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Getting to Cambridge: STEP by STEP!

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These integrals remind me of Cleo's solutions on MathsStackExchange. I am not sure if you know her but she is the biggest troll on StackExchange. She solves some extremely complicated graduate level integrals (afaik, they are gibberish to me) and then just gives the answer without explaining her logic through it. :rofl:

Here is one example of it: http://math.stackexchange.com/a/563063 (scroll up to see the actual integral)

I'm far too familiar with her to be comfortable. She scares me. :lol:

I much preferred Ron's solution to that question! :biggrin:

By the way, you on math.stack? :biggrin:

Reply 1221

Ethereal World

Original post by Zacken

This is why I love you :rofl:

@Ethereal World appreciate this :rofl:

looooolll Spoder is always so on form with gifs and reks.

He's original favourite TSRian :yep:

I actually like just reading your GYG for his bantz. (and yours :h:

)

Reply 1222

Insight314

Original post by Zacken

I'm far too familiar with her to be comfortable. She scares me. :lol:

I much preferred Ron's solution to that question! :biggrin:

By the way, you on math.stack? :biggrin:

I know right, there are so many conspiracy theories about her on 4chan/sci/.

"I have a medical condition that makes it very difficult for me to engage in conversations, or post long answers, sorry for that." :lol:

Yeah, I kind of lurk and have answered 2 questions but tbh most of MathStackExchange is too high level for even undegraduates. :biggrin:

I don't want to give any private information (real name), but if you want my profile I can PM it to you

Reply 1223

Insight314

Original post by Zacken

I'm far too familiar with her to be comfortable. She scares me. :lol:

I much preferred Ron's solution to that question! :biggrin:

By the way, you on math.stack? :biggrin:

http://math.stackexchange.com/questions/507425/an-integral-involving-airy-functions-int-0-infty-fracxp-operatornameai

Oh my god, Cleo asked an integral question back in 2013. If I was good enough with such complicated integrals, I would troll her and just post the exact solution like she does. That would be so funny. :rofl:

Reply 1224

Zacken

Original post by Insight314

I've seen that one before. Yeah, that'd have been hilarious. :rofl:

I'm actually quite active on math.stack, have like 7k point now. :biggrin:

Reply 1225

Marxist

Original post by Zacken

I've seen that one before. Yeah, that'd have been hilarious. :rofl:

I'm actually quite active on math.stack, have like 7k point now. :biggrin:

Stackexchange introduced me to the beauty of maths man. <3

Reply 1226

Duke Glacia

Original post by Zacken

STEP II, 2005:

Total time: 2:50.
Total mark: 109.

Q1: Started with this. Decent question, I ended up playing it safe and went with a quintic instead of a quartic that lead to more effort but was just as valid. 20/20 and 18 minutes.

Q3: Moved on to this one because I knew that it was a straightforward mindless IBP plow that required zero insight and just algebraic manipulation, my judgement ended up being correct. Made an algebraic slip with a factor of a

\frac{1}{2}

and spent a good bit of time looking checking that out. Cute inequality at the end. 20/20 and 20 minutes.

Q4: Bog standard question. I overcomplicate the middle part hugely and got lost in a swath of algebra that I only just managed to escape unscathed. The final bit proved tricky and really worked my arithmetic. Otherwise s'all good. 20/20 and 17 minutes.

Q8: Fairly standard, I feel like I had a more elegant approach to the integration that the official solutions (you lot aren't going to be surprised), but It was easier to note that:

Unparseable latex formula:

\begin{equation*}\frac{x^3}{(x^2 +1)^{5/2}} = \frac{x^3 + x - x}{(x^2 + 1)^{5/2}} = \frac{x(x^2+1)}{(x^2 +1)^{5/2}} - \frac{x}{(x^2 +1)^{5/2}} = \frac{x}{(x^2+1)^{3/2}} - \frac{x}{(x^2 +1)^{5/2}}\end{equation*}

.

This trick is literally a life-saver. Sketches worked out okay, I cut myself 2 marks just to be on the safe side for some lack of justification of my sketches. :dontknow:

18 marks and 27 minutes.

Q2: Looked like an okay question, bit fiddly and I overkilled b (iii) by using a contradiction instead of a counter example which annoyed me as that meant I hadn't fully gotten a grasp of the concept introduced. I mis-read one part of the question and forgot to evaluate

f(180)

but was advised to cut only one mark for that, but I'm going to cut two just to be safe. 18/20 and 25 minutes.

Q14: Bit of a weird question, my method was slightly wonky and I didn't quite get there. So I'm giving myself 10/20, I spent forty minutes on it as well...

Q12: I tried the first part, got that, gave myself 5/20 and then gave up because I had no clue what the rest was asking of me. :lol:

Q11: Not a bad question, I've never done a pulley one on STEP before but this was surprisingly tame, the algebra was quite ugly and it was quite partial-y. Managed 13/20 in 20 minutes.

Overall thoughts: Not bad. Wish I'd been able to do more questions, not during the mock but as being able to attempt them tomorrow or something; but I don't think any of the remaining questions are accessible to me, which isn't a very good sign. Fairly okay though. III 2005 to be done soon, probably next week. :yep:

Reply 1227

Student403

Original post by Ethereal World

looooolll Spoder is always so on form with gifs and reks.

