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Further Mathematics

Overview

Further Mathematics is designed to broaden and deepen the mathematical skills developed when studying A-Level Mathematics.

It develops your mathematical ability and introduces you to new topics such as matrices and complex numbers, which are extremely useful for a variety of maths-rich degrees.

Entry requirements

GCSE - 7 or above in Maths

Learning & Assessment

Why study this subject?

Further Mathematics will introduce you to new and interesting mathematical concepts. It will also help to develop your problem solving skills, which will help to boost your performance in A level mathematics. If you plan to apply for a degree that has a high mathematical content, an AS or A level in Further Mathematics will give your application additional value.

What can you expect from this A level?

Further Mathematics is divided into Core Pure Mathematics, Further Mechanics, and Decision Mathematics. Core Pure Mathematics extends A level maths content, covering topics like proof, complex numbers, and differential equations. Further Mechanics builds on A level mechanics, focusing on momentum, energy, and elastic collisions. Decision Mathematics explores algorithms, graph theory, critical path analysis, and linear programming, with connections to Computer Science.

What can you do with a qualification in this subject?

Further Mathematics is a useful course for degrees in sciences, engineering, statistics and computing, as well as mathematics itself. There is also a wide range of career opportunities including roles in engineering, data analysis, actuarial science, finance, and economics.

Assessment

The subject is assessed fully through exams. For the AS qualification, there are 2 exams at the end of Year 12. Both exams are 1 hour 40 minutes long. The first assesses the core pure maths content and the second assesses the further mechanics and decision content.

For the A level qualification there are 4 exams at the end of Year 13.

All of the exams are 1 hour 30 minutes long. two of the exams cover the core pure content, one covers the further mechanics content and one covers the decision mathematical content.

Modules / Topics

Component 1

Core Pure Mathematics.

Component 2

Further Mechanics.

Component 3

Decision Mathematics.

Trips / Visits / Enrichment

Enrichment Opportunities

Engineering Pre-Course Preparation
This enrichment helps students explore the diverse field of engineering and identify the areas most suited to their interests and career ambitions. Through structured research activities, students investigate university courses, entry requirements and future progression pathways, while gaining insight into student life through blogs, videos and case studies. The programme is supported by STEM Careers Week and the Physics Department's annual visit to Northumbria University, providing opportunities to engage with university ambassadors and learn more about studying engineering and related subjects.

Emma Christian

Head of Maths, Physics and Computer Science

"I love doing maths all day, every day and I love seeing students gain their own passion for the subject. If you enjoy puzzles and logic then A-level maths is for you. Maths opens up so many doors for you, from engineering and other science routes to sports analytics and data management."

Joseph Davenport

Year 13 Student

"The foundations of maths are intuitive, logical and mystical. I find the links between all of the areas and the progression of this type of thinking very intriguing. Not only do the links between areas of maths, such as geometry and mechanics, interest me, but the wider exploration of mathematical thinking- such as logic within philosophy."

Engineer

Design and analyse structures, systems, and processes in civil, mechanical, or electrical engineering fields, applying advanced mathematical principles to solve real-world challenges.
Conduct simulations and use mathematical models to test and improve designs, ensuring safety and efficiency.

Data Scientist

Collect, interpret, and analyse large datasets to identify trends and insights that can influence business strategies and decisions.
Develop predictive models using statistical techniques to forecast outcomes and guide organisational decision-making processes.

Actuary

Assess financial risks and uncertainties using complex mathematical models, providing critical insights for insurance companies and pension funds to ensure financial health.
Conduct research on statistical data to inform the pricing of insurance products and evaluate the likelihood of events.

Financial Analyst

Analyse financial data and market trends to provide insights into investment opportunities and develop strategies that guide clients or organisations in their financial decisions.
Create financial models and forecasts to predict future performance and assess the risks associated with various investments.

Statistician

Design and conduct experiments or surveys to collect data, ensuring rigorous methodologies yield reliable results.
Analyse data using statistical techniques to provide insights and recommendations for various sectors, including healthcare, business, and government.

Economist

Apply quantitative methods to evaluate economic theories and analyse market behaviour, using statistical tools to understand and predict economic conditions.
Prepare reports and summaries contributing to policymaking and business strategy, presenting findings to stakeholders.

Software Developer

Develop algorithms and software applications that solve complex problems, utilising mathematical concepts to enhance computational efficiency and effectiveness.
Collaborate with cross-functional teams to gather requirements and iteratively refine software solutions based on user feedback.

Operations Research Analyst

Utilise mathematical and statistical modeling to analyse and optimise business processes, helping organisations improve efficiency and effectiveness.
Collaborate with decision-makers to interpret findings and implement strategies that enhance operational performance.

November Open Evening 2026

Wednesday 4th November 2026
4:30pm - 7:00pm

Find out more

Open Evening - 2nd December 2026

Wednesday 2nd December 2026
4:30pm - 7:00pm

Find out more

16 October 2026

Up and Running - Enrichment Success

This first half term for our Year 12 students has been the most successful ever for our Enrichment programme, which takes places on Tuesday afternoons. With a range of activities covering skills development, social, physical and practical extra curricular, we have over 700 students participating in 42 activities. Ranging from British Sign Language and IBM Cyber Security to Music and Film Production and even Dungeons and Dragons, these weekly sessions are an important part of our ASPIRE programme, and develop the community and ambition of our students in their first couple of weeks as part of NSFC. A major success this year has been our running club, which builds on our sponsorship of the Great North 10k and Great North 5k runs, which happened over the Summer, and saw over 400 participants from across our colleges. The group meet weekly and have both a competitive 5k run, and a less challenging run for those who simply want to get out and get some exercise. Led by Director of Curriculum Kate Gardner, this is a great example of our students engaging in physical activities and working together as a college community. Our first student experience survey illustrated the huge success of a range of our wider enrichments with great reviews of ‘A Taste of China’ for Chinese language beginners, ‘Performance Lab’ where students prepare a Christmas showcase and Film Production which is hosted and managed by a professional production company Digital Sidekick and builds real industry leading skills.

15 October 2026

'Unloc'king our Real Potential - Student Governor Event

A selected group of students, attended a one day conference and selection event to find our new Student Governor, hosted by Unloc, a youth organisation dedicated to empowering young people with programmes designed to develop skills and experience in developing leaders and the student voice. Nadine Dosky, Lauren Dudley, Yasemin Aysa Yildiz and Niamh Richardson attended the event as part of the NSFC group and engaged amazingly throughout the day, gaining valuable experience and eventually selecting Nadine as our next Student Governor for the academic year 2026-2027. The NCG Prospective Student Governors Event was a practical and creative hybrid day that explored the key skills needed for student leadership and representation, with sessions including, ‘being a changemaker,’ ‘creating your pitches’ and ‘selecting your new governors.’ The small group of students from NSFC really benefitted from the activity led by Ben and Kellie from Unloc, and were really grateful to have been selected as potential leaders from among our fabulous students at the sixth form.

9 October 2026

Ready to Aspire

The students at Newcastle Sixth Form College are taking on a new vision for our college community, with the acronym ASPIRE, to help them succeed and really enjoy their A Level experience.

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Your courses

Further Mathematics

Overview

Entry requirements