UKMT SMC Past Papers & Solutions
Senior Mathematical Challenge
Senior Mathematical Challenge past papers with full solutions, plus the Senior Kangaroo and BMO1 progression route.
- Eligibility
- Year 13 and below (England & Wales)
- Format
- 25 multiple-choice questions
- Duration
- 90 minutes
- Scoring
- 5 marks for Q1–15, 6 marks for Q16–25, penalties in the back section
The Senior Mathematical Challenge is the gateway to BMO1 and, ultimately, the UK IMO squad. It assumes A-Level algebra and trigonometry but tests them sideways. Past papers are essential because the SMC style — elegant one-line answers hiding behind ugly-looking setups — is unlike anything in the A-Level syllabus.
UKMT SMC 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.
Stuck on a UKMT SMC question?
Send us the question number. A mentor who has sat and medalled in UKMT SMC will reply with a step-by-step walkthrough and the faster competition method.
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Other official UKMT SMC resources
What the paper tests
Algebra & functions
Trigonometry
Combinatorics
Geometry
Proof habits
Where it leads: Leads to the Senior Kangaroo and BMO Round 1, then BMO2 and the IMO squad. See our coaching programme.
Book personalised UKMT SMC classes
Past papers show you the gap; a mentor closes it. Our UKMT SMC mentors are medal winners who walk through every solution 1-to-1, then set targeted practice on the archetypes you lost marks on.
Want the full UKMT SMC paper pack and score guide?
Tell us your target and we will send the UKMT SMC paper list, the official scoring rules and a preparation plan built around the questions you keep losing marks on.
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Frequently asked questions
- What SMC score is needed for BMO1?
- Qualification thresholds vary annually and by year group, but a score in the low-to-mid 90s out of 125 has typically been in the BMO1 range for Year 13 students. Senior Kangaroo cut-offs sit roughly 10–20 marks lower.
- Do SMC past papers help with BMO1?
- They build speed and topic coverage, but BMO1 needs written proof. Our route is SMC past papers for fluency, then BMO past problems for full write-ups with mentor feedback on rigour.
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.