Exam Board: AQA

  • Complex issues: why is √-1 an ‘imaginary’ and ‘complex’ number?
  • Storm in a teacup? Learn how to use the Poisson distribution to see if the number of events such as hurricanes is actually higher than usual or within the bounds of expectation.
  • One formula: learn how the Maclaurin series formula ties together sin x and x, x3, x5, x7 ...
  • A to Bees -  find out how bees fly from flower to flower using the shortest distances.


Entry Requirements

You must have achieved at least 5 GCSEs at grade 4 or above including Maths and English Language, with at least a grade 7 in GCSE Maths. You must also be studying A Level Maths alongside Further Maths. Entry onto the course is subject to a discussion with the Head of Department.


Is this course for me?

  • You would like to consolidate and reinforce your standard A Level Mathematics work, helping you to achieve the best possible grades.
  • You would like an extra challenge and the chance to explore new and/or more sophisticated mathematical concepts.
  • Further Mathematics is a challenging course designed to extend gifted Mathematicians. It broadens and deepens the Mathematics covered at A Level as well as introducing new topics.
  • Further Mathematics is good preparation for those students aiming to study the subject at university, or other Maths-rich subjects such as Engineering or some Sciences.


Where does it lead?

Further Mathematics provides the bedrock for getting to the heart of numbers, shapes, movement, data and relationships. Advanced Mathematics is used in many jobs and has clear and obvious associations with Physics, Chemistry, Biology, Economics, Business Studies, Geography and Computing. Perhaps less apparently it has strong links, both aesthetically and practically with Art, Design, Music, Psychology, Law, Sociology and Sports Studies. Further Mathematics is a very useful, adaptable qualification. A Mathematics degree can lead to a great variety of careers including weather forecasting, computer games programming, in accounting or finance, scientific research design and developments, statistics, environmental science, aircraft design or drugs trial analysis – the list is endless. Mathematics is also an essential basis for careers in engineering and architecture.


What will I learn?

Year 1

The course covers topics such as advanced algebraic functions, complex numbers, matrices, Maclaurin series, volumes of revolution, vectors, Hamiltonian cycles, Eulerian trails, Euler’s formula, Kuratowski’s theorem, bipartite graphs, adjacency matrices, spanning trees, route inspection, travelling salesperson problem, network flows, critical path analysis, linear programming, game theory, binary operations, discrete and continuous random variables, Poisson distribution and Chi tests.


Year 2

You will study a mixture of new topics and topics covered in Year 1 in more depth including de Moivre’s theorem, eigenvectors, partial fractions, inverse trigonometry, arc length, lines and planes, differential equations, simple harmonic motion, damped oscillations, numerical methods, loci, the Simplex algorithm, group theory, probability density functions, distribution functions and Yates’ correction.


Learning is offered through lectures, discussion, interactive whiteboard activities, PC software (graphs, spreadsheets, mathematical word processing etc), texts, internet research, mechanics apparatus, videos, audio material. You will engage in class-based and independent learning, making use of our rich and diverse collection of reading, audio and video material. Our innovative online Maths tutorials are also provided to help with your revision.


How will I be assessed?

All assessment in the Further Maths A Level is by written examination in all areas studied.


What activities can I get involved in?

You will have the opportunity to take part in national competitions such as the UKMT Challenge and the code-breaking National Cipher Challenge as well as attending lectures independently by visiting speakers 
at Liverpool University, recent ones including ‘Maths, Pigs, Chickens and Criminals.’ There is also a wealth of non-curriculum activities to explore, built up over many years, via our College virtual learning environment.


We have made every effort to ensure that the information displayed is accurate. The College reserves the right to make changes and cannot accept liability arising out of, or in connection with any revision. 
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