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# The 2012 STEP Results Discussion Thread

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1. (Original post by gff)
The formulae booklets are available in the exam, although our teacher told us that "we wouldn't need them, unless somebody's going statsy".
I think there are some integrals and stuff that cut out a lot of effort. Eg in a question I managed to get an integrand down to cosecxcotx which the integral for was thankfully already in the formula book.

Plus I still don't know binomial expansion off the top of my head haha, I just never bothered paying attention to it (I'm sure if I spent 2 or 3 minutes I could think of it myself but I'd rather not waste the time - plus it's nice to have a sort-of template to copy the formula from (less likely to make errors).
2. (Original post by Rahul.S)
I think ive seen the name of few results in mark schemes and examiner reports.....if I remember right Ceva's theorem is one

quoting it is enough? wouldn't a quick proof be required?
The question you are thinking about was asking people to prove half of Ceva's theorem (and candidates noticed it as such) - you definitely CAN'T assume results from outside the A-level syllabus
3. (Original post by matt2k8)
The question you are thinking about was asking people to prove half of Ceva's theorem (and candidates noticed it as such) - you definitely CAN'T assume results from outside the A-level syllabus
My understanding is that you CAN use results from outside the A-level syllabus, but not if they rely on the result you're being asked to prove, or if they "trivialise" the question.

For a really clear (and real-life) example: you'd definitely not get away with quoting Ceva's theorem to prove a STEP question that was essentially asking you to prove one half of Ceva's theorem.

Similarly with the STEP question that was essentially about Laplace transforms: you wouldn't get away with quoting results about transforms of derivatives etc.

But on the other hand, if you are asked to find the maximum value of some kind of sum, they don't say "hence" or similar, and you solve it using Jensen's inequality, then I am sure you would get the marks, even if they might be annoyed at you using a sledgehammer.

Edit: A better example of something I'd be amazed at losing marks for is modular arithmetic, which I don't believe is on any A-level syllabus any more.

Anyone in a position where they might want to quote a post-A-level result should also be sensible enough to see whether or not that's a reasonable action for a particular question.
4. For example: STEP III 2000 Q7 where in one of the bits I basically had to use the fact that monotonically increasing bounded sequences tend to a limit despite this obviously not being a level stuff.
5. (Original post by DFranklin)
Jensen's inequality... a sledgehammer.
If I wasn't on PRSOM, I would've repped you just for this description.

(Original post by ben-smith)
... that monotonically increasing bounded sequences tend to a limit despite this obviously not being a level stuff.
That's what this question is about, and indeed, I don't believe any examiner will be annoyed from the fact that you actually know what this means. Otherwise, it would be silly.
6. Hi, please could someone explain something for me as I'm having a bit of a blank moment

I'm just working on STEP II 2004 question 4 and I'm trying to get my head around the first part.

If we let f(t) = L, so f(t) = acosect + bsect we find f'(t) = 0 to get tan^3t =a/b...why do we do this?

Is it because f(t) is at a minimum to enable the rod to be moved into corridor b..? or have I completely got the wrong end of the stick?!

Thanks
7. (Original post by matt2k8)
The question you are thinking about was asking people to prove half of Ceva's theorem (and candidates noticed it as such) - you definitely CAN'T assume results from outside the A-level syllabus
yh it was half of it.......most STEP questions aren't about using anything outside really so its fine. I was doing another question involving Jensen's Inequality.....would STEP go one step further to ask for a proof of it?
8. (Original post by Rahul.S)
yh it was half of it.......most STEP questions aren't about using anything outside really so its fine. I was doing another question involving Jensen's Inequality.....would STEP go one step further to ask for a proof of it?
IIRC the question on Jensen's Inequality said explicitly "You may assume this result without proving it."

And I think if you know a result that utterly trivialises a question, they'd like a proof, but it's fine to use very well-known results without proof. (Not sure though.) (Edit: just noticed DFranklin said the same above, pretty much.)

Personally I think STEP's all fine and dandy with just the formula book so far, but that's just me!

(Original post by DFranklin)
Edit: A better example of something I'd be amazed at losing marks for is modular arithmetic, which I don't believe is on any A-level syllabus any more.

Anyone in a position where they might want to quote a post-A-level result should also be sensible enough to see whether or not that's a reasonable action for a particular question.
Modular arithmetic is used sometimes in the official solutions: STEP II 2008 Q2 for instance. (Actually, there it's used more for clarity in presenting the answer rather than to get the solution. But it's definitely used.)

Seems silly that it's not on A-level, but ho hum...
9. (Original post by Xero Xenith)
IIRC the question on Jensen's Inequality said explicitly "You may assume this result without proving it."

And I think if you know a result that utterly trivialises a question, they'd like a proof, but it's fine to use very well-known results without proof. (Not sure though.) (Edit: just noticed DFranklin said the same above, pretty much.)