He's original favourite TSRian :yep:

I actually like just reading your GYG for his bantz. (and yours :h:

)

Reply 1228

BBeyond

How is M5 compared to M4? Considering doing it atm... Would I be any more disadvantaged by not doing Physics than I am when doing any of the other mechanics modules?

(edited 8 years ago)

Reply 1229

Zacken

Original post by BBeyond

How is M5 compared to M4? Considering doing it atm... Would I be any more disadvantaged by not doing Physics than I am when doing any of the other mechanics modules?

M5 is nicer than M4, tbh. Not particularly, no. Physics barely has any mechanics in it. :dontknow:

Reply 1230

Duke Glacia

Original post by BBeyond

How is M5 compared to M4? Considering doing it atm... Would I be any more disadvantaged by not doing Physics than I am when doing any of the other mechanics modules?

why do u need m5 for economics ???

Reply 1231

BBeyond

Original post by Zacken

M5 is nicer than M4, tbh. Not particularly, no. Physics barely has any mechanics in it. :dontknow:

Hmm okay cheers, really? I always thought physics was basically mechanics lol

Original post by Duke Glacia

why do u need m5 for economics ???

I don't but I quite like mechanics and have already done m4 so thought I may as well do M5 and can get the AS AFM

(edited 8 years ago)

Reply 1232

Duke Glacia

Original post by BBeyond

Hmm okay cheers, really? I always thought physics was basically mechanics lol

I don't but I quite like mechanics and have already done m4 so thought I may as well do M5 and can get the AS AFM

gr8 idea m8 ! it is interesting but beware the circular motion is a bit hard and tough to understand

Reply 1233

Zacken

Original post by BBeyond

Hmm okay cheers, really? I always thought physics was basically mechanics lol

Proper Physics is basically maths, A-Level Physics is shambles. :tongue:

Reply 1234

Ayman!

Original post by BBeyond

Hmm okay cheers, really? I always thought physics was basically mechanics lol

A level physics has very little mechanics; it's very awkward essay writing.

Original post by Duke Glacia

gr8 idea m8 ! it is interesting but beware the circular motion is a bit hard and tough to understand

Did you do IAL Duke?

Reply 1235

Marxist

Original post by Zacken

Proper Physics is basically maths, A-Level Physics is shambles. :tongue:

Are you with Edexcel for Physics, too?

Reply 1236

Duke Glacia

Original post by aymanzayedmannan

A level physics has very little mechanics; it's very awkward essay writing.

Did you do IAL Duke?

yes i did ial. #IALrules

Reply 1237

Zacken

Original post by Marxist

Are you with Edexcel for Physics, too?

Yes.

Reply 1238

Kvothe the Arcane

Original post by Zacken

Here's something a little sexier:

Let

I = \int \sqrt{\tan x} \, \mathrm{d}x

and

J = \int \sqrt{\cot x} \, \mathrm{d}x

, then:

Unparseable latex formula:

\displaystyle[br]\begin{align*}I + J &= \int\left(\sqrt{\tan x} + \sqrt{\cot x}\right) \;\mathrm{d}x \\&= \sqrt{2} \int\frac{\sin x + \cos x}{\sqrt{\sin 2x}} \;\mathrm{d}x \\[5pt]&= \sqrt{2} \int\frac{(\sin x - \cos x)'}{\sqrt{1-(\sin x - \cos x)^2}} \;\mathrm{d}x \\[5pt]&= \sqrt{2} \sin^{-1}(\sin x - \cos x) + \mathcal{C}_1 \tag{1} \\\end{align*}

Unparseable latex formula:

\displaystyle[br]\begin{align*}I - J&= \int\left(\sqrt{\tan x} - \sqrt{\cot x}\right) \;\mathrm{d}x \\&= \sqrt{2} \int\frac{(\sin x - \cos x)}{\sqrt{\sin 2x}} \;\mathrm{d}x \\&= -\sqrt{2} \int\frac{(\sin x + \cos x)'}{\sqrt{(\sin x + \cos x)^2 - 1}} \;\mathrm{d}x \\&= -\sqrt{2} \ln\left|(\sin x + \cos x) + \sqrt{(\sin x + \cos x)^2 - 1}\right| + \mathcal{C}_2 \tag{2} \\\end{align*}

Adding (1) and (2):

Unparseable latex formula:

\displaystyle\begin{equation*} I = \frac{1}{\sqrt{2}} \sin^{-1}(\sin x - \cos x) - \frac{1}{\sqrt{2}} \ln\left|\sin x + \cos x + \sqrt{\sin 2x} \vphantom{x^{x^x}} \right| + \mathcal{C}\end{equation*}

Pretty

Reply 1239

Marxist

Original post by Zacken

Yes.

Ahh, I'm with OCR, so I think it's a bit worse. :frown:

I love Physics, so I try to learn more about the topic that I'm learning by doing extra. It is amazing because IOP have lectures for students and I get so much out of it.