A Level Further Maths

Further Mathematics is a stimulating and rigorous A-level designed for students who excel in maths and want to deepen their understanding. It complements A-level Mathematics and is highly recommended for those considering degrees in mathematics, engineering, physics, or computer science.

Core content (Compulsory for All Students)

All students must study this content:

• Mathematical argument, language and proof
• Mathematical problem solving
• Mathematical modelling

Advanced Topics Covered

• Proof
• Complex numbers
• Matrices
• Further algebra and functions
• Further calculus
• Further vectors
• Polar coordinates
• Hyperbolic functions
• Differential equations
• Trigonometry
• Numerical methods Options

Optional Applications (Choose Two):

• Mechanics
• Statistics
• Discrete mathematics

Three written exams, each 2 hours long and worth 33⅓% of the final grade.

Paper 1 & Paper 2: Core and compulsory content

Paper 3: Two application areas chosen from:

Mechanics & Statistics

Statistics & Discrete

Mechanics & Discrete

Each paper includes a mix of short questions and multi-step problems to assess depth of understanding and mathematical reasoning.

5 GCSEs at grade 4 or above including Maths at grade 7 or above.

Aside from A level mathematics opening the door to leading universities in the UK, there are many varied career paths that heavily lean on mathematics skills at this level. There are many new applications of mathematics in technology, games design, internet security, programming and communications. On-going applications in engineering, such as aircraft modelling, fluid flows, acoustic engineering, electronics, civil engineering and new scientific processes such as modelling populations, diseases, quantum physics, astronomy, forensics and DNA sequencing.

Financial systems and online purchasing systems are underpinned by mathematics, relying heavily on online security and encryption. GCHQ has the largest group of mathematicians working anywhere in the country. A good understanding of mathematics is beneficial for the study of chemistry, biology and geography. Psychologists use statistics to analyse the relationships between variables and predict behaviours. Lawyers rely on statistical data and the logical thought processes developed through the study of mathematics.