Personally I think STEP's all fine and dandy with just the formula book so far, but that's just me!

Modular arithmetic is used sometimes in the official solutions: STEP II 2008 Q2 for instance. (Actually, there it's used more for clarity in presenting the answer rather than to get the solution. But it's definitely used.)

Seems silly that it's not on A-level, but ho hum...
Oh did he I was trying to prove it via induction......read some articles....alot of it is based on statistics....makes sense as mean etc. lol

I was wondering if there is a good simple proof out there just out of curiosity.....the step question involving jensen's inequality as you correctly mentioned didn't require to prove it.
10. Should we use pen or pencil in the STEP exams?
11. (Original post by Xero Xenith)
And I think if you know a result that utterly trivialises a question, they'd like a proof, but it's fine to use very well-known results without proof.
This sentence doesn't seem sufficiently careful (paranoid) to me.

For example, suppose a question asked you to show

x^3+y^3 = z^3 had no solutions where x and y are multiples of 7 but z is not.

Then this question is trivialised by Fermat's Last Theorem, which is definitely a well known result. I don't think for a moment it would be fine to do that without proof. (And given the lamentable margin sizes on typical answer booklets, good luck with fitting that proof in...)
12. (Original post by Rahul.S)
Oh did he I was trying to prove it via induction......read some articles....alot of it is based on statistics....makes sense as mean etc. lol

I was wondering if there is a good simple proof out there just out of curiosity.....the step question involving jensen's inequality as you correctly mentioned didn't require to prove it.
The wiki proof at http://en.wikipedia.org/wiki/Jensen&#39;...finite_form.29
seems reasonably straightforward to me.
13. (Original post by DFranklin)
The wiki proof at http://en.wikipedia.org/wiki/Jensen&#39;...finite_form.29
seems reasonably straightforward to me.
I dont usually trust the things on wiki....I will give it a look after my online lecture thanks
14. (Original post by gff)
If I wasn't on PRSOM, I would've repped you just for this description.

That's what this question is about, and indeed, I don't believe any examiner will be annoyed from the fact that you actually know what this means. Otherwise, it would be silly.
Well you could give an intuitive explanation but I feel that what I said covers it better.
15. A heads up for anyone who has a go at question 12 on STEP III 1998, the order of p outside the bracketed expression is 3, not 2 like it says on the paper. Have spent a good couple of hours expanding all the summed probabilities trying to work out why the coefficients weren't fitting what was required in the question, only because the expression required had a misprint
16. (Original post by Rahul.S)
I dont usually trust the things on wiki...
In my experience, the maths articles on wiki are pretty reliable (although sometimes pitched at a rather inappropriate level). I think I've only seen one or two fairly subtle errors in what must be hundreds of articles.
17. (Original post by ben-smith)
For example: STEP III 2000 Q7 where in one of the bits I basically had to use the fact that monotonically increasing bounded sequences tend to a limit despite this obviously not being a level stuff.
Where it asked you to explain briefly why P(n) tends to a limit? I can't see any other way of doing that. I think you would've got a smile from the person marking if you wrote that - I'm guessing most people under exam conditions would've struggled to articulate that if they didn't know the result.
18. (Original post by DFranklin)
This sentence doesn't seem sufficiently careful (paranoid) to me.

For example, suppose a question asked you to show

x^3+y^3 = z^3 had no solutions where x and y are multiples of 7 but z is not.

Then this question is trivialised by Fermat's Last Theorem, which is definitely a well known result. I don't think for a moment it would be fine to do that without proof. (And given the lamentable margin sizes on typical answer booklets, good luck with fitting that proof in...)
(I wouldn't be able to resist making the joke either)
19. (Original post by DFranklin)
In my experience, the maths articles on wiki are pretty reliable (although sometimes pitched at a rather inappropriate level). I think I've only seen one or two fairly subtle errors in what must be hundreds of articles.
true point....the proof is quite straightforward....I would think only STEP III would possibly demand a proof.
20. (Original post by sianem)
Hi, please could someone explain something for me as I'm having a bit of a blank moment

I'm just working on STEP II 2004 question 4 and I'm trying to get my head around the first part.

If we let f(t) = L, so f(t) = acosect + bsect we find f'(t) = 0 to get tan^3t =a/b...why do we do this?

Is it because f(t) is at a minimum to enable the rod to be moved into corridor b..? or have I completely got the wrong end of the stick?!

Thanks
Yes, you are right.

by looking at the diagram we can see that for any angle t, f(t) is the largest stick that could be put in the corridor at that angle. So when we find the minimum of f(t) and rearrange for t, we find the angle that minimises the "longest possible" stick that can be put in the corridor at any angle.

Thus f(t) at that particular t is the longest possible stick passable through though corridor. This is because a stick that is passable through the corridor can be put in the corridor at any angle t with (90>t>0).

But you probably knew that anyway :P, and probably didn't really need the lengthy explanation.

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