Whilst the A level Mathematics course builds on the knowledge gained in your GCSE years, the emphasis is different. Algebra still has a central place, as this is the language in which the subject is expressed, but more importance is attached to being able to produce clearly reasoned arguments. You will build up a mathematical toolkit, which will be both of intrinsic interest and contain the methods which you will need to become an effective problem solver. Being a sixth form mathematician, though, is not solely about examination preparation: you will also have opportunities to take part in competitions, go on study visits, and work with younger pupils.
Students starting their A level Mathematics course in September 2017 will be the first to follow the new linear specifications. These are still at a draft stage, so we have yet to make a final decision about which to adopt. All the new A level courses have identical subject content as prescribed by the Qualifications and Curriculum Authority (QCA); two thirds of this is pure mathematics and the remainder applied.
Pure mathematics is the study of mathematical methods for their own sake, and you will gain a grounding in topics such as algebra, calculus (the study of gradients and areas under curves), numerical methods, trigonometry, vector geometry and differential equations. In applied mathematics, you put the techniques you have learnt to use in modelling real life situations: in mechanics you study forces and motion, and in statistics how to use mathematical rules to simplify complex probability calculations and how to analyse sets of data and draw reliable conclusions.
The course is linear, leading to examinations at the end of the U6. Assessment will be entirely by three equally weighted written components. The likely assessment structure is:
Calculators are permitted in all three papers.
Above all, we hope that you will choose to do mathematics in the sixth form because you enjoy it. Mathematics fits well with almost any other combination of subjects. It is a useful back up to the sciences, and adds breadth to arts subjects. Many of skills you need are surprisingly similar to those used in, for example, learning a language or analysing a philosophical argument. An A level qualification in mathematics is highly regarded by universities and employers as it gives evidence that you are at home with numbers and are a logical thinker.
A level Mathematics is an essential requirement not just for further study in mathematics but for most degree courses in physics and engineering, and for many in subjects such as economics, architecture and computing.
We will expect you to have studied IGCSE or GCSE Higher Level Mathematics and we recommend strongly that you have gained a minimum of an A grade at IGCSE or a grade 7 at GCSE. In itself this is not a guarantee of A level success, so seek the advice of your current teacher: they are in the best position to judge whether continuing beyond GCSE is a sensible choice.
Further Mathematics A level is offered in conjunction with Mathematics. This combination normally forms two of your four option choices.
What the Further Mathematics course is not is simply more mathematics at a similar level to the single subject A level. Having gained a working knowledge of the essentials, you go on to study pure mathematics in much greater depth. You will learn advanced techniques in areas such as integration and matrix theory which are fundamental to physics and engineering at degree level and beyond. You will look at a wide variety of mathematical applications, from how to model the behaviour of elastic strings and springs to the theory behind linear regression. More time will be spent in proving results and you will learn to think creatively and to look for elegance. The interconnectedness of seemingly unrelated topics, which is one of the things that gives mathematics its beauty, will start to become much more apparent.
Taught completely separately from single subject mathematicians, you will work towards the equivalent of a full A level in Mathematics in the L6, before tackling the Further Mathematics course in the U6. 50% of the course will be compulsory pure mathematics prescribed by QCA; the remainder of the course is most likely to be evenly split between mechanics and statistics but there may be some flexibility in this to accommodate the particular interests of the group.
As with A level Mathematics, the assessment details have yet to be finalised. It is likely that you will sit 4 equally weighted papers of 1 hour 30 minutes each, with two of the papers covering the compulsory pure content, one mechanics paper and one statistics paper.
Why study Further Mathematics?
Many students take Further Mathematics simply because they enjoy mathematics for its own sake and thrive on intellectual challenge. It is quite usual for Further Mathematicians to complete full A levels in all four of their subjects, so choosing it need not restrict the breadth of your sixth form studies in any way.
You will want to take Further Mathematics if you are considering a degree course in mathematics or a closely related subject. Not only will some universities expect you to have taken it given that it is offered here, but, unlike single subject Mathematics, it will give you a flavour of what mathematics at university entails. If you hope to read physics or engineering at universities such as Oxford, Cambridge and Imperial College, studying Further Mathematics will improve your chances of gaining a place. Further Mathematics (as one of four A levels) is also strongly preferred for some of the most competitive economics courses, such as that at LSE.
Like Mathematics, Further Mathematics is a highly regarded qualification whatever direction you choose at university.
Even though Further Mathematics is not listed as an essential requirement for university mathematics courses (because not all schools are able to offer it), we would strongly recommend that you opt for it if you are considering further study in mathematics.
As explained above, it is also recommended if you wish to study physics, the physical branches of engineering or economics at certain universities: if you have a particular direction in mind at this stage, it is worth checking the specific course requirements.
The pace in the Further Mathematics set is fast and you will need to reach A level standard by the end of the L6. In addition to the requirements for single subject Mathematics, you must be capable of picking up ideas quickly and of thinking on your feet. Discussing your suitability with your current teacher is therefore crucial.