In the first year, topic areas studied include complex numbers, which allow the solution of a range of equations that would otherwise have no solutions through the introduction of ‘imaginary’ numbers, and matrices which consist of grids of numbers that can be used to represent transformations and are used to solve simultaneous equations amongst many other uses.

In the second year, other areas of pure mathematics are covered such as polar co-ordinates, differential equations and hyperbolic functions. Each of these builds on earlier topics and encourages the development of a wider understanding of the ways in which mathematical topics are interconnected. Both years include a mixture of pure and applied mathematics.

You will use a variety of methods and techniques to help you develop and understand the concepts and techniques used.

During lessons you will:

• extend your ability to solve equations in more complex situations
• learn more about drawing graphs and be introduced to calculus, which is the foundation stone of much advanced mathematics 
• use computer software such as “Autograph” to investigate series, functions and graphs 
• investigate practical problems in statistics, mechanics, or decision mathematics and write reports to explain what you have done 
• work independently and in groups to tackle problems and then present their solution

AS further mathematics is examined in two 1 hour 40 minute exam papers at the end of year 12.   

A level further mathematics is examined in four 1½ hour exam papers at the end of year 13. As further maths must be taken as a fourth subject, all further maths students will sit external AS exams at the end of the first year and therefore have the option not to continue to the second year.

• Further mathematics can be studied as a fourth course, either as an AS level in the first year or full A level.  We are proud to have one of the largest cohorts of further mathematicians anywhere in the country;
• Maths Inspiration Trip - a trip to the Maths Inspiration Lectures which is a national programme of interactive maths lecture shows for teenagers (open to all first and second year maths students);
• Senior Maths Challenge - the UKMT Individual Maths Challenges are lively, intriguing multiple choice question papers, which are designed to stimulate interest in maths in large numbers of pupils (open to all first and second year maths students, compulsory for further maths students);
• External speakers from education and industry regularly come in to speak to students about the use of maths beyond A level (open to all maths students);
• Reading Maths - recreational mathematics books are read by classes who present what they have learned in class (for further maths students);
• STEP and Admission test preparation lessons - once per week in year 12, twice per week in year 13 (for more information click here;
• Support for BMAT candidates;
• Weekly stretch and challenge problems set as part of homework.

Double mathematics students take a wide variety of other courses.  Many take one or more from the sciences.  However, students do take a wide range of other subjects including languages, arts, humanities and music.

If you want to apply for maths/engineering/physics/computer science at a competitive university it is advisable to add 1st year support for admissions tests to your programme.

Mathematics and further mathematics are highly regarded and provides strong support to any application for employment or further study.  It is important to have studied further mathematics for some courses in mathematics, physics and engineering at some universities. The applied units in mechanics and/or statistics are necessary for many courses in science and engineering.  The statistics and decision mathematics studied is very useful for many courses in the social sciences.

The study of pure mathematics develops logical thinking and a systematic approach to problem solving - attributes which are highly valued in the workplace.

Please see below for careers and labour market information for further maths - use the refresh buttons to find out about different courses and careers, and use the left and right arrows to view more detailed information.

You can find the prep work for this course at prepwork.farnborough.ac.uk.

Q:  What is the benefit of studying Further Maths?
A:  Further Maths would be beneficial to anyone planning to study maths or a maths-based subject at university e.g. maths, engineering, physics, computer science or economics.  Studying further maths also increases the likelihood of getting a top grade for A level maths.

Q:  How is it structured?
A:  In the first year, further maths is 50% pure maths, 25% mechanics and 25% statistics. In the second year, it's 50% pure maths and there are some options about what is studied for the other 50%. These options include mechanics, statistics, decision maths and further pure maths. All students sit an external AS exam (for which there are 2 papers) at the end of their first year. Since further maths is taken as a fourth subject, it is possible to drop it after one year and still have a qualification to show for the year's study. The AS exam does not contribute to the overall A level in further maths, for which there are four exams at the end of the two years of study.

Q:  Is it a lot of work?
A:  You would certainly be spending a lot of hours, both within and outside of lessons, doing maths. However, if you really enjoy maths then this may not feel like work! The number of hours needed is usually considered manageable, especially in the first year since most students who study further maths tend to find the maths A level relatively straightforward. 

Q:  Is it hard?
A:  Further maths builds on the ideas introduced in the maths A level and hence the content is more challenging. However, most students who study further maths enjoy challenging problems and so are happy with the level of difficulty. Our excellent results show that even though the course is more demanding than the maths A level, our students still finish with an excellent knowledge and understanding of the content.

Q:  What do you offer in terms of enrichment and stretch and challenge?
A:  Our usual yearly programme includes guest speakers visiting college to give lunchtime talks on a range of interesting maths related topics. In addition, we offer a Support for University Admissions Tests (SUAT) programme to both first and second years to assist with applications to competitive universities for maths and maths related degree courses.