United Kingdom · Year 7 to Year 13 · Every round, one table

Maths olympiad training in the UK

Parents meet the olympiad ladder in the wrong order: a letter comes home saying a child has qualified for something, and nobody explains what it is or what comes next. This page is the map. Every UK olympiad round with its date, its year groups, how many questions it asks and how long it gives, from a two-hour paper for twelve-year-olds to the three and a half hours that choose the national team. And one observation that reassures almost every pupil who reads it: as the papers get harder, they give you more time per question, not less.

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Every figure quoted from UKMT or BMOS with the date · Our own arithmetic, labelled · No promise about any result

In short

The UK olympiad ladder runs from the Junior Mathematical Olympiad, "a 2 hour Challenge consisting of 6 Olympiad style questions" on 15 June 2027 for Year 8 and below, through the Cayley, Hamilton and Maclaurin papers, "six Olympiad style problems" in two hours on 18 March 2027 split by school year, to the British Mathematical Olympiad: BMO1, a "3 1/2-hour paper" of "6 problems" on 18 November 2026, and BMO2, the same length with "4 problems", on 20 January 2027. Alongside them the Mathematical Olympiad for Girls runs "2.5 hours" of "five challenging problems" on 22 September 2026, two answer-only and three written. Around 1,200 pupils qualify for the junior olympiad each year and around 1,800 for the intermediate ones. Everything above the first challenge is marked by hand on the reasoning. We teach the mathematics and the writing: the first class is free, a group place is USD 100 a month and one-to-one teaching USD 150.

Where to start

Three courses for an olympiad candidate

The limit at every rung is technique and written argument, not syllabus.

Maths Olympiad & Competition Course course thumbnail

MOT / 01

Olympiad and competition maths

The core course at every level: unfamiliar problems, and solutions written so that a marker is convinced.

Open the syllabus →
Middle School Mathematics Mastery course thumbnail

MOT / 02

Middle school maths mastery

For Years 7 to 9, where the algebra and geometry the junior papers lean on are still being built.

Open the syllabus →
High School Mathematics course thumbnail

MOT / 03

High school mathematics

For sixth formers, so that technique never becomes the thing slowing an olympiad answer down.

Open the syllabus →

The ladder

Every UK olympiad round, in one table

Each row was read at UKMT or the British Mathematical Olympiad on 20 September 2026, and each links to the page behind it.

The UK mathematical olympiad rounds for 2026-27
RoundWho sits itDatePaper
Mathematical Olympiad for GirlsYear 11 and above, S4 and above, Year 12 and above in Northern Ireland22 September 2026Five problems in two and a half hours
British Mathematical Olympiad 1Open entry, full-time secondary education18 November 2026Six problems in three and a half hours
British Mathematical Olympiad 2Those above the threshold20 January 2027Four problems in three and a half hours
CayleyYear 9 and below, S2 or below, Year 10 or below in Northern Ireland18 March 2027Six problems in two hours
HamiltonYear 10, S3, Year 11 in Northern Ireland18 March 2027Six problems in two hours
MaclaurinYear 11, S4, Year 12 in Northern Ireland18 March 2027Six problems in two hours
Junior Mathematical OlympiadYear 8 and below, S2 or below, Year 9 or below in Northern Ireland15 June 2027Six questions in two hours
The multiple-choice challenges that qualify pupils for them
ChallengeDateLeads to
Senior Mathematical Challenge7 October 2026The Senior Kangaroo and the British Mathematical Olympiad
Intermediate Mathematical Challenge27 January 2027Cayley, Hamilton, Maclaurin and the Grey and Pink Kangaroos
Junior Mathematical Challenge5 May 2027The Junior Kangaroo and the Junior Mathematical Olympiad

Two numbers give the shape of the thing. UKMT says around 1,200 pupils qualify for the Junior Mathematical Olympiad from the Junior Challenge each year, and around 1,800 for the three intermediate olympiads. These are small rooms: a pupil who sits one is already among a few hundred per year group nationally.

Everything in the first table is written out in full and marked by a person. Everything in the second is multiple choice and marked by a machine. That is the only real dividing line in the ladder, and it falls between the Challenge in the spring and the olympiad six weeks later.

Scotland runs its own ladder alongside this one. The Scottish Mathematical Challenge has been going since 1976, spreads three rounds across the year, and has always marked "explanations of answers rather than ... simply getting the correct answer". A Scottish pupil can sit both.

Nothing here is entered by a family. Schools enter pupils for the challenges and UKMT invites the qualifiers, and no tutor, service or payment shortens that route.

Sources: the UKMT competitions calendar, its round pages and the British Mathematical Olympiad, all read 20 September 2026. We have no connection with UKMT or the BMO Subtrust.

The observation

The harder the paper, the more time you get

This is arithmetic on the published formats, and it is the most reassuring thing on the page.

Every exam a pupil has ever sat works one way: as the content gets harder, the questions get shorter and the clock gets meaner. The olympiad ladder does the opposite, and once you see the numbers you cannot unsee them.

