Structure of maths comps in the UK

Before I delve into my journey through maths competitions in secondary school, I think it is a good idea to give a basic overview of what I understand to be the structure of maths competitions in this country. This acts as a preface and gives structure to the rest of this blog.

Maths competitions exist in many forms, teams or individual. However, the most important maths competition globally is the International Mathematics Olympiad, also known as the IMO. Almost all nation’s best high school mathematicians gather together to compete in this 9-hour maths contest. Every country’s IMO team, usually around 6 contestants, represents the pinnacle of a nation’s mathematical competence at pre-university level. And to select the most capable mathematicians, every country has their own system of selection for the international maths Olympiad. Being a UK student, I will describe UK’s IMO selection process.

The UK’s maths competition is largely governed by a charity organization called the UKMT. The charity organizes a series of competitions based towards different age groups.

1.     Junior maths competitions.

This competition is largely targeted towards pupils in year 7 and year 8 (age 11 to 13). The first round is known as the Junior Maths Challenge (JMC) where nearly all pupils across the UK would compete. The competition lasts 60 minutes, containing 25 multiple choice questions. With the maximum mark being 135. The top 50% of participants are awarded a certificate – Bronze, Silver, Gold in the ratio of 3:2:1.

The top 1200 participants are invited to a follow-up round – the Junior Maths Olympiad (JMO) lasting 2 hours consisting of 16 problems. Out of the 1200 pupils, the top 25% are awarded a certificate of distinction, and the next top 40% a certificate of merit. The top 100 pupils are awarded medals, with the top 20 being a gold, the next 20 being a silver and the next 60 being a bronze.

Those who performed well in the JMC but not enough to be selected for the JMO are invited to a follow-up round called the Junior Maths Kangaroo (JKang). With question style very similar to the JMC but slightly harder. The top 25% of the participants are awarded a certificate of merit.

2.     Intermediate maths competitions

This competition is largely targeted towards pupils in year 9, 10, 11. (age 13 to 16). The first round is known as the Intermediate Maths Challenge (IMC), lasting 60 minutes containing 25 multiple choice problems. With the maximum mark being 135. The top 50% of participants are awarded a certificate – Bronze, Silver, Gold in the ratio of 3:2:1.

The top 500 participants in every year group are invited to the follow-up round – the Intermediate Maths Olympiad (IMOK). With year 9s being the Cayley Mathematical Olympiad, year 10s being the Hamilton Mathematical Olympiad and year 11s being the Maclaurin Mathematical Olympiad. All levels of the IMOK lasts 2 hours, consisting of 6 very challenging Olympiad style problems that require full written solutions. Each question is worth a maximum of 10 marks, hence the maximum mark of 60. the top 25% are awarded a certificate of distinction, and the next top 40% a certificate of merit. The top 100 pupils are awarded medals, with the top 20 being a gold, the next 20 being a silver and the next 60 being a bronze.

Those who performed well in the IMC but not enough to qualify for the IMOK are invited to sit the follow-up round Intermediate Maths Kangaroo (IKANG), with year 9s sitting the Grey Kangaroo and year 10s and year 11s sitting the Pink Kangaroo. With question style very similar to the IMC but slightly harder. The top 25% of the participants are awarded a certificate of merit.

3.     Senior maths competitions

This stage is aimed at year 12 and year 13s (age 16 to 18). At this stage, competitions gets much more formal and much more difficult. Requiring fully written proofs, attaining answers using logical induction. It is also at this stage where the UK IMO team are selected.

The first stage is the Senior Maths Challenge (SMC), this is a national competition where most pupils studying Alevel maths can compete in. Around 700,000 pupils compete nationwide, lasting 60 minutes with 25 questions. Each question is worth 4 marks, with a deduction of 1 mark for an incorrect answer and none for an unanswered answer. And all begin with 20 marks. Hence the maximum mark is 125.

