UKMT IMC Past Papers & Solutions
Intermediate Mathematical Challenge
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.
- Eligibility
- Year 11 and below (England & Wales)
- Format
- 25 multiple-choice questions
- Duration
- 60 minutes
- Scoring
- 5 marks for Q1–15, 6 marks for Q16–25, penalties in the back section
The Intermediate Challenge sits between GCSE fluency and genuine olympiad reasoning. Most of the paper is accessible with a solid Year 10 toolkit, but the last third demands proof-flavoured thinking under time pressure. Every year below links straight to the official UKMT PDF: the question paper to sit timed, the solutions sheet to mark against, and the extended solutions and investigations to read once you have written up your own attempt.
UKMT IMC past papers and solutions by year
Every link below opens the official UKMT PDF directly. Sit the paper timed, mark it against the solutions, then read the extended solutions once you have written up your own attempt.
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Other official UKMT IMC resources
What the paper tests
Algebraic manipulation
Geometry
Counting
Number
Speed drills
Where it leads: Leads to the Pink or Grey Kangaroo and the Cayley, Hamilton and Maclaurin olympiads. See our coaching programme.
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Frequently asked questions
- How do I prepare for the IMC using past papers?
- Sit one paper a week under exam conditions, mark it immediately, and rewrite full solutions for every question you missed or guessed. Track which of the five topic areas your losses cluster in — that is your revision plan.
- What follows the IMC?
- Depending on your score and school year, you are invited to the Pink Kangaroo, the Grey Kangaroo, or one of the Cayley (Y9), Hamilton (Y10) and Maclaurin (Y11) olympiad papers.
- Are IMC past papers free to download?
- Yes. UKMT publishes every Intermediate Mathematical Challenge paper and its solutions as a free PDF, and each year on this page links straight to the official UKMT file. We do not re-host the papers — we add topic tagging, revision plans and mentor-led walkthroughs on top.
- What is the difference between the solutions and the extended solutions?
- The solutions PDF gives the correct option letter and a short justification for each of the 25 questions, so it is what you mark against. The extended solutions and investigations PDF explains the full reasoning, alternative methods and follow-up problems — read it after you have written up your own attempt.
- Which IMC years are available here?
- Direct PDF links are listed for every sitting from 2015 through to 2026, including question papers, solutions and extended solutions, plus the UKMT sample answer sheet and the 2025 problem comments.
Related paper libraries
Preparing beyond past papers? See our 1-to-1 Maths Olympiad tutoring hub for the full UKMT, BMO, AMC and AIME pathway with verified expert mentors.