Maths competitions explained

The main maths competitions for secondary students come from two families: the UKMT challenges and the American Mathematics Competitions. Here is what each one is, who can take it, when it is, and where it leads. Dates are for the 2026-27 season.

UKMT challenges

Run by the UK Mathematics Trust, a charity, and taken in schools across the UK and overseas. Three levels by age, the Junior, Intermediate and Senior Challenges, each with follow-on Kangaroo and Olympiad rounds for the top scorers. The UK's main school maths competitions, recognised by schools and universities.

Official site ↗

American Mathematics Competitions (AMC)

Run by the Mathematical Association of America and taken by over 300,000 students in more than 30 countries each year: the best-known maths competitions in North America. The AMC 8, AMC 10 and AMC 12 lead to the AIME and the USA Mathematical Olympiad. In the UK, students take them through AMC Europe.

Official site ↗

At a glance

Tap a competition for the details. Rounds in orange need a top score in an earlier competition first.

Competition	Date	UK school years	Age	How to take part	Format
UKMT challenges
Junior Mathematical Challenge (JMC)	5 May 2027	Year 8 and below	About 13 and under	Open entry, through a school	25 multiple-choice questions, 60 minutes
Junior Kangaroo and Junior Mathematical Olympiad	15 June 2027	Year 8 and below	About 13 and under	By invitation, from a top JMC score	Kangaroo: 25 multiple-choice questions, 60 minutes. Olympiad: 6 problems, 2 hours
Intermediate Mathematical Challenge (IMC)	27 January 2027	Year 11 and below (mostly Years 9 to 11)	About 13 to 16	Open entry, through a school	25 multiple-choice questions, 60 minutes
Intermediate Kangaroo and Olympiads (Cayley, Hamilton, Maclaurin)	18 March 2027	Grey Kangaroo and Cayley: Year 9 and below. Pink Kangaroo: Years 10 and 11. Hamilton: Year 10. Maclaurin: Year 11	About 13 to 16	By invitation, from a top IMC score	Kangaroos: 25 multiple-choice questions, 60 minutes. Olympiads: 6 problems, 2 hours
Senior Mathematical Challenge (SMC)	7 October 2026 (next: autumn 2027)	Year 13 and below (mostly Years 12 and 13)	About 18 and under	Open entry, through a school	25 questions, 90 minutes. From 2026, the last 3 have a three-digit answer (000 to 999) instead of multiple choice
Senior Kangaroo and British Mathematical Olympiad (BMO1)	18 November 2026 (BMO2: 20 January 2027)	Year 13 and below	About 18 and under	By invitation, from a top SMC score (BMO2: from BMO1)	Senior Kangaroo: 20 integer-answer questions, 60 minutes. BMO1: 6 problems, 3½ hours
American Mathematics Competitions (AMC)
AMC 8	22 to 25 January 2027 in the UK and Europe (register by 31 December 2026)	US grade 8 and below (UK Year 9 and below)	Under 15½ on the day	Open entry, through a school or AMC Europe	25 multiple-choice questions, 40 minutes
AMC 10	5 November (A) or 13 November (B) 2026; in Europe, register by 31 October 2026	US grade 10 and below (UK Year 11 and below)	Under 17½ on the day	Open entry, through a school or AMC Europe	25 multiple-choice questions, 75 minutes
AMC 12	5 November (A) or 13 November (B) 2026; in Europe, register by 31 October 2026	US grade 12 and below (UK Year 13 and below)	Under 19½ on the day	Open entry, through a school or AMC Europe	25 multiple-choice questions, 75 minutes
AIME	February 2027	As for the AMC 10 or 12 taken	As for the AMC 10 and 12	By qualification, from a top AMC 10 or AMC 12 score	15 questions, each with a whole-number answer from 0 to 999

How they lead on

UKMT challenges

JMC (Year 8 and below)
IMC (Year 11 and below)
SMC (Year 13 and below)
British Mathematical Olympiad

American Mathematics Competitions (AMC)

AMC 8 (Year 9 and below)
AMC 10 (Year 11 and below)
AMC 12 (Year 13 and below)
AIME

Each UKMT challenge also has its own Kangaroo and Olympiad rounds for the top scorers.

UKMT challenges

Junior Mathematical Challenge (JMC)

The first of the UKMT's three challenges. The questions are about logic and clever reasoning more than school methods, and get harder as the paper goes on. A good first competition for younger students.