Our arithmetic of 20 September 2026, from the published formats
RoundQuestionsMinutesMinutes per question
Junior Mathematical Olympiad612020.0
Cayley, Hamilton and Maclaurin612020.0
Mathematical Olympiad for Girls515030.0
British Mathematical Olympiad 1621035.0
British Mathematical Olympiad 2421052.5

What it tells a pupil

Nobody expects an answer in three minutes. Nearly an hour a question at the top of the ladder is permission to sit and think, which is exactly what these papers are testing.

What it tells a parent

Speed drills are the wrong preparation. They help in the multiple-choice challenges and do almost nothing for an olympiad paper.

What it tells a teacher

If a pupil is finishing early, they are not writing enough. A complete argument takes far longer than finding the answer did.

The reason for the pattern is simple once stated. At the bottom of the ladder a question can be seen through: find the trick, write it down, move on. At the top it cannot, and the time is there for the part that is genuinely hard, which is being sure and then being convincing.

It also explains why finishing is not the goal. Two complete solutions on a BMO1 paper is a real result, and three well-written answers on a two-hour olympiad beats six hurried ones every time.

The marking backs it up. UKMT tells candidates that "just stating an answer, even a correct one, will earn you very few marks", and the British Mathematical Olympiad has around sixty people gather in December to read every BMO1 script by hand over three days.

A pupil who understands that the clock is generous and the marking is human prepares completely differently, and usually enjoys it far more.

The minutes-per-question figures are ours, computed on 20 September 2026 from the question counts and durations each organiser publishes.

How to train

One problem, written up, every week

Olympiad training looks slower than exam revision because it is. It is also the only thing that works.

What moves an olympiad score, at every rung
Worth the hoursWhyNot worth it
Writing up problems already solvedThe writing is the half being marked and the half nobody practisesSolving more and writing none
Sitting with one problem for an hourThese questions are built to resist a first readingTwenty quick questions to feel productive
Reading the organiser's own solutionsThey show the standard of explanation expectedChecking only whether the final answer matched
Building a repertoireInvariants, extremal cases, pigeonhole, bounding, colouringHoping for a flash of insight on the day
Stamina, before the senior roundsThree and a half hours of concentration is a physical skillAny drilling in the last fortnight

The commonest mistake families make is buying harder material. The mathematics in a junior or intermediate olympiad question is rarely beyond a good pupil in that year group; what is unfamiliar is the packaging and the demand for proof. More topics do not help. More writing does.

The second commonest is treating a qualification as a verdict. Nothing depends on these papers, no school place turns on them, and a pupil who enjoys one will come back next year a rung higher against the same people.

What a teacher adds is reading. A pupil can tell whether their answer is right; they almost never can tell whether their explanation convinces a stranger, and that is the thing worth an hour a week of somebody else's attention.

The individual pages for each round set out the technique that round rewards, from writing a first proof at the junior olympiad to invariants at the British Mathematical Olympiad.

The route

Four rungs, climbed over five years

A pupil usually spends two years on each rung, and the habit carried up matters more than the score at any of them.

From a challenge paper to a written proof
YearsRungThe paper that tests it
7 to 81. Fast, accurate, unfamiliarThe Junior Mathematical Challenge and Kangaroo
8 to 92. A first written solutionThe Junior Mathematical Olympiad
9 to 113. Complete argumentsCayley, Hamilton and Maclaurin
11 to 134. Proof and staminaThe Mathematical Olympiad for Girls and the British Mathematical Olympiad

If a paper is close

Write up three problems already solved, properly, and have someone read them as a stranger would. It is the highest-return evening available at any rung.

Do not add topics. Every one of these papers is built from mathematics the pupil has already met.

At the top of the ladder

The top BMO2 scorers are invited to a training camp at Trinity College, Cambridge, from which an IMO squad and then a team of six is chosen.

Pupils who like proving things often take to informatics olympiads as well, where the marker is a compiler.

The full list

Courses for every rung of the ladder

Grouped by the stage a pupil is at, with each syllabus a click away.

I

Before the ladder

Years 5 to 7

MOT / A / 01

Primary maths, Years 1 to 5

The number work everything above stands on.

Open the syllabus

MOT / A / 02

Mental maths for kids

Calculation that stops costing thinking time.

Open the syllabus

MOT / A / 03

Maths through coding

Test a claim on a thousand cases, then prove it.

Open the syllabus
II

Junior and intermediate

Years 7 to 11

MOT / B / 01

Olympiad and competition maths

Unfamiliar problems, finished in writing.

Open the syllabus

MOT / B / 02

Middle school maths mastery

Algebra and geometry, argued not drilled.

Open the syllabus

MOT / B / 03

GCSE maths

The school course, taught to the board in use.

Open the syllabus
III

Senior rounds

Years 11 to 13

MOT / C / 01

High school mathematics

Technique that should never be the obstacle.

Open the syllabus

MOT / C / 02

A-level maths

Pure, mechanics and statistics, taught to the exam.

Open the syllabus

MOT / C / 03

Statistics and probability

Counting arguments made rigorous.

Open the syllabus
IV

The other olympiads

For pupils who also program

MOT / D / 01

Algorithms and data structures

Where proof meets running time.

