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UK Maths Challenges, explained.

The JMC, IMC and SMC — plus the Kangaroo and Olympiad rounds that climb all the way to the International Mathematical Olympiad. The whole ladder, in five minutes.

700,000+ students a year 6,000+ schools Run by the UKMT since 1996
Arcvision Education · Updated July 2026 · 5 min read

What is the UKMT?

The UK Mathematics Trust is a charity that runs the country's biggest school maths competitions. The point isn't the curriculum — it's problem-solving: clever ideas over memorised methods.

🧩Insight, not memory

Questions reward a spark of insight — rarely anything beyond your school year.

🎯Open to everyone

Early questions suit all abilities. About half of all entrants earn a certificate.

🚀A ladder up

Do well and you're invited to Kangaroo and Olympiad rounds — the route to the IMO.

The ladder at a glance

Every student sits a multiple-choice Challenge. Score well and it branches two ways:

Kangaroo

Another timed, multiple-choice round for high scorers — speed and accuracy under pressure.

Olympiad

Two hours, a handful of hard problems, full written proofs. This is the road to the IMO.

Three tiers, same shape

The ladder repeats at three age levels — join at the one that matches your school year.

Junior Year 8 & below
Junior Maths Challenge · JMC
Junior Kangaroo
or
Junior Mathematical Olympiad

One route or the other — never both. About the top 1,000 JMC scorers are invited to the Olympiad; roughly the next 10,000 to the Kangaroo. Cut-offs set each year.

Intermediate Year 9–11
Intermediate Maths Challenge · IMC
Grey Kangaroo (Yr 9–10)Pink Kangaroo (Yr 11)
or
Cayley (Yr 9)Hamilton (Yr 10)Maclaurin (Yr 11)

One route or the other — never both. Grey and Pink are simply the Kangaroo split by year group; Cayley, Hamilton and Maclaurin are the Olympiad split by year. You sit the one paper that matches your school year.

Senior Year 12–13
Senior Maths Challenge · SMC
Senior Kangaroo
or
BMO Round 1

One route or the other — never both. The top SMC scorers sit BMO Round 1; a wider band sit the Senior Kangaroo. From there: Round 1 → Round 2 → IMO selection.

Scoring & awards, in full

Now the full picture, one level at a time. Every student sits a multiple-choice Challenge; strong scorers go on to a Kangaroo or an Olympiad. Challenges and Kangaroos give certificates; only the Olympiads give medals (plus Distinction and Merit certificates). Every figure is approximate and re-set each year.

1 · Junior — Year 8 & below

📝 Challenge — Junior Maths Challenge (JMC) · out of 135 · no penalty
CertificateMark
🥇 Gold certificate75+
🥈 Silver certificate59+
🥉 Bronze certificate47+

Top ~50% earn a certificate (Bronze : Silver : Gold ≈ 3 : 2 : 1).

Then one route only — the Kangaroo or the Olympiad, never both:

⚡ Kangaroo — Junior Kangaroo · out of 135 · no penalty
CertificateShareMark
🥇 Gold certificatetop 10%≈ 114+
🥈 Silver certificatenext 20%≈ 100+
🥉 Bronze certificatenext 30%≈ 80+
✍️ Junior Mathematical Olympiad (JMO) · out of 60 · written proofs
AwardWhoMark
🥇 Gold medaltop 4051+
🥈 Silver medalnext 6042+
🥉 Bronze medalnext 10035+
✦ Distinction certificatetop 25%31+
✦ Merit certificatenext 40%19+

Every medallist also receives a book prize.

2 · Intermediate — Years 9–11

📝 Challenge — Intermediate Maths Challenge (IMC) · out of 135 · small penalty on the hard questions
CertificateMark
🥇 Gold certificate61+
🥈 Silver certificate46+
🥉 Bronze certificate35+

Top ~50% earn a certificate.

Then one route only — the Kangaroo or the Olympiad, never both:

⚡ Kangaroo — Grey & Pink · out of 135 · no penalty · you sit the one for your year
CertificateShareGrey (Yr 9–10)Pink (Yr 11)
🥇 Gold certificatetop 10%≈ 101+≈ 85+
🥈 Silver certificatenext 20%≈ 85+≈ 73+
🥉 Bronze certificatenext 30%≈ 67+≈ 59+
✍️ Olympiad — Cayley · Hamilton · Maclaurin · out of 60
AwardWhoCayley (Yr 9)Hamilton (Yr 10)Maclaurin (Yr 11)
🥇 Gold medaltop 2044+33+40+
🥈 Silver medalnext 3039+23+34+
🥉 Bronze medalnext 5031+17+31+
✦ Distinction certificatetop 25%29+14+29+
✦ Merit certificatenext 40%15+6+15+

3 · Senior — Years 12–13

📝 Challenge — Senior Maths Challenge (SMC) · out of 125 · start on 25, −1 if wrong
CertificateMark
🥇 Gold certificate72+
🥈 Silver certificate57+
🥉 Bronze certificate46+

Top ~two-thirds earn a certificate.

Then one route only — the Kangaroo or the Olympiad, never both:

⚡ Kangaroo — Senior Kangaroo · out of 100 · no penalty
CertificateShareMark
🥇 Gold certificatetop 10%≈ 70+
🥈 Silver certificatenext 20%≈ 55+
🥉 Bronze certificatenext 30%≈ 40+
✍️ British Mathematical Olympiad (BMO) Round 1 · out of 60 · written proofs
AwardWhoMark
🥇 Gold medaltop 2048+
🥈 Silver medalnext 3037+
🥉 Bronze medalnext 5031+
✦ Distinction certificatetop 25%18+
✦ Merit certificatenext 45%7+

💡 The top ~100 from BMO Round 1 go through to Round 2 (4 problems, 3½ hours) — the final step before UK International Mathematical Olympiad squad selection.

How to actually do well

1

Bank the easy marks. Questions 1–15 win most certificates — slow down and get them right before chasing the hard ones.

2

Practise against the clock. Timed past papers build the speed and nerve that theory alone never will.

3

Learn to write proofs. On Olympiad rounds the marks are in clear reasoning — not just the final answer.

4

Climb one rung at a time. Each round builds on the last; steady progress up the ladder beats cramming.

Aiming past the certificate?

Our coaches are IMO and BMO medallists who've climbed this exact ladder — and now teach it in small live groups. Book a free consultation and we'll map your child's next step.

Scores and thresholds shift slightly each year to keep the intended proportions earning each award — always check ukmt.org.uk for the official, current numbers. This guide is an independent overview by Arcvision Education and is not affiliated with the UK Mathematics Trust.