I want to start learning what I need to know for A-Level further maths to take some of the "weight" off of year 12 and 13. What topics should I begin learning and what key ideas do I need to grasp and understand. Are there any books you would recommend? I don't wont to just learn the "simple AS" topics, like differentiation; that's like GCSE.

  • $\begingroup$ I would suggest you go through the specification, such as section 5 of this from OCR until you hit something which looks like an extension of what you already know. You might also talk to other British students, for example at The Student Room. $\endgroup$ – Henry May 24 '11 at 22:06
  • $\begingroup$ Did you look at the questions and their in the "Related column" on the right? We already had many similar questions with many good general and specific answers. Unfortunately, I can't tell you anything more specific since I don't have the slightest clue what "A-level", "simple AS" and "GCSE" mean. $\endgroup$ – t.b. May 24 '11 at 22:07
  • $\begingroup$ @Theo It's the English system for exams, GCSE is year 10 and 11, A-Level is year 12 and 13 and AS is the first unit of A-Level $\endgroup$ – Will03uk May 24 '11 at 22:20
  • $\begingroup$ Thank you for the clarifications. Essentially, I only tried to point out that I (and probably many others on this site) simply aren't familiar enough with the English system in order to be able to give answers specifically adapted to your situation and thus going beyond mere generalities. Be that as it may, I wish you all the best and hope you'll get some helpful input! $\endgroup$ – t.b. May 24 '11 at 22:34
  • $\begingroup$ This seems like a candidate for a "too localized" question: as phrased, it applies only to students in the British educational system. Can the question be rephrased so as to be of broader interest and usefulness? $\endgroup$ – Pete L. Clark May 25 '11 at 5:54

I'm taking Further Mathematics and am about to sit for my P2 (Applied) in two weeks time.

Since Further Mathematics is essentially 1st year undergraduate engineering mathematics, you could reference such materials, especially for content on Calculus 1, 2 and 3 in an American system

I've personally used Mathematical Methods for Physics and Engineering: A Comprehensive Guide by K. F. Riley, University of Cambridge, M. P. Hobson, University of Cambridge, S. J. Bence


As in any mathematical course, mathematical intuition is fundamental, so don't hesitate to Google relevant areas if unsure. Sites e.g. Math.Stackexchange, relevant subreddits (/r/math, /r/engineeringstudents etc.), Proofwiki (mathematical induction) can be useful at times. As far as preparing for the exams themselves once you've familiarized yourself with the course content, past year papers are a good way to begin with. Do check your college's library for availability of previous examination papers. Mine has some dating back to 1978.

On a more immediate note, you should familiarize yourself with trigonometric identities, e.g. product to sum formulaes, addition formulaes etc., various precalculus concepts such as the Chain Rule.

For those uninformed about the course itself, here's an outline of the syllabus (Cambridge A Levels - Further Mathematics 9231)


  • $\begingroup$ Thanks, this will help loads. Good luck in your exam $\endgroup$ – Will03uk May 25 '11 at 16:29
  • $\begingroup$ That's helpful. Thanks! $\endgroup$ – B.Jenkins Apr 6 '16 at 10:30

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