Date: 5 May 2027
Who can take it: Year 8 and below · About 13 and under
How to take part: Open entry, through a school
Format: 25 multiple-choice questions, 60 minutes
Scoring and awards: 5 marks each for questions 1 to 15 and 6 marks each for 16 to 25, out of 135. No marks lost for wrong answers. The top 50% receive Gold, Silver or Bronze certificates in the ratio 1:2:3.
What it leads to: The top 1,000 to 1,200 are invited to the Junior Mathematical Olympiad; around the next 10,000 to 15,000 to the Junior Kangaroo. After that, the IMC.
How to enter: Through school: ask the maths department. If the school doesn't take part, some schools and test centres accept outside candidates.

Our course for it: AMC 8 and JMC, small group →↑ Back to the table

Junior Kangaroo and Junior Mathematical Olympiad

The two follow-on rounds of the JMC. The Junior Kangaroo is a harder multiple-choice paper; the Junior Mathematical Olympiad asks for full written solutions, a big step up and great practice for later olympiads.

Date: 15 June 2027
Who can take it: Year 8 and below · About 13 and under
How to take part: By invitation, from a top JMC score
Format: Kangaroo: 25 multiple-choice questions, 60 minutes. Olympiad: 6 problems, 2 hours
Scoring and awards: Junior Kangaroo: out of 135, no marks lost for wrong answers; the top 10% receive Gold, the next 20% Silver and the next 30% Bronze Kangaroo certificates. It is open to UK schools only. Junior Olympiad: 6 questions worth 10 marks each, with partial marks for clear working.
What it leads to: The IMC and its follow-on rounds.
How to enter: By invitation, from a qualifying score in the round before, or entered by the school at its discretion.

↑ Back to the table

Intermediate Mathematical Challenge (IMC)

The UK's main maths competition for secondary students, taken in schools across the country. It rewards careful reasoning over guessing, and its certificates are a recognised achievement for school and university applications.

Date: 27 January 2027
Who can take it: Year 11 and below (mostly Years 9 to 11) · About 13 to 16
How to take part: Open entry, through a school
Format: 25 multiple-choice questions, 60 minutes
Scoring and awards: 5 marks each for questions 1 to 15 and 6 marks each for 16 to 25, out of 135. A wrong answer loses 1 mark on questions 16 to 20 and 2 marks on 21 to 25, so leaving a hard question blank can be the right call. The top 50% receive Gold, Silver or Bronze certificates in the ratio 1:2:3. In 2026, Gold was 61 and above.
What it leads to: Around 1,800 top scorers are invited to an olympiad (Cayley, Hamilton or Maclaurin, by school year), and several thousand more to the Grey or Pink Kangaroo.
How to enter: Through school: ask the maths department. If the school doesn't take part, some schools and test centres accept outside candidates.

Our course for it: IMC, small group →↑ Back to the table

Intermediate Kangaroo and Olympiads (Cayley, Hamilton, Maclaurin)

The follow-on rounds of the IMC. The Kangaroos are harder multiple-choice papers; the Cayley, Hamilton and Maclaurin olympiads ask for full written solutions and are a real test of mathematical thinking.

Date: 18 March 2027
Who can take it: Grey Kangaroo and Cayley: Year 9 and below. Pink Kangaroo: Years 10 and 11. Hamilton: Year 10. Maclaurin: Year 11 · About 13 to 16
How to take part: By invitation, from a top IMC score
Format: Kangaroos: 25 multiple-choice questions, 60 minutes. Olympiads: 6 problems, 2 hours
Scoring and awards: Kangaroos: out of 135, no marks lost for wrong answers; the top 10% receive Gold, the next 20% Silver and the next 30% Bronze Kangaroo certificates. They are open to UK schools only. Olympiads: 6 questions worth 10 marks each, with partial marks for clear working; the top 25% receive a Certificate of Distinction and the next 40% a Certificate of Merit.
What it leads to: The Senior Challenge and the British Mathematical Olympiad.
How to enter: By invitation, from a qualifying score in the round before, or entered by the school at its discretion.

↑ Back to the table

Senior Mathematical Challenge (SMC)

The UKMT's senior challenge, for sixth form students and strong younger students. Problems that reward insight over routine methods, and a common step for students thinking about maths at university.

Date: 7 October 2026 (next: autumn 2027)
Who can take it: Year 13 and below (mostly Years 12 and 13) · About 18 and under
How to take part: Open entry, through a school
Format: 25 questions, 90 minutes. From 2026, the last 3 have a three-digit answer (000 to 999) instead of multiple choice
Scoring and awards: Everyone starts with 25 marks; each correct answer adds 4 and each wrong answer loses 1, out of 125. The top 66% receive Gold, Silver or Bronze certificates in the ratio 1:2:3.
What it leads to: About 1,000 are invited to the British Mathematical Olympiad Round 1, and about 8,000 more to the Senior Kangaroo.
How to enter: Through school: ask the maths department. If the school doesn't take part, some schools and test centres accept outside candidates.

