Twenty-five multiple-choice questions, sixty minutes, 135 marks. Sat at school by hundreds of thousands of UK students each year. The entry rung of the UKMT pyramid — with 23 free years of past papers on the official site.
The Junior Mathematical Challenge is the entry-level paper in the UKMT's three-challenge pyramid. It is sat at school in a single sixty-minute sitting by Year 8 and below across the UK each spring. The questions are multiple choice (A–E), arranged in roughly increasing difficulty; questions 1–15 are worth five marks each, questions 16–25 are worth six. There is no negative marking, which makes the paper friendly to students new to competition mathematics — every question should be answered, including guesses.
Top performers are invited to the follow-on rounds: the Junior Kangaroo (a 60-minute, 25-question multiple-choice paper) and the Junior Mathematical Olympiad (a two-hour, six-question long-form proof paper). Both are entered by invitation on a qualifying JMC score; those qualifying marks are reset every year.
The UKMT publishes 23 years of free JMC content (2004–2026) on ukmt.org.uk. Coverage varies by era: 2015–2026 offer full Questions + Solutions + Extended Solutions PDFs; 2011–2014 provide the Extended Solutions PDF and image galleries; 2004–2010 are image galleries only. The canonical starting point for any year is ukmt.org.uk/free-past-papers/junior-mathematical-challenge-{YEAR}. Pre-2004 papers are sold via the UKMT shop.
The UKMT publishes a full Award-Threshold History going back over two decades. The thresholds shift year on year — in 2026, the Junior Kangaroo cut-off sat at 80 and the Junior Mathematical Olympiad cut-off at 112 — but the broad shape is stable. Certificates go to roughly the top-scoring half of entrants, awarded as Bronze, Silver, and Gold in a 3:2:1 ratio. Above that, the top 1,000–1,200 students qualify for the Junior Mathematical Olympiad, and the next band of around 10,000–15,000 UK students qualifies for the Junior Kangaroo.
| Band | What it is | Approximate reach |
|---|---|---|
| Junior Mathematical Olympiad | Written-proof paper, 6 questions, 2 hours | Top ~1,000–1,200 students |
| Junior Kangaroo | MCQ paper, 25 questions, 60 minutes | ~10,000–15,000 UK students |
| Gold certificate | Certificate, best-in-school badge | Top ~8% |
| Silver certificate | Certificate | Next ~9% |
| Bronze certificate | Certificate | Next ~8% |
No negative marking. Try every question, including the ones that look terrifying.— Editor's note
Continue to the Student Edition for an eight-week study plan, test-day strategy, and topic coverage guide, or download the Advisor Edition PDF for the instructor's coaching workflow.
What the JMC is, who can enter, how marks are awarded, where to find the 23 years of free past papers, an 8-week study plan, and test-day strategy.
Coaching workflow, classroom logistics, follow-on round briefing (Junior Kangaroo and Junior Mathematical Olympiad), and the complete source-boundary map for this audit.
23 free years on ukmt.org.uk (2004–2026) enumerated with access tiers. Full Questions + Solutions + Extended Solutions for 2015–2026. Image galleries for older years.
Official pages
Community resources
Context within the UKMT pyramid