three and a half hours, no calculators.
- 3 hours 30 minutes · 4 problems requiring full written proofs
- 16 years archived
TMUA Past Papers
Every official TMUA past paper from 2016 to 2023 plus the specimen set — Paper 1, Paper 2, worked answers and answer keys as direct PDF links, with mentor-led walkthroughs.
- 75 minutes per paper · Two papers of 20 multiple-choice questions each
- 8 years archived
Physics olympiads
BPhO Round 0 Past Papers
BPhO Round 0 sample paper and official information — the new 1-hour, 25-question multiple-choice qualifying round introduced before BPhO Round 1.
- 1 hour · 25 multiple-choice questions — knowledge, calculation, elimination and problem solving
- 1 years archived
BPhO Round 1 Past Papers
BPhO Round 1 past papers and mark schemes with worked solutions — extended mechanics, electricity, waves and astrophysics problems for A-Level physicists.
- Approximately 2 hours 45 minutes · Two sections of long-answer physics problems (Section 1 short questions, Section 2 extended problems)
- 23 years archived
BPhO Physics Challenge Past Papers
Junior and Senior Physics Challenge past papers with worked solutions — the GCSE-level entry point to the British Physics Olympiad ladder.
- About 1 hour · Short and structured written physics questions
- 18 years archived
BPhO Round 2 Past Papers
BPhO Round 2 past papers and solutions from 2003 to 2024 — direct PDF links to every problem paper and available solution booklet, plus mentor-led derivation coaching.
- About 3 hours · Long multi-part physics problems requiring full derivations
- 21 years archived
Senior Physics Challenge Past Papers
Senior Physics Challenge past papers and solutions, 2007–2024 — direct PDF links to every problem paper and solution booklet for Year 11 physicists.
- About 1 hour · Structured written physics questions with extended parts
- 17 years archived
Intermediate Physics Challenge Past Papers
Intermediate Physics Challenge past papers and solutions, 2004–2024 — direct PDF links to every paper and solution booklet on the BPhO ladder.
- About 1 hour · Short-answer and structured written physics questions
- 22 years archived
USAPhO & F=ma Past Papers
F=ma and USAPhO past papers with solutions — mechanics-first selection, then the full free-response semifinal that leads to the US Physics Team.
- F=ma: 75 minutes · USAPhO: 3 hours · F=ma: 25 multiple-choice mechanics questions · USAPhO: long free-response problems
- 20 years archived
Chemistry olympiads
UK Chemistry Olympiad Past Papers
UK Chemistry Olympiad Round 1 past papers with answers and worked solutions — context-rich problems on organic mechanisms, equilibria and quantitative chemistry.
- About 2 hours · Written problem-solving questions built around real chemistry contexts
- 16 years archived
USNCO Past Papers
USNCO local and national exam past papers with answer keys and worked solutions covering the full ACS syllabus.
- Local: 110 minutes · National: three parts across the day · Local exam: 60 multiple-choice · National exam: multiple-choice, free-response and a lab practical
- 16 years archived
Biology olympiads
British Biology Olympiad Past Papers
British Biology Olympiad past papers with worked answers — data interpretation, physiology, ecology and genetics beyond the A-Level syllabus.
- Two 45-minute papers · Two online multiple-choice papers with data-interpretation questions
- 14 years archived
USABO Past Papers
USABO Open Exam and Semifinal past papers with worked solutions across the full IBO content distribution.
- Open Exam: 50 minutes · Semifinal: 2 hours · Open Exam: multiple-choice and true/false · Semifinal: multiple-choice and free response
- 14 years archived
Computing olympiads
British Informatics Olympiad Past Papers
British Informatics Olympiad Round 1 past papers with solution approaches — algorithmic problem solving in any programming language.
- 3 hours · 3 programming problems, each with several parts, solved on a computer
- 16 years archived
USACO Past Papers
USACO past contests by division with solution approaches — Bronze through Platinum, with the algorithm list you actually need at each level.
- 4 hours (from opening the contest) · 3 algorithmic problems per contest, judged automatically on hidden test data
- 11 years archived
Frequently asked questions
- Are the past papers free?
- Yes. Every paper links to the official awarding body — MAA, UKMT, BPhO, RSC, ACS, RSB, USACO and others — and our topic breakdowns, difficulty maps and solution walkthroughs are free to read. Only 1-to-1 mentoring is paid.
- Do you host the actual PDF papers?
- No. Olympiad papers are copyrighted by the organisations that set them, so we link directly to their official archives and add our own worked solutions, topic tagging and revision plans on top.
- Which olympiads are covered?
- Maths (AMC 8/10/12, AIME, UKMT JMC, IMC and SMC, BMO Rounds 1 and 2), physics (BPhO Round 1, the Junior and Senior Physics Challenge, F=ma and USAPhO), chemistry (UK Chemistry Olympiad, USNCO), biology (British Biology Olympiad, USABO), computing (BIO, USACO) and astronomy (BAAO and the Astro Challenge).
- How should I use past papers effectively?
- Sit each paper timed, mark it the same day, and rewrite complete solutions for every question you missed or guessed. Track your errors by topic — after four papers a clear pattern emerges and that becomes your revision plan.