↑ Back to the table

Senior Kangaroo and British Mathematical Olympiad (BMO1)

The follow-on rounds of the SMC. BMO1 asks for full written solutions; the top 100 or so go on to BMO2, the UK's hardest national maths competition and the start of selection for the UK International Mathematical Olympiad team.

Date: 18 November 2026 (BMO2: 20 January 2027)
Who can take it: Year 13 and below · About 18 and under
How to take part: By invitation, from a top SMC score (BMO2: from BMO1)
Format: Senior Kangaroo: 20 integer-answer questions, 60 minutes. BMO1: 6 problems, 3½ hours
Scoring and awards: Senior Kangaroo: 20 questions worth 5 marks each, no marks lost for wrong answers; the top 10% receive Gold, the next 20% Silver and the next 30% Bronze Kangaroo certificates. It is open to UK schools only. BMO1: 6 questions worth 10 marks each, with partial marks for clear working; Distinction and Merit certificates.
What it leads to: BMO2, then UK team selection.
How to enter: By invitation, from a qualifying score in the round before, or entered by the school at its discretion.

↑ Back to the table

American Mathematics Competitions (AMC)

AMC 8

The first level of the MAA's American Mathematics Competitions, the best-known maths competitions in North America. Topics include counting and probability, number, geometry and early algebra, and the short time limit rewards quick, accurate thinking.

Date: 22 to 25 January 2027 in the UK and Europe (register by 31 December 2026)
Who can take it: US grade 8 and below (UK Year 9 and below) · Under 15½ on the day
How to take part: Open entry, through a school or AMC Europe
Format: 25 multiple-choice questions, 40 minutes
Scoring and awards: 1 point for each correct answer, out of 25. No marks lost for wrong answers, so every question is worth an answer.
What it leads to: The AMC 10 and AMC 12.
How to enter: In the UK, through AMC Europe (amceurope.net), the MAA's organiser for Europe. Ask your school first; if it doesn't take part, you can register as an individual and AMC Europe matches you with a school that hosts you on the day.

Our course for it: AMC 8 and JMC, small group →↑ Back to the table

AMC 10

The MAA's competition for younger high school students: algebra, geometry, number theory and probability, without trigonometry or advanced algebra. Harder than the AMC 8 and the IMC at the top end, and the first step towards the AIME.

Date: 5 November (A) or 13 November (B) 2026; in Europe, register by 31 October 2026
Who can take it: US grade 10 and below (UK Year 11 and below) · Under 17½ on the day
How to take part: Open entry, through a school or AMC Europe
Format: 25 multiple-choice questions, 75 minutes
Scoring and awards: 6 points for each correct answer and 1.5 for each blank, out of 150. Wrong answers score 0. Students can sit both the A and B papers.
What it leads to: Top scorers qualify for the AIME.
How to enter: In the UK, through AMC Europe (amceurope.net), the MAA's organiser for Europe. Ask your school first; if it doesn't take part, you can register as an individual and AMC Europe matches you with a school that hosts you on the day.

↑ Back to the table

AMC 12

The MAA's senior competition, covering the whole high school syllabus including trigonometry and advanced algebra, but not calculus.

Date: 5 November (A) or 13 November (B) 2026; in Europe, register by 31 October 2026
Who can take it: US grade 12 and below (UK Year 13 and below) · Under 19½ on the day
How to take part: Open entry, through a school or AMC Europe
Format: 25 multiple-choice questions, 75 minutes
Scoring and awards: 6 points for each correct answer and 1.5 for each blank, out of 150. Wrong answers score 0.
What it leads to: Top scorers qualify for the AIME.
How to enter: In the UK, through AMC Europe (amceurope.net), the MAA's organiser for Europe. Ask your school first; if it doesn't take part, you can register as an individual and AMC Europe matches you with a school that hosts you on the day.

↑ Back to the table

AIME

The American Invitational Mathematics Examination, for students with a qualifying AMC 10 or AMC 12 score. Much harder than the AMC, and a strong achievement to show on applications.

Date: February 2027
Who can take it: As for the AMC 10 or 12 taken · As for the AMC 10 and 12
How to take part: By qualification, from a top AMC 10 or AMC 12 score
Format: 15 questions, each with a whole-number answer from 0 to 999
Scoring and awards: 1 point for each correct answer, out of 15.
What it leads to: In the US, the USA Mathematical Olympiad and Junior Mathematical Olympiad.
How to enter: Qualifying students are invited after the AMC 10 or 12; in Europe, AMC Europe arranges it at no extra cost.

↑ Back to the table

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