Open the syllabus

MOT / D / 02

Competitive programming

The informatics version of the same patience.

Open the syllabus

MOT / D / 03

Python from start to finish

Enough code to explore a conjecture.

Open the syllabus

How lessons run

One hard problem a week, and someone who reads the write-up

Teaching is live on video from India, five and a half hours ahead of the UK in winter and four and a half in summer, at a time agreed and kept in UK time.

Weekday evening

The usual slot from Year 7 upwards.

Weekend morning

Long enough to take one problem to a finished proof.

Holiday intensives

For stamina before the senior rounds.

A cold reader every week

Someone who has not seen the problem reads the solution and says where they stopped following it.

A named toolbox

Each technique is taught with a name so a pupil can reach for it deliberately rather than hope.

Groups of five to ten

Big enough that somebody solves it differently, small enough that nobody goes unheard.

Being stuck is the work

Twenty minutes without progress is normal here and we say so, because pupils assume it is failure.

Problems we wrote

Ours, in the same idiom. The organisers give their past papers away and that is where the real ones belong.

No outcome sold

Qualification is not ours to give and we do not pretend otherwise.

Student work

What our students build

Four published projects by students at our school, none of them competition work. The student labs page collects them.

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Fees

Fees

The same price each month in US dollars outside India, nothing charged to start, and no commitment past the month you are in.

Free first class

USD 0

no card required

  • A single hard problem, taught properly
  • A plain answer about which rung fits
  • Nothing asked for but a number
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Group batch

USD 100

a month, billed in US dollars

  • Five to ten pupils at one level
  • The same teacher weekly
  • Written arguments marked by hand
  • A certificate at the end
Start here

One to one

USD 150

a month, billed in US dollars

  • A teacher working with one pupil
  • Aimed at the round they are sitting
  • For pupils well beyond their year group
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Olympiad ladder questions

What parents and teachers ask

What are the UK maths olympiads?

A ladder of written papers run by the UK Mathematics Trust and the British Mathematical Olympiad: the Junior Mathematical Olympiad, the Cayley, Hamilton and Maclaurin papers, the Mathematical Olympiad for Girls and the two British Mathematical Olympiad rounds.

How does a pupil get into one?

Through a multiple-choice Mathematical Challenge sat at school, after which UKMT invites those above a qualifying score, with discretionary entries also possible. Around 1,200 pupils qualify for the junior olympiad each year and around 1,800 for the intermediate ones.

What are the 2026-27 dates?

The Mathematical Olympiad for Girls on 22 September 2026, British Mathematical Olympiad 1 on 18 November 2026, BMO2 on 20 January 2027, Cayley, Hamilton and Maclaurin on 18 March 2027 and the Junior Mathematical Olympiad on 15 June 2027.

How long are the papers?

Two hours for the junior and intermediate olympiads, two and a half for the girls olympiad, and three and a half hours for both British Mathematical Olympiad rounds.

Do the harder papers give less time?

No, and this surprises everyone. Per question it is 20 minutes at the junior and intermediate olympiads, 30 at the girls olympiad, 35 at BMO1 and 52.5 at BMO2. The ladder gives more time as it gets harder.

Why is my child not finishing the paper?

Because finishing is not the goal. Three complete, well-written solutions on a two-hour olympiad beats six hurried ones, and two on a BMO1 paper is a real result for a first attempt.

How are they marked?

By hand, on the reasoning. UKMT tells candidates that just stating an answer, even a correct one, will earn very few marks, and around sixty markers gather in December to read every BMO1 script over three days.

What is the best preparation?

Writing up problems the pupil has already solved, spending an hour on single problems, reading the organiser's own published solutions for the standard, and building a repertoire of techniques. Not speed drills and not new topics.

Is there a Scottish route?

Yes. The Scottish Mathematical Challenge has run since 1976, spreads three rounds across the year and marks explanations rather than answers. A Scottish pupil can sit it alongside the UKMT ladder.

What is at the top?

The top British Mathematical Olympiad round 2 scorers are invited to a training camp at Trinity College, Cambridge, from which an IMO squad and then a team of six plus reserves is chosen.

The pages behind this one

Each round in full

Every rung has its own page, with the organiser's words and the technique that rung rewards.

Junior Mathematical Olympiad

Why forty examples are not a proof.

Cayley, Hamilton and Maclaurin

Why a complete answer means all of them.

British Mathematical Olympiad

Finding the thing that cannot change.

Mathematical Olympiad for Girls

Two questions want a number, three want the reason.

UKMT Kangaroo rounds

The multiple-choice follow-ons, and what the wrong options are for.

Primary Maths Challenge

Where it all starts, at ages 9 to 11.

Start here

Book a free olympiad lesson

Tell us the year group and which round is next. The free lesson takes one problem from first reading to a written argument.

Rather read first? Every syllabus is on its course page, the method on how we teach, and the order of topics on the roadmap.

WhatsApp us · +91 91233 66161 · contact@modernagecoders.com

The quickest reply usually comes on WhatsApp, which is free from a UK mobile. The number is registered in India, as we say everywhere, and no British office sits behind it.

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