Additional Further Maths Discussion Thread

I'm doing FM next year so why are you doing all these extra units? Will you get 3 Maths A-levels?

I see what he did there

I'm doing FM next year so why are you doing all these extra units? Will you get 3 Maths A-levels?

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I will be sitting S3, M4 and FP2 as part of an AS in AFM. I'm also going to resit FP3 for the lulz

Have you already sat FP2 and FP3? If so, what did you achieve?

Yes, but I'm not too bothered about the "extra a-level". I finished off the first two into my first year because I found them pretty easy. Then, since I had another year of sixth form to kill thought I might as well do AFM. Annoyingly Cambridge decided to put it as part of my offer and so I'm doing it all a bit last-minute (hence why I made the thread - to try and meet others in my position in order to make it feel less tedious).

So yeah.. I'm kind of forced into it :/ Taking further maths is certainly a good thing but, in my opinion, you must take it upon yourself to explore a few extra topics in order to have any hope of being truly passionate about the subject pre-university. I would suggest, at some point over the course of your a-levels, exploring the concept of "Irrationality" and having a go at a few related questions. Also things like more advanced "Recurrence Relations" and the link with infinite series are a must. The concept of proof and an exploration of induction and contradiction are certainly a must! Also the applications of inequalities like "AM-GM" and "Cauchy-Schwartz" (among others) are also very fun, though falling down the rabbit-hole of olympiad mathematics is of little importance (though trying the questions and reading relevant texts most definitely is!)

I'm sure the things I've mentioned seem a little tangential and irrelevant, but the fact that they are not included in pre-univeristy education is what is truly strange!

Sounds pretty cool. I do some maths outside the syllabus and some number theory stuff along with proofs is quite exciting for me. However, I did badly in S1 and M1 but this might be due to lack of preparation. Can I do FM together with AFM next year then? Although I will probably die if I'll do any kind of stats again (who even included this in the maths syllabus?) but it's a good preparation to uni. Also does it give any advantage if you apply for top unis? (Looking at my average UMS because of applied units Cambridge and Imperial will probably say no straight away but I think I've got chances for Warwick).

Great to hear

Well, avoiding stats would mean avoiding three modules and so you would only be able to get an AS in AFM

I think statistics is quite nice actually. The emphasis of the later modules is on applying specific knowledge of distributions etc.. which is helping no-one! Try some combinatorics and try learning about the concept of a portability density function (and it's formal link to calculus - i.e. through variance, mean, etc...). I would suggest trying a few STEP questions to develop your understanding of them though!

I've found a-levels can occasionally be stimulating though but only if you haven't read the book first e.g. try a random fp3 mock before you've even done C4 The funniest part is that half of the questions are readily accessible if you have the imagination Others would certainly be swell if you got someone to write a sentence before them (similar to STEP) e.g: "given that cosh(x) is such that ....."

When you say "did badly", do you mean TSR standards of badly (99UMS), Oxbridge applicant's standard of badly (85UMS), russell-group applicant's standard of badly (70UMS), typical student's standard of badly (59UMS), really badly (10UMS) or "bad luck brian" badly (-3UMS)?

Is AFM likely to give you a serious advantage of other applicants? Almost definitely not. But is it likely to be a good way to demonstrate enthusiasm and capacity for a large workload? Certainly, though whether this would actually advantage you is up for debate

Well I regard Warwick's maths course as begin superior to that of Imperial's. Though Warwick have no "real" admissions process so I suppose you are right Warwick I've out offers to everyone with predicted grades greater than or equal to AAB, everyone gets the same offer. They give out 1900 per year (95% offer rate) for roughly 250 places. Over half of these people will realise they will never get two A*s and will likely try a STEP paper, cry, and move on. A large chunk of their yearly intake are those who have narrowly missed Cambridge or Oxford offers as well as many who get rejected initially

For Cambridge, your average UMS should be above 85 to be taken seriously. The higher your average is above that the less they care I'd imagine. A student with both a-levels already done and 600UMS would not impress them. They would almost certainly remark to each other when reading the UCAS form something like "well he's (/she's) certainly good at exams. Now lets see if he (/she) can think"

Statistics isn't that bad if you actually learn something new and see how it's applied in the real world. But most of the time you just put numbers into formulae which is quite boring and mind-exhausting.

