The 16+ Mathematics Entry Exam for St Paul’s School

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 all schools offer additional problem-solving clubs but there is a huge amount of online material on offer and we want to know what you have discovered.

Here are some questions that have been set in previous years to give you a flavour of the level of questions that we set:

There are a number of things you can do to develop your problem-solving skills.

The last 5 questions of GCSE and IGCSE papers are certainly worth practising. They have become more challenging over the last few years and have little or no scaffolding. You have to develop the solution yourself devising a series of stages that lead you to the answer. It is not always obvious where to start.

Have a look at the questions set by the UKMT for the Intermediate and Senior Mathematical Challenges. The skills required for the challenging questions at the end of the papers use standard number, algebra and geometry skills. However, initially it will not be easy to work out how to apply the skills. With practice, and some guidance from your mathematics teacher, you will gradually improve until you are confidently tackling the majority of the questions.

Encourage your school to enter you for these challenges. You could even start your own mathematics club where similar minded pupils can share ideas to solve the problems.

- Mr Ashworth Jones

Head of Mathematics

The Hans Woyda Trials

The Hans Woyda Maths competition is a London based interschool challenge. A big difference to other competitions is that it is a vertical year group team containing a Fourth, Sixth, Lower and Upper Eighth student (Years 9, 11, 12 & 13). The Hans Woyda’s main focus is speed, with seven sections of fast-paced questions. For instance, in the first section students only have 30 seconds to give their answers, and in the last section the first student to answer correctly gets all the points! The trials took place over multiple mornings and lunch breaks and students had to complete a time pressured test in order to claim a place in the St Paul’s squad. The top 3 students of each year group will each compete in one of the group matches of the Hans Woyda competition and will challenge other schools for the illustrious trophy. Here is a selection of some of the questions:

Problem Solving with Mykhailo

The maths society had the pleasure of welcoming one of our own, Mykhailo who presented a captivating talk on problem solving in mathematics. He began by telling us of his journey through mathematics, starting in Ukraine at the humble age of 7, where he agreed to compete in his first Olympiad in return for some Lego - a worthy reward. By the age of 11, however, he began to lose interest until a remarkable geometry teacher reignited his passion. From that point on, he was completely hooked on geometry, so much so that his Olympiad scores r eflected his singular focus: 0/7, 0/7, 0/7, and finally, 7/7, as he excelled in geometry alone. He, therefore, decided that it would be best for his progress if he stopped doing geometry altogether, focusing instead on the other 3 areas of math: Algebra, Arithmetic, and Number theory. He led us through a series of questions, seemingly impossible at the face of it but very manageable after explanation. Among the problems were a complex simultaneou...

Preparation for the Senior Maths Challenge (SMC)

With the Senior Maths Challenge (SMC) a week away, 8 th form students are preparing at the Senior Problem-Solving Club. The Senior Problem-Solving club is a lunch time activity where students work through a mix of interesting and stretching questions. The focus this week was on the hard final question on the paper with Dr Hemery and Mr Morris providing the last 20 years of question 25. Here is an example: As the final and typically the most demanding question of the SMC, it provided an excellent test for even some of SPS’s best problem solvers.

SPS Mathematics Blog