Maths and Further Maths

A unique curriculum,  designed to challenge, delivered by dedicated and passionate staff.


In year 13 all students are entered for:
• A2 Mathematics
• A2 Further Mathematics

We will use the OCR B (MEI) A-Level Specifications

At the University of Liverpool Maths School, all students study both Mathematics and Further Mathematics A levels. This allows us to deliver the two curriculums simultaneously, giving students the opportunity to make strong links between topics and explore mathematics in different ways. Our approach makes the Further Mathematics content more accessible to students, building their confidence with a wider range of areas within maths, allowing them to engage with visitors from universities and industry who frequently deliver talks at the school.

Lessons are delivered to classes of approximately 15 students, with a large amount of contact time with a variety of teachers. Students have the opportunity to work in smaller groups once a week during supervision time, when a teacher will work with them to support their learning or extend the topics currently being taught. From September 2021, students will be exposed to a lecture style of teaching once a week, with the whole cohort being taught at the same time. The intention here is to allow students to familiarise themselves with this approach so that their transition to university learning is a more manageable one.

The curriculum is carefully planned so that students have the opportunity to develop as mathematical thinkers, with a solid foundation of skills which allow them to solve problems and articulate their reasoning clearly. Assessment is rigorous but with the focus being on identifying areas for improvement and creating further opportunities for dialogue between teachers and students. Learning is fast-paced and dynamic but there are always opportunities for students to seek support from all members of the teaching staff within the department.

In the first term of Year 12 the students will focus primarily on the pure maths content of the AS Level Mathematics course. This allows them to consolidate their knowledge of higher level GCSE topics and become accustomed to the demands our teachers place upon them; they will be relentlessly challenged to think and to work independently, both individually and with peers. Teachers use a variety of pedagogical approaches but building students understanding of mathematics is at the core of our approach, with formal proofs an integrated part of our teaching. The term concludes with the students meeting topics many will not be familiar with, such as basic calculus and logarithms.

As students progress through Year 12, they move onto the pure maths content from the A2 section of the A level course, whilst also beginning to study some of the Further Mathematics content; topics such as matrices and complex numbers broaden their mathematical horizons whilst deepening their knowledge of calculus and trigonometry enables them to solve increasingly complex problems.

Having completed the pure content of the A level, students begin the applied modules in statistics and mechanics. Making links with their studies in Physics is a rewarding experience whilst understanding the necessity of strong statistical skills in modern society leads many to see more clearly where their mathematical studies could take them. Students become skilled in predicting the path of projectiles, evaluating a system of forces, working with complex probability problems and being able to carry out hypothesis tests.

This approach to Year 12 means that the entirety of the A level Mathematics curriculum is concluded by the end of May, allowing students to sit full mock examinations and have a clear expectation of their progress as they embark upon the university application process. This also enables them to engage more readily with the entrance examinations required by many of the UK’s top universities, particularly Oxford and Cambridge Universities.

Having completed the content required for A level Mathematics in Year 12, the focus for Year 13 lies with the Further Mathematics A level. Students continue to extend their skills into areas such as differential equations and multi-variable calculus, whilst also studying further topics in statistics and mechanics. The OCR MEI Further Mathematics course requires students to study 3 optional minor modules and we have chosen to deliver the statistics and mechanics minor modules, to supplement the work completed in Year 12, along with the Extra Pure minor option. This third option introduces students to even more new areas of mathematics, such as group theory, and we believe that this will be of most benefit to them as they transition into STEM based degrees.

Throughout Year 13 the students will be given guidance about how to continually revise content from Year 12 and there will be opportunities for them to support younger students in their studies; explaining topics to others is a powerful mechanism for understanding the topic more clearly for themselves.

It is our belief that our approach to working with our students will develop them into confident and skilled mathematicians, capable not only of examination success but, more importantly, able to go onto thrive in their chosen studies and careers once they have left us. 

If you wish to explore further the work students do outside of the examined curriculum, including individual and group projects, please visit our AMP page. 

If you have any further questions regarding mathematics at the school, please contact Head of Mathematics, Colin Thomas, via our contact us page.