From what I've seen FP1 is fairly good and I don't think I will have many problems with FP2-3. I don't mind Mechanics btw.

I got 77 for S1 (and decided not to resit) and will get around 70 for M1 (might consider resitting; I know all the stuff, I've just made silly mistakes). 100 for C1, will probably get 90+ for C2 (again pure silliness). If I'll average more than 90 in C3-4 (and I have to in order to get an A*) I'll get more than 85 UMS. I just hope that I will at least get an interview so I can talk to them and show that I'm interested in the subject.

After all I'm not even 100% if I'm going to do Maths at the uni. My other options are Physics and Mechanical Engineering. I like Maths very much but I'm not sure where the Maths degree leads to apart from becoming a greedy banker (which I'm not interested in at all despite all the money) and staying in academia.

Thanks for all the advice. I assume you're going to study Maths at the uni? Why did you chose it?

x

But from the looks of things, there seems to be only three people on TSR doing AFM!

Jkn, that was truly beautiful

But from the looks of things, there seems to be only three people on TSR doing AFM!
One of them is not me.. I started off wanting to do an AS in it, but lost a bit of motivation and so only did S2 as an extra module (I initially wanted to just squeeze in M4 and M5 too, still gutted i didn't!)

Well, I believe the statistic is less than 100 people across the entire country doing AS Additional Further Maths with Edexcel, let alone A2. There are a fair few doing an AS in the subject on here, but very few doing A2.

Also, I am going to disagree with a lot of what's been posted and say that doing Additional Further is worth it, for several reasons:

- More relevant to a Maths courses than other fourth subjects (e.g. Chemistry)
- As very few places offer support for AFM, if you want to do it then you're self-teaching which is very good experience for later on as independent study is more prevalent at uni.
- The Maths involved is a lot of fun!

Only crap exam boards offer it anyway. I'm doing 3 extra modules but only for the sake of it, and I'm with aqa so they don't even offer me a special name like ADDITIONAL FURTHER !11

Sorry mate, but the things I've put in bold would suggest that it would be very unlikely for you to get an offer from Cambridge to study maths. Sorry to be blunt, but you might as well hear it now :/ Are you in your first year doing a-level maths all at once? They might be concerned that you haven't started further maths!

Cambridge is ranked number 1 in the world for maths at the moment and, hence, the competition is high! There were roughly 80 people applying to the college I applied to this year at yet their average intake (after STEP etc.) has been 9 over the last few years! :|

People they're interested are people who love the subject in a way that few other people do and have an exceptional academic ability in the subject. The emphasis, though, is on the second point. At the interview, it is very unlikely that they will ask you "Why did you like maths?", "Who is your favourite mathematician?" or even "Why Cambridge?". Let alone stupid questions about maths a-levels. They are there to test to ruthlessly and see how you cope under pressure. My interview must've been the most stressful thing in my life! Despite being able to do every question they gave me, they still made me doubt myself by asking for justification repeatedly until you aren't able to give anymore! The questions are also non-standard. One of mine even involved Christmas Crackers! The interview process will differ but I'd imagine many would be like this (feel free to chime in anyone that's reading this and had had a Cambridge interview.)

That's okay, I like giving people long boring lectures...

Yes, unless something disastrous happens when I sit my STEP exams!

Well, it's something I've always been interested in and good at since I was really young. My mum was telling me the other day that when I was in year one/two they used to have an advisor come in to test me and set me all my work (because they didn't know what to do with me) and apparently, when he gave me problems, I used to solve them but wasn't able to explain how... which, sounds pretty awesome looking back now!

Unfortunately when I went to "the next school up", I didn't really get any support and so was stuck in the regular classes with teachers trying to get me to memorise times table for 4 years and me insisting that theres no point in memorising them because I already figured out how it worked the first time I was told what a times table was!

