A Level Further Mathematics Tutors

The experts at The Profs look at the A level further mathematics syllabus, entry requirements and options for onward study.

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Why study A Level Further Mathematics?

A level further mathematics is intended to provide a broader and deeper grounding in mathematics than that provided by the standard maths A-level. Many university courses require you to have a maths A level, but only a handful specifically require you to have one in further mathematics.

Nevertheless, studying A level further mathematics demonstrates significant prowess and only students who have done exceptionally well at GCSE mathematics are usually allowed to take it. This is not because it is exceptionally hard (most students say it isn’t) but more because it entails extra work. It is also very important to have an enthusiasm for the subject.

Who needs A level further mathematics?

Certain leading universities make it a condition for an offer of a place on their mathematics related courses. Clearly, this includes students who intend to major in mathematics itself, but also those who combine it with disciplines such as mechanical engineering or computer science. Colleges known to insist on it include Oxford, Cambridge, Warwick, and Imperial College London. UCL also recommends it.

Most other colleges provide foundation courses in the first year to get students up to speed before embarking on modules which are dependent on advanced maths. If you already have A level further mathematics, you may not need this foundation module.

Overlap considerations

It should be noted that if you are taking ordinary A level mathematics and A level further mathematics at the same time, some elements of the syllabus will overlap. This could be an advantage or a disadvantage: it might help reinforce some ideas, or you might consider it a waste of time.

When you apply for a university course, most will only count one mathematics A level toward your entrance requirements. That means you are effectively taking an extra A level. Relatively few schools provide advanced mathematics as a single comprehensive subject. Many do not provide A level further mathematics at all and you will need to find alternative tuition.

What is studied in A level further mathematics?

The majority of examination boards now divide the subject into six modules (your school may allow you to complete half the course for an AS level). They are based upon the same groundwork as your ordinary maths A-level modules, but every module must be different. They are still loosely grouped into pure maths, mechanics or statistics, but some examination boards allow a greater degree of choice in modules than others.

Topics typically covered by the pure maths modules may include; complex numbers, matrices, methods of proof, the Maclaurin series, improper integrals, hyperbolic functions, domains, Argand diagrams, Cartesian-modulus translation, quartic equations, partial fractions, de Moivre’s theorem, network theory and critical path analysis.

In the mechanics-focused modules you will work in areas such as; momentum and impulse, Hooke’s Law, the work-energy principle, friction, Newton’s experimental law, circular motion, harmonic motion, differentiation and integration of vectors and centre of mass calculations.

Statistical modules may introduce you to; the Poisson process, probability distributions, goodness of fit, statistical inference, Spearman’s rank correlation, chi-squared tests, Central Limit Theorem, Mann-Whitney and Wilcoxon signed rank tests, standard deviation, regression, interpolation, unbiased estimators and variance criteria.

What other GCSEs should I have?

Because of its broad applications, you can accompany mathematical studies with almost any combination of other subjects. Mathematics is used by artists as well as scientists and by engineers as well as stockbrokers.

However, if you are considering A level further mathematics because you are interested in a physics, computer science, social science or mechanical engineering career, you should choose other GCSEs and A-level mathematics modules geared toward those specialities.

Physics, engineering and mechanical design courses will benefit most from mechanics-oriented modules and other science subjects. Social sciences, information sciences and economics courses will benefit more from your statistics-oriented modules but also work well with languages and environmental studies.

If you are taking on the extra work of an A level further mathematics course, it may prove valuable to have access to some additional expert help. The Profs private tuition service can provide expert one-to-one help where you really need it. If your place in a leading university is at stake, this may be a valuable investment.

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