I have only written at length about the FM Mechanics and the Differential Equations. That is simply because these were the topics where I found textbooks provided less than I wanted to present. There is a need for extensive examples of the use of DEs in real life using the range of those solvable at school level (which for many includes early university). To me, that would go a long way toward a justification of calculus too.

I wrote about torque, rotation, and three more pages on inertia for precisely the reason given in the previous paragraph, based on the difficulties discovered by classes year on year. I think that, by the time one has worked through the two examples pages, the FM content under both Edexcel and MEI is well understood. Of course, while answers are visible, there will be people who say they have worked the pages, but actually leant hard on the existence of results. One of the difficulties with this topic (like some of those in the Stats), it is relatively easy to produce an answer but relatively difficult to demonstrate that your answer is the correct one (and sometimes that your reading of the question is consistent with your answer). There are consequences at exam level: it is very much easier to mark a paper where the student is not given the answer but has the same answer as the examiner; conversely it is relatively difficult to find what was wrong with a wrong answer (especially if the student was right for their reading of the question). On the other hand, if all are given the target answer, this helps all students identify a wrong result but makes careful marking harder where students have recognised that they are close but have not actually written enough down to constitute proof they really worked the question. From a marker’s point of view, if the paper as a whole is looking as an A* (the maths is of a standard equal to or batter than the marker’s maths), then the marker will accept what he or she might describe as ‘missing lines of working’; for a B-grade candidate the marker will insert an arrow and write something like ‘missing working’, or ‘fudge here’ and try to deduct marks. Like I say, difficult. From a student point of view, you should be internally honest — know when you’re fudging and only do it when desperate. What is more, those doing fudging need to recognise that unless they work at discovering what they missed (when the question is worked in class, for example), this will happen when they least want it to, i.e. in the exam that matters.

I have written some work on Matrices, which is Edexcel Further Pure, but the transfer between software packages caused a loss of content, specifically the example matrices. I may be able to restore these.

DJS 20171116

You will find some relevant material in the FPM section. Hyperbolics, for example.