Anyway, went on like this until year 10 where my teacher used to get annoyed with me because I would just draw pictures in my maths book instead of doing (what it was the the education system called) "maths". I ended up falling out with the guy about the fact that, when I told him I had already done "exercises 1-40" (or whatever) whilst he was writing them up, he would always tell we "do 40-80" (or whatever). So he dared me to sit the GCSE the following week "If I'm so clever". Which I did... and got an A*

Since then I started teaching myself almost all of my maths (with the exception of 6 out of the 18 a-level modules) and a whole work started to open up to me! A perfect world that is the our essence of imagination and yet bounded by objectivity! Lately I've become so obsessed with it all that I can't spent a hour without an idea or solution popping into my head

I also see maths as more of an art than a science. I've never been too bothered about "practical applications" as you mention when talking about statistics. I feel so creative when doing maths, like how you might think a professional juggler would feel when doing something ridiculously complicated. The beauty in maths gives me the same joy that I get from music and that's the true essence of pure mathematics Once you're bitten by the bug, I few people who stick to the curriculum, ever are, you're hooked! I feel like I've always known I wanted to pursue maths and yet always thought it was about solving problems in the real world and doing something "useful". The poetry of mathematical beauty has come as an entirely unexpected pleasure

More relevant to what exactly? I have no idea how memorising random obscure facts like "if there are 3 deltas in an expression before we take a limit it .... somehow.... cancels out"

This is not a random obscure fact, and you should actually have come across it before, such as when proving the product rule for differentiation.

or "the reciprocal of the F distribution gives you a shortcut and so we don't need as large a table" or "to runt the simplex algorithm first me must blah blah blah" are going to help us. Do they help us with mathematical thinking?

You are cherry picking topics here. For example, using integration to find moments of inertia in M5 has helped me to appreciate integration as the limit of a sum a lot more, and so yes, it has helped mathematical thinking.

No, they introduce us to the idea that it's okay to use a piece of mathematics that you haven't derived let alone proved rigorously. This is a plague on the minds of a generation of both mathematicians and scientists. Can you seriously say that, when reading through things in S4 you don't feel that horrible stomach-wrenching feeling that, even if something is wrong, you wouldn't know? :s

The only things in Stats which I'm not 100% comfortable with are the derivations of the distributions (Apart from Poisson, I know that one) which I understand is potentially too difficult/time consuming to stick into an A level course for the typical student. It should also be said that S3 and S4 are not the modules that I took the course for, but I have enjoyed them.

To leave like that it to lose the point of mathematics! That said, the problem is even worse in the physics a-level where everyone is so used to accepting things unquestionably that when a student pauses to think "why do we know this?" or "Isn't what you've said a circular argument?", the general attitude is that of derogatory condescension. As a result (though people might have better teachers than me), Ive simply got answers like "The universe had to have come from a an infinitely small point because it is expanding. Oh but remember, the universe is finite and infinities are impossible in the real world".

They might as well stick me back in reception if that's the kind of borderline-retarded answer they expect us to be happy with. The sad truth is that almost everyone sitting the a-level is happy with an answer like that! Evidence that the exams have, in many ways, destroyed the students ways to think creatively and develop logical reasoning. In my situation, asking a question like "if space-time stretches faster than the speed of light, which is hypothesised, then we wouldn't not be able to see the majority of the universe anyway and so this offers no evidence for the big bang theory" would lead to everyone thinking I "against Science" even though science, by definition, must and can only side with scepticism (the scientific method builds upon the concept of a null hypothesis).

Ignoring these as neither are relevant to Additional Further Maths A Level.

Lets say that Additional Further Maths takes a student 2 hour a week all year (which is a GROSS overestimate). Surely that 2 hours a week would be better spent doing maths that's actually useful or challenging!

I spend a lot more time on the subject than that (Spent a week each doing all the questions in the M5/S3/S4 textbooks, and that felt fairly short) and do a couple of papers for each every week and I do not regret it. In addition, you can do AFM alongside, and not instead of, the other Maths you're talking about. I do a good amount of work for AFM and still have had time to do tons of STEP work.

We both know that, without lying, you could not seriously tell me that AFM has actually challenged you. It is clearly nowhere near the level of difficulty you are capable of and surely you know by now that there is no point spending an extra week of 2 revising just to get the difference between 100UMS and 80/90

No, AFM is not as challenging as some extension materials you can do, but that is because at the end of the day it as an A Level and not an extension upon A Level, like what you're probably thinking of (STEP, AEA).