The top 1000 scorers are invited to sit the British Maths Olympiad round 1 (BMO1). Usually, the requirement for this ranges from 95-105 in the SMC. The BMO1 lasts 3.5 hours involving 6 questions. These questions are very tough, an average grade 9 GCSE maths student would struggle to answer a single question. Each question is worth 10 marks with a total mark of 60. A ‘perfect solution’ is worth 10 marks, a ‘partial solution’ with mostly correct reasoning but not a fully convincing answer would obtain around 7 marks, and a ‘partial solution’ with some rudimentary ideas would score less than 4 marks. The top 60% are awarded a certificate of Merit, the top 25% are awarded a certificate of Distinction. The top 100 are awarded medals, with the top 20 being gold, the next 20 being a silver and the rest being a bronze medal.

Top performers of the BMO1 are invited to the Hungarian New year camp where pupils train with the Hungarian IMO squad.

Around 100 best scoring participants of the BMO1 are invited to sit the BMO2. However, the threshold depends on the year group of the pupil. In 2022, a score of 36 is required for a y12 pupil an a score of 38 for a y13 pupil.

The British Maths Olympiad round 2 (BMO2) lasts 3.5 hours consisting of 4 questions each worth 10 marks. As well as challenging high-attainers from the BMO1 it is also an entry point to the training and selection program for international competitions. The top 24 scorers of the BMO2 are invited to an Easter maths camp at Trinity College, Cambridge. At the end of the six day camp, students sit two IMO style papers and 10 students are selected at the end of the camp. The team for the Balkan maths Olympiad is then selected from the 10 pupils.

At the end of May a team of 7 from the 10 pupils is finalized for the IMO, with the last being a reserve.

A pre-IMO camp is also held immediately before the IMO that is joint with the Australian IMO team.

Aside from the usual maths selection process, there are also a separate route making it more accessible for female candidates. There is the UKMT mathematics Olympiad for Girls (MOG), where high scores are gained automatic entry into the BMO2. The top four female candidates in the BMO2 exam is then selected to participate in the European Mathematics Olympiad for Girls.

Above is the entirety of maths examinations at pre-university level in the UK as of my knowledge.

my thoughts

Although I hardly believe that I would come any close to achieving anything near to what the IMO students can achieve, I believe that looking at their journey is a large source of personal motivation for myself. The UKMT competitions had always been a large part of my academic journey and my performance were a source of encouragement and a testament to my hard work. The UKMT competitions and competitive mathematics in general are largely based around problem solving and using mathematical ideologies to come up with ingenious ways of solutions. In fact, competitive maths is quite far fetched from a mathematical degree. It requires a greater level of creativity rather than simply regurgitating what is taught in class. I believe problem solving to some degree is more important to some degree as it is a skill that can be applied in real life scenarios. However, I am also aware that competitive maths is simply pattern spotting to some degree, where your brain is wired to respond a certain way to a specific question type by doing repetitively hundreds or even thousands of similar questions prior. To an extent, it is a reflection of eastern asia’s exam-orientated education system. Where students are overtrained to simply work around the examination system in order to maximise marks, rather than understanding and enjoying the essence of the subject.

I think Jonathan Lee’s quote summarises it pretty well: “if you build your own sort of private house of cards on getting into the IMO team, and then you don’t, then the all the hopes will collapse with it”. “I think it is better to hope for the best and plan for the worst”

Junior stage

In year 5, my primary school participated in a teams maths challenge. There were four of us and I still remember vividly the journey to the site in our maths’ teacher’s Ford Focus. I had always enjoyed the atmosphere of a maths competition. The adrenaline rush from answering a question correctly within a time limit and the proud feeling of winning something for the team. This was my very first experience of teams maths and, despite sounding very geeky, I enjoyed every bit of it.

In year 7, I had basically no knowledge of competitive maths. I achieved a Gold Medal in the Junior Maths Challenge with a score that placed me 4th in my year, and qualified for the follow-up Junior Kangaroo round. It was in fact rather fun, and was a score I was very content with. A year later, lockdown hit. The year 8 Junior Maths Challenge was held online, so there were no follow-up rounds.

