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.
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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)