Yes some of the ideas touches on in M5 are curious but can you seriously say you will actually gain anything from learning them?

As stated above, M5 has already got me to consider more thoroughly the basic principles of differentiation and integration, and so this is an immediate "mathematical" gain. However, I feel that you're missing the most important point, which is simply that Additional Further Maths is a hell of a lot of fun. I've enjoyed every bit of it (FP3, M3, M4, M5, S3 and S4 are the modules I've gained from AFM) and, independently of what qualification I get or how much stronger it has made me mathematically, the fact that I've enjoyed it means it's already paid for itself.

I mean, what's the point in being able to churn out rote-memorised strategies to solve variable has problems to rotational bodies problems? Until you have actually proved something for yourself, you are working within the confines of a bubble of ignorance.

Firstly, there is such a thing as reading outside the confines of the syllabus. Secondly, I do not see how this makes AFM any less of an A Level than any other, as none have any emphasis on proof.

The cruz of the matter: If there was a mistake in the textbook, would you notice? (and I'm not talking about the endless typos and then past that at least 1 in 4 of the answers at the back are wrong - I mean the syllabus itself)

Anyone would provided they spent 5 minutes looking at their syllabus past the textbook. I agree that perhaps some of the derivations given aren't sufficiently rigorous but I'm comfortable that the key content is correct.

It's as worthless as Critical Thinking as a qualification.

Debatable. AFM is a very niche qualification but it's good to specific courses (Maths, maybe Physics and Engineering).

Unfortunately few people who are actually doing it want to admit it's barely harder than AS maths and so the vicious cycle continues

Are you high? There is a monumental difference between the likes of FP3 and M5 in terms of difficulty. Whilst it might be less apparent to someone who has not struggled with the modules it is still there.

Only crap exam boards offer it anyway. I'm doing 3 extra modules but only for the sake of it, and I'm with aqa so they don't even offer me a special name like ADDITIONAL FURTHER !11

you guyss.. please help me.
I did AS level edexcel maths c1, c2 and s1.
next year, i'll do A level: c3, c4 and s2.

plus im also taking further maths AS and A level in one year. but i'm not sure what other units i should do (other than stated above). i need you guys to recommend me. since i don't take physics im not sure i can take m1 or m2. here's what im thinking:

AS further maths: fp1, D1, D2 A level further maths: fp2, s3, s4. are s3, s4 and d2 hard ? compare to mechanics ? please suggest bigg thankss

Mechanics 1 is not particularly difficult, a diagram sorts out most things.
The overlap between physics and M1 is pretty small, so certainly, M1 is not too hard.
Also some universities (I believe) prefer mechanics modules to stats, but I guess it depends on what you want to do at uni, for economics I imagine Decision and stats is good.

I'm planning to take mathematical science in university. you think mechanics would be better for me ?

Perhaps M1 instead of S4? Personally I find stats tedious, M1 is an easy module really, it would be odd to not do it, it's also (IMHO) more fun

I have a feeling I read somewhere that for maths Mechanics is preferred to Stats, though that may have been for maths with physics of course

Statistics isn't that bad if you actually learn something new and see how it's applied in the real world. But most of the time you just put numbers into formulae which is quite boring and mind-exhausting.

From what I've seen FP1 is fairly good and I don't think I will have many problems with FP2-3. I don't mind Mechanics btw.

I got 77 for S1 (and decided not to resit) and will get around 70 for M1 (might consider resitting; I know all the stuff, I've just made silly mistakes). 100 for C1, will probably get 90+ for C2 (again pure silliness). If I'll average more than 90 in C3-4 (and I have to in order to get an A*) I'll get more than 85 UMS. I just hope that I will at least get an interview so I can talk to them and show that I'm interested in the subject.

After all I'm not even 100% if I'm going to do Maths at the uni. My other options are Physics and Mechanical Engineering. I like Maths very much but I'm not sure where the Maths degree leads to apart from becoming a greedy banker (which I'm not interested in at all despite all the money) and staying in academia.

Thanks for all the advice. I assume you're going to study Maths at the uni? Why did you chose it?