Intermediate stage

In year 9, our school forgot to sign us up to the UKMT competitions… lmao

In year 10, this is when everything became much more competitive. I realised that these maths competitions could be something that I write in my university applications, so I tried to train and practice much harder. Seeing my name up there on the list of results also gave me a feeling of pride and self-esteem. This all motivated me to work harder. I began to research about the competition system, I bought competitive maths practice books and began to do more specialised practice. Soon, the intermediate maths challenge came, I scored a Gold of 105 however, just short of qualifying for the Hamilton Olympiad. Participating in the follow-up pink kangaroo, I achieved a merit. What should I do with the merit certificate? Put it in the dishwasher? Feed it to my cat? Even though it was an improvement from year 7 (2nd in the year), I was far from pleased.

Febuary 2023. A month prior to the intermediate maths olympiad. The year 11 self brought the practice book, which he had flipped through many times the year before, down from the shelves to work through again. This time round, I did every single past paper available on the UKMT website and every paper I can find elsewhere. Even olympiad questions, preparation was solid. I averaged 110+ in most of the practice papers and was more than ready. The exam day came, and my performance exceeded my expectations. Scoring 115 placed myself best in the year/best in the school. This was a huge ego booster for me, and was a testament to the effort I put in. I smashed the threshold for the maclaurin olympiad by 10 marks. There was only two pupils including me participating in the maclaurin maths olympiad. I received a promising 22/60 (merit). 10, 7, 0, 3, 2, 0

Senior stage

October 2023. A few weeks before the senior maths challenge. Surprisingly, this year I was relaxed. I wasn’t as competitive knowing that I already qualified for the olympiad stage before. In fact, I lowered my expectations knowing that there are some able year 13 pupils in the year above, so the chances of my getting best in school are slim…

I was wrong

The paper was so fucking easy! In the exam, I finished 18 questions without a problem, looked up, half an hour remaining. I spend 10 minutes checking and the rest of the time working through the harder questions. Two days later, UKMT released the mark scheme on the website. I checked, and knew I got a score of 108, which should qualify me for the BMO1. A few weeks later, my head of maths stumbled into our maths lesson holding a laptop. He announced that someone in the class received the highest ever SMC score that the school had ever attained, an astonishing 108. To be honest, I am shocked that 108 is my school’s highest ever score. Top grammar schools (Westminister, St Paul, King’s college of maths and technology, Perse School) they have dozens beating my score every year. I knew it was me. And so did everyone else. The weeks that followed were amazing, self-esteem were maxed out.

I was also selected for the school’s senior teams maths challenge squad. (Top 4 in the school). Both the BMO1 and STMC were on the same day – Nov 15, a big day for me.

Weeks leading up to Nov 15, I did some BMO1 practice, but more STMC practice. Since I know BMO1 questions are so fucking hard that revising barely makes a difference. Me and my team organised several practice sessions together working through the STMC questions, it was actually really fun for some reason.

Nov 15, 10:30 This year’s BMO1 questions were largely doable. As I am writing this, I am awaiting my BMO1 results. I believe I managed to obtain a perfect solution for question 1 and question 3, and partial solutions for q2,4,5. I am estimating a score of 25-30, fingers crossed for a distinction!!!

I finished the BMO1 at 2:25, eyes red, brain wobbling. Tired yet satisfied with my performance, I headed to the main hall to continue the day of maths. There were 20 schools there, the main hall was filled with people. We are SHSB team A. We scored 36/60 on the group round. 78/80 on the crossnumber and absolutely  fucked up the shuttle. OMD we came third, absolutely atrocious. Imagine getting beaten by Westcliff! I’m dying. But to be honest, it was really fun. I loved the atmosphere just like I loved every bit of a teams maths competition nearly 7 years ago. The adrenaline rush is unreal and I loved working with everyone in my team. A massive shoutout to Luke Saville (C), Robby Fogg, Enzo Fong. Also a massive shoutout to Keith Fitzerald, an amazing person and an even better teacher, who helped me and our team along the way. It was a great experience. I would love to do it again next year 🙂

That’s the end of it so far. I will update my BMO1 score and maths competition journeys in the near future, stay tuned.

UPDATE: BMO1: 24/60 (merit) 10, 0, 10, 1, 3, 0