Self teaching as further maths?

Next year I will be self teaching further maths (edexcel) to gain an AS in it. Anyone have any tips or useful links for it?

It's certainly possible, but you need to take total responsibility for your own learning and understand when (and how) to seek assistance when you get stuck, if necessary.

In Year 12 I successfully self-studied Edexcel C1-C4, S1, S3, S4, M1, M4, M5, D1 and D2, with the bulk of the work taking place during the Year 11 summer holidays and during the various 1 or 2-week breaks scattered throughout the year. (FP1-3, S2, M2 and M3 were done in class.) It was the workload itself that I found trickiest: it's one thing to get A grades in those modules, but it's quite another to consistently maintain 90%+, so you need to make sure that you allocate as much of your time as possible towards doing as many of the textbook questions as you possibly can, including all possible exam questions, ensuring that you fully understand all of the steps involved in those calculations. In my opinion, the summer holidays after Year 11 and Year 12 are incredibly useful, because they really allow you to hit the ground running during term time: you don't necessarily need to go all out doing exam papers and the like during this time, but it is feasible that you could learn the bulk of your course content if you put in a few hours each day.

I don't know if Edexcel still do this, but they used to have an online 'solution bank' where they provided detailed solutions to all of their textbook questions. If you have access to a library containing the legacy textbooks (called 'Heinemann Modular Mathematics for Edexcel AS and A-Level', then borrow them -- some of the newer textbooks do take questions from there, but you'll find a few hidden gems of difficult questions in there, which I found particularly useful for Mechanics. (These were designed with the 2000 specifications in mind, so they're pretty old, but for general interest, you can find the old textbooks for S5, S6 and M6, which haven't had exam papers for something like 13 years, but are interesting reads nonetheless. (As I recall, S5 contains some stuff on generating functions which are quite useful if you plan to do any probability and stats at uni.) Here's an example M6 paper from back in the day: https://papers.xtremepapers.xyz/Edexcel/Advanced%20Level/Maths/2005-Jun/23_M6_June_2005.pdf

Other resources include the Solomon papers, which as I recall were 'harder' versions of the Edexcel papers, so these are great if you're running out of prep material, and I believe there are a few other versions like this ('Zig-Zag' might have been another, and one other brand whose name I can't quite remember).

I'd also recommend my own YouTube channel, CrystalMath, for some integration examples and some stuff that might be relevant to the complex numbers topics in the Further Pure spec.

I watched your videos before, they're great! I take it you've done maths at uni? Have you sat the STEP?

Thanks! How did you find my videos, if you don't mind me asking? Yes, I graduated a couple of years ago -- I sat the STEP exams in 2013.

I was procrastinating on flammable maths and they were on the recommended. Ah nice! Do you have any tips for it?

During my preparation, I made a spreadsheet enumerating all of the questions from every STEP paper dating back to 1987. (The current STEP papers have 13 questions I believe, whereas some of the older ones had more, including some off-spec questions on matrices or groups, so you may have to delete or add cells where appropriate.) I focused on just doing as many questions as I could throughout the year, with the aim of doing at least 6 STEP questions every day, saving the recent exam papers (2010-2012) for mocks in the month leading up to the exam. The STEP preparation thread on TSR was quite useful, including the solutions provided (which are generally good, but I remember finding errors in some, so use them for guidance). I definitely didn't end up doing all the questions, but I ended up doing at least 800 or so, which was enough for me to feel confident going into the exams. Don't be afraid of the probability and stats questions, either: a lot of people shy away from those, particularly in STEP III, but it can be nice to have a potential safety net if the pure questions just aren't working out!

Thanks! Would you recommend someone to start ASAP after learning fm? I don't know whether to finish all of step 1 then 2 then 3 or do all simultaneously?

I don't know if things have changed since I sat them, but I remember STEP I and II being accessible with just A-Level Mathematics, and STEP III required elements of Further Mathematics. STEP I is a good place to start, but once you've got a feel for the question styles, including some of the techniques used to solve those questions, then you should quickly move on to STEP II and III. I wouldn't necessarily recommend the procedural style of doing all of one thing and then another, though (e.g. some of STEP III can be done even if you have only done a little bit of FM): it can't hurt to just get dip your toe in the water just to see how well you do at first.

Thanks! Would you recommend learning stuff like combinatorics or NT?

It's not really necessary, no. It might be useful to look up modular arithmetic, and perhaps some stuff on generating functions (Generatingfunctionology by the late Herbert Wilf is a nice book), but the best practice would be to use the existing STEP questions involving combinatorics or number theory. Although if you want to learn about these topics for general interest and development, then yes, please do! They are beautiful, rich fields in their own rights.

I self taught FM and the books are amazing. Plenty of challenging and realistc questions. If stuck, consult TSR people or YT or examsolutions

Same!

Did you do the new spec Edexcel this year?

Yeah I was thinking to, to prepare for the Olympiads. Have you sat them back then? I quite like number theory but I'm quite weak at combi😂😅