Will the real TeeEm please stand up!

It's not in the Edexcel spec, but I think that I can remember the formula (opposite of x axis). Integrating arcsin^2(y) might be a bit difficult, can't really remember too much from FP3.

Here are my workings for the easier question too

Determine the volume produced when the finite region bounded by y = x² and y = x is revolved by a full turn about the line y = x

Can't you just avoid first principles by using matrices?

Oh, sure I've seen the log one before in an old FP1 textbook...

depends

Here it is not too bad as the rotation is 45 and the equations for the curve and the line are both silly.

But try to do that with the first question that I posted.
I started that by shifting to the origin then I rotated successfully until I saw the equation of the resulting curve ....
Immediately I quit that approach.

Centres of mass (m3) and moments of inertia (m5)

centre of mass in M3, and moment of inertia in M5

The M3 first principles stuff isn't very hard and if the question was limited rotation about either the x or y axis, it would be very easy (the difficulty coming from the resulting integral). What makes it horrible is just the fact that it's about a slant line, and the steps to deriving the formula that TeeEm used being pretty abstract, at least to me.

Ah I see. It seems very unconventional, which is the point I was trying to make with regards to the 'difficulty'. But then again, the unconventional-ness is what TeeEm is going for in these questions. The 'easier' one was my max, the 'harder' one you guys were talking about earlier seemed out of my reach.

I just added these into my resources, so here is the neat versions of these two beautiful questions

Unusual doesn't do it justice :P

Eh, after realising that the equations of the rotated curve and line were impossible (at the level I'm at) to integrate, it was beyond me. I should make an effort to understand the proof that I found though, may come in use some day tbh.

I haven't actually tried the easier one, but it doesn't look too terrible...

@TeeEm said something very wise weeks ago after I did one his questions where a typo made it void as the sequence didn't converge. Something about it getting filed at the back of your head then maybe something comes up similar to it in the future and you retrieve the approach to the original question and adapt it for the new one. Sounds silly but idk, I quite liked his description. Maybe he remembers what he said.


I didn't try it myself, but I could see where it was going and looked at solution to confirm my idea. I shouldn't have ruined it by looking at the solutions but tbh, I'm not that enthusiastic at the moment. Need to get off to college to reinvigorate!

What happened yesterday I wrote Paper X of my Special papers.
I realised that I need to make some tough questions on volume of revolutions but I went over the top today. Now I am trying to write the 2 "hard but sensible questions" that I should have written in the first place.

Nevertheless I think these 2 questions are very beautiful (almost marriage material...)

@TeeEm said something very wise weeks ago after I did one his questions where a typo made it void as the sequence didn't converge. Something about it getting filed at the back of your head then maybe something comes up similar to it in the future and you retrieve the approach to the original question and adapt it for the new one. Sounds silly but idk, I quite liked his description. Maybe he remembers what he said.


I didn't try it myself, but I could see where it was going and looked at solution to confirm my idea. I shouldn't have ruined it by looking at the solutions but tbh, I'm not that enthusiastic at the moment. Need to get off to college to reinvigorate!

If an examiner could somehow guide you through the intermediate part of the harder problem, it would make a damn good STEP I question.

I think you said what I said and I replied what my professor replied although the circumstances were not exactly the same.

You complained after my typo that you wasted an entire day trying that question that would not solve.

My reply was:
You learned more maths by trying over and over different things, even if you did not solve the problem. That is far more useful that doing a question in 5 minutes although the second scenario gives more satisfaction to the ego.

Well, if you're doing FP1 first you might be in for a let down! I've been looking at solutions too quickly too atm. I just want to get my maths back up to scratch for uni tbh, forgotten most of the less-obvious/memory stuff that I could do easily months ago

I'm not entirely sure what I'm doing next year as a matter of fact My situation is a bit unique and my college are frankenstein-ing a timetable together for me, hopefully the irregularity of it should spice things up a bit, so long as there is a bunch of mechanics I'll be happy
I presume you're doing straight maths at Uni then?

You can by presenting the 2 diagrams and asking students to derive things bit by bit.

If I am going to use the easier of the 2 in one of my special papers that is haow it will be done.

I kinda struggled with mechanics throughout my two years, but for some reason I found it really easy in exams. I wish that I knew enough linear algebra stuff so that I could properly learn about computer graphics and stuff like that- not too much a fan of deciding whether an odd, unrealistic shape will topple down a slope.

Do you intend to take M4 and M5? There is a really interesting M5 topic on deriving differential equations from first principles if you are.

Yeah, doing straight maths and hoping to do a few computing modules here and there.

That made me laugh

I initially struggled with M1 but ended up doing really well in it, and M2 just really interests me.

Yep. I will be taking all 18 modules (already done 6). I've heard from a few people now that M4/M5 are the most interesting modules in general. I am genuinely looking froward to them now. Should be great, although it seems I will be self-teaching them....

Ah that sounds interesting. Do you have a career in mind once you've graduated?

M2 is just M1 with a few more complications added; I found it a bit boring tbh, M3 was much better.

M4 and M5 textbooks are extremely easy to find online (applies to all textbooks tbh), so it shouldn't be that bad. Why are you putting yourself through the pain of doing D1 and D2 Wish I was allowed to do AFM though, my college explicitly said no in Y12 and I had to sit through 2 years of computing... (I should say, A Level computing is terrible and isn't even required for most cs courses)

Not really. I have things that I'd like to do, but I don't know how feasible they are and what the downsides are to doing them professionally.

Thanks for the heads up, I look forward to it. Yeh a lot of people have said mechanics starts getting interesting from M3 onwards.

Haha, don't. I'm dreading it tbh. I purposely put it off in normal A Level Maths because it looked so boring and I just know that, despite their ease, they will be my lowest scoring modules Thats the reason why Im doing it tbh, I don't want to be forced into some 'mathsy' fourth that I don't want to do.

Fair enough. You have 3 years to decide anyway