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Mega A Level Maths Thread MK II

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Original post by ryanb97
Could anyone have a go at this question please:

i posted it a while a go and i still cant see what i have done wrong
i am actually defumbled!!!

i can do part A and part B
part C is a killer

i can see that we need to know a value for A' since i did like a whole page of calculation then to see at the end that A' doesnt cancel out!! - and it couldnt anyway...grr

any help will be great

oh and i think its C4..might be wrong though :biggrin:

this is what i did

picture059 - Copy (2).jpg
picture058 - Copy.jpg

notice the :qed: lol

oh and i sort of left it as that...unfinished :O

thanks

ryan

math1.jpg


Draw a diagram to c). Essentially, you'll be rotating the normal volume of revolution (From 0 to a) about the x-axis, but you'll also be rotating the triangle with vertices (a,a), (a, 0), and (7a/2, 0) (i.e the one enclosed by the normal, the x-axis, and the normal volume of revolution). This will mean that you have the volume of revolution of y between 0 and a, plus a cone added on the end. You can work out the volume of the total thing by finding the volume of the solid of revolution, the volume of the cone, and adding these together.

Does that help at all? I don't want to just do the entire question for you as it won't help you in the long run.
(edited 10 years ago)
Original post by Endless Blue
A fair few people on here and IRL that I've spoken to (including myself) seemed to struggle for time in this S1 paper, which has never really been a problem for me at least. Why do you think that is? I'm putting it down to me being extra careful in checking work and then the venn diagram question threw me slightly (but at least I got it in the end! :tongue:). Which is very annoying because I don't think it was an especially difficult paper, but I've lost 4 marks right off the bat due to lack of time


hmm, I'm not sure, maybe they didn't get enough practice so they spent too much time figuring out how to do the questions? You don't really have time to waste on pondering every question at A-level, unfortunately.

It was only 6 questions though, iirc? Were there a lot of diagrams or graphs to be drawn? I occasionally struggle for time if there's more than one graph sketching / drawing question in a paper, as I'm a horrendous artist and take ages to draw a graph that doesn't look like a 5 year old did it :redface:
(edited 10 years ago)
Well I've finally woken up now so I feel like I'm going to get a hell of a lot of Chemistry and Maths done today! Think I'll start with some FP2 first. I can't believe I actually slept in this late though considering I set my alarm for half 8.


Posted from TSR Mobile
Original post by justinawe
tbh, you only get 6 IMO competitors every year, and no offense but, UK IMO competitors are rarely near the top of the competition :mmm:

Most top international IMO people (like the Chinese, those guys get dedicated IMO training every year! :eek:) go somewhere closer to home rather than Cambridge. UK education is extremely expensive, especially for non-EU residents, and full scholarships are extremely hard to come by for non-vocational subjects like maths.

I bet half of them go and do something like engineering anyway :rolleyes: what a waste of mathematical talent!

Maybe not in the IMO as a whole but anyone on the UK IMO maths team is in a completely different league to most people on TSR :redface:
That's true - have you heard about this Serbian school though whose whole curriculum is like prep for various Olympiads? :redface: I heard they get like 7 of 11 Trinity scholarships or something :redface:
Hmm, who knows. xD I read something a while ago about the most successful UK IMO candidate in history (3 gold medals/ 42s or something) is now a recluse living in his basement :redface:
Original post by justinawe
I only really glanced through the paper, but I think it was pretty standard.

I got a good look through the international paper some of my friends sat though, I think it was slightly trickier than the ones you guys sat.

Ah. Again, I was under the mistaken impression that you sat a paper you didn't. Sorry!
Original post by justinawe
hmm, I'm not sure, maybe they didn't get enough practice so they spent too much time figuring out how to do the questions? You don't really have time to waste on pondering every question at A-level, unfortunately.

It was only 6 questions though, iirc? Were there a lot of diagrams or graphs to be drawn? I occasionally struggle for time if there's more than one graph sketching / drawing question in a paper, as I'm a horrendous artist and take ages to draw a graph that doesn't look like a 5 year old did it :redface:


Yeah, there were only 6 and at least 2 diagrams IIRC had to be drawn. That's the weird thing as well, I finished nearly every past paper (and did all of them available) in at most 1hr 15 mins and was comfortably above 70 marks, but sadly this one went to pot. I realise I spent ages on drawing the venn diagram because it was a really odd one even though not especially difficult when thinking about it.
Original post by reubenkinara
Ah. Again, I was under the mistaken impression that you sat a paper you didn't. Sorry!


