SPS Mathematics Blog

It was another successful year for the students who qualified for the British Mathematical Olympiad Round 1 (BMO1). Of the 85 students who took part, 35 received merits, 25 received distinctions, and 7 students qualified for BMO2. Having 7 students qualify for BMO2 is a fantastic achievement, especially given that only around 100–120 students nationwide reach this stage each year. This is also the highest number of merits and distinctions the school has ever attained in BMO1. Well done to all the students who took part — your hard work is truly paying off! Here is a selection of questions from the six problems on the BMO1 2025 paper, courtesy of UKMT. The full paper and mark scheme are available here :

SPS held a maths partnership event with a variety of the partnership schools in the local area. The event included a series of UKMT Team Challenge problems where groups were composed of one student from each school. The event kicked off with a 10 question quick fire quiz, followed up by a maths crossword, called the crossnumber. The event finished with a unique maths relay, in which each group was split in half and the teams competed in finishing a 20 question quiz, where the questions had to be completed sequentially with one half doing odd numbered questions and the other half doing the even ones.  There were two competitions those with 3 team members and those with 4. The scores were very tight and so huge congratulations to the winning team in both category. The top team was outstanding, almost scoring almost full marks. Overall, it was a great day where everyone enjoyed themselves and had their fill of maths. - Shorta  

A match report by Yidong from Cloete house: The First Round & Semi Final : In the first round, Cloete knocked out Nilsson by 34 points to 26, despite the scores being tied with just four race questions left. Gilks narrowly edged out Harrison by 24 points to 22, a gap of just one question, whilst Langley and Blurton won against Stewart and Warner respectively. Cloete beat Langley 34-26 in a replay of the semi-final that had gone the other way last year, and Blurton were victorious against Gilks to seal their spot in the final. The Final : The usual buzz spread throughout the school on the day of the final, and a large queue had even formed outside room 220 before the match! Unfortunately, most filtered into Chess Club in room 221, but a large crowd of four people came to watch, nevertheless. The line-ups for the match were Aryan (4th), Yidong (5th), Lucien (6th), Ashok (L8th) and Terry (U8th) of Cloete House, against Blurton’s team of Haoming (4th), Aron (5th) Kevin (6th), Richard (...

St Paul's hosted a set of morning revision sessions with its partnership schools. This was led by SPS staff and supported by teachers of the partnership schools. The skills involved targeted level 7 - 9 questions of the GCSEs, with topics students tend to struggle with: Quadratic Inequalities Proof of Circle Theorems Geometric Problems with Vectors Tree Diagrams for Dependent Events Using Bounds in Calculations The sessions were a success and it was pleasing to see the cooperation between students and teachers of different schools. Anyone walking past the John Colet Hall could hear the buzz of students engaged in mathematics!

The British Maths Olympiad (BMO) comprises of two rounds, the BMO1 and BMO2. Qualification for the BMO1 is determined by attaining at least 110 out of 125 in the Senior Maths Challenge. St Paul's ente red 95 students into the BMO1, of which 34 attained merits and 19 distinctions. Further to this, 5 students qualified for the BMO2. Approximately 100 of the top students in the country sit the BMO2 so qualification in itself is quite the achievement.  Of the 5 that completed the BMO2, 4 students achieved distinctions Rishab (29/40), Michael (34/40), Adavya (40/40) and Aman (22/40). Adavya and Michael  have been invited to the UKMT BMO Training Camp at Trinity College, Cambridge over the Easter holidays, where they will undergo intensive training and testing, after which the British team for the IMO will be selected. Congratulations to Adavya for achieving a remarkable complete set of full marks in SMC, BMO1 and BMO2 this year.  

Two students who joined St Paul's in L8th, Conrad and William, discuss the their experience of joining the school. Arav of the Maths Society volunteered to interview the students. 

The mathematics entrance exam at 16+ is taken in November for entry to study A Levels in the following September. The content of the exam is the Edexcel IGCSE syllabus but does not include the topics of arithmetic series and differentiation.  The emphasis is on number and algebra skills. The test for entry in September 2026 onwards will be non-calculator. When you apply to St Paul’s, we need to know whether you intend to take single mathematics A Level or further mathematics A Level. Pupils who do well on the entrance papers across all their chosen subjects are invited for interview. Interviews are taken by subject specialists at St Paul’s School and last 20-30 mins. The aims of the interview are to: gauge your ability to apply the GCSE mathematics skills in unfamiliar questions. to understand your reasons for choosing the subject. to investigate the additional problem-solving skills you have developed through classes and your independent studies. We realise that not ...

We hosted approximately thirty Year 10 pupils from partner schools in London (including Fulham Boys School, Grey Coat Hospital, Christ’s School, St Paul’s Girls School, and West London Free School). In addition to the mathematics sessions, break-out activities included a bridge-building engineering challenge in which teams of six pupils constructed a load-bearing bridge exclusively out of A3 paper, lollipop sticks and Sellotape, spanning 50cm, which was then tested – to destruction – by incrementally adding more and more weight for the bridge to bear. The pupils also took on a cypher challenge, again in teams of six, to construct a cypher using fifty 1p coins and fifteen 2p coins, and then – in half-teams – to encrypt and decrypt as much plaintext as possible. Here are some of the activities on offer: Mathematical Proof ( a report by Mr Cullen-Hewitt ) What constitutes a proof? Images of dusty chalkboards heavily laden with obscure symbols and inscrutable diagrams might spring to mind,...

On the morning of Wednesday 19th June, a group of pupils and teachers gathered at King’s Cross station for a trip to visit Trinity College in Cambridge. Mr Morris and Mr Cullen-Hewitt filled the taxi ride with commentaries on several of the more famous landmarks on our route, and provided some insight into their own experiences during their time in Cambridge. When we arrived at the Centre for Mathematical Sciences, we were greeted by an Old Pauline, Imre Leader, who, since graduation, has done lots of research in Combinatorics and become a professor of Pure Mathematics at Trinity College Cambridge. After leading us through to the centre of the CMS, our first of two Mathematics sessions began. The lecturer began by posing a question on Euclidean Geometry, and, when only one of us was able to solve it, the idea of the Miquel point was introduced and its subsequent generalisation regarding a triangle and a cyclic quadrilateral. We then proved some facts about the Miquel point, which g...