It's fine, not a big deal. The only paper we're both sitting for is C4 I think, but Edexcel seem to be giving out different papers to students in certain countries including mine, so we probably won't sit for the same paper.
Original post by Endless Blue
Yeah, there were only 6 and at least 2 diagrams IIRC had to be drawn. That's the weird thing as well, I finished nearly every past paper (and did all of them available) in at most 1hr 15 mins and was comfortably above 70 marks, but sadly this one went to pot. I realise I spent ages on drawing the venn diagram because it was a really odd one even though not especially difficult when thinking about it.


I see. I learnt some set theory when I was in year 10, so S1 venn diagram questions have always been, in comparison, ridiculously easy to me... I wouldn't really know how to judge whether it's easy or difficult for most S1 candidates.
Original post by Endless Blue
Yeah, there were only 6 and at least 2 diagrams IIRC had to be drawn. That's the weird thing as well, I finished nearly every past paper (and did all of them available) in at most 1hr 15 mins and was comfortably above 70 marks, but sadly this one went to pot. I realise I spent ages on drawing the venn diagram because it was a really odd one even though not especially difficult when thinking about it.


Lets hope TSR isn't representative, a lot of my class mates struggled as well with this paper (timing) rather than difficulty
Original post by Felix Felicis
Maybe not in the IMO as a whole but anyone on the UK IMO maths team is in a completely different league to most people on TSR :redface:
That's true - have you heard about this Serbian school though whose whole curriculum is like prep for various Olympiads? :redface: I heard they get like 7 of 11 Trinity scholarships or something :redface:
Hmm, who knows. xD I read something a while ago about the most successful UK IMO candidate in history (3 gold medals/ 42s or something) is now a recluse living in his basement :redface:


Of course, but again, it's only 6 every year! :colone:

Never heard of that school. It's kind of unfair to the rest of us that have to prepare on our own, tbh :redface:

Hah! Why am I not surprised? :lol:
Original post by Robbie242
Lets hope TSR isn't representative, a lot of my class mates struggled as well with this paper (timing) rather than difficulty


I don't think TSR is ever representative! :tongue:
Original post by justinawe
Of course, but again, it's only 6 every year! :colone:

Never heard of that school. It's kind of unfair to the rest of us that have to prepare on our own, tbh :redface:

Hah! Why am I not surprised? :lol:

Yeah but there'll be 2 others from the reserves and probably several people who were very good but fell short at the selection test, not to mention internationals from Europe/ some from all the way from Australia apparently this year :eek:

That's it :redface: http://en.wikipedia.org/wiki/Matemati%C4%8Dka_gimnazija 121 IMO medals :eek:

Haha. xD Real shame as well - he got 3 degrees and 3 firsts from Cambridge. :redface:
Original post by Felix Felicis
Yeah but there'll be 2 others from the reserves and probably several people who were very good but fell short at the selection test, not to mention internationals from Europe/ some from all the way from Australia apparently this year :eek:

That's it :redface: http://en.wikipedia.org/wiki/Matemati%C4%8Dka_gimnazija 121 IMO medals :eek:

Haha. xD Real shame as well - he got 3 degrees and 3 firsts from Cambridge. :redface:


Suddenly I'm getting quite nervous about my Cambridge application :redface:
Original post by justinawe
I don't think so :eek: I definitely would if I can, though. They'll have an "Oxbridge applicants briefing" of sorts at my college soon, so I guess I'll find out.

For Cambridge, I've narrowed it down to Pembroke, King's and Emmanuel. I'd make an open application, but I don't want to end up somewhere like Girton :teehee:


What's wrong with Girton?
Original post by Boy_wonder_95
What's wrong with Girton?


Everything :mmm:
Reply 1235
Avatar for Albino
Albino
11
Was wondering how'd id go about integrating this :tongue:

∫x1−x2 dx\displaystyle \int \frac{x}{\sqrt{1-x^2}}\ dx

what substitution would i have to make?
Original post by justinawe
Everything :mmm:


Imagine getting pooled by Girton and fished by Trinity :teehee:
Any S2 peeps here? How would I manipulate for continous uniform distribution X~U[4,28] and to find P(∣X−16∣<3)P(|X-16|<3) I don't understand the effect of the modulus on probabilities I know its magnitude but can anyone clear this up
(edited 10 years ago)
Original post by Albino
Was wondering how'd id go about integrating this :tongue:

∫x1−x2 dx\displaystyle \int \frac{x}{\sqrt{1-x^2}}\ dx

what substitution would i have to make?

It's just a direct reversal of the chain rule but substitute u = 1 - x^2 if you're unsure.
Reply 1239
Avatar for Reyoru
Reyoru
1
Original post by Albino
Was wondering how'd id go about integrating this :tongue:

∫x1−x2 dx\displaystyle \int \frac{x}{\sqrt{1-x^2}}\ dx

what substitution would i have to make?


You don't need a substitution as it is of the form f'(x)[f(x)]^n

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