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The 2012 STEP Results Discussion Thread

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Right, thanks everyone.
I got my paper out.
Assuming I won't notice Farhan's short-cut on the actual exam, I will stick with this nasty stuff.
If m=-2, the integral is ln2-0.5
If m=-1, the integral is 1-ln2

If it's correct (hopefully), what can I do from here?
(edited 11 years ago)
Reply 1341
Original post by Dog4444
Right, thanks everyone.
I got my paper out.
Assuming I won't notice Farhan's short-cut on the actual exam, I will stick with this nasty stuff.
If m=-2, the integral is ln2-0.5
If m=-1, the integral is 1-ln2

If it's correct (hopefully), what can I do from here?


Read my other post regarding this formula, it should be just 2^(m+1) not 2^(m+1)-1 in your first term, assuming your values for m=-1, and m=-2 are correct, just state the values for m=-1 and m=-2 and state that the formula gives the value of the integral for all other values of m, you'll also need to state why the formula doesn't work when m=-1,-2.
(edited 11 years ago)
Original post by Aurum
Read my other post regarding this formula, it should be just 2^(m+1) not 2^(m+1)-1 in your first term, assuming your values for m=-1, and m=-2 are correct, just state the values for m=-1 and m=-2 and state that the formula gives the value of the integral for all other values of m, you'll also need to state why the formula doesn't work when m=-1,-2.


Edited, thanks. :angry:
Oh, ok. I thought "different cases" implies we should find something interesting. It might mean cases when m=-1 and -2.
Thanks.
Do you know how it works with part points? ..with solutions there should be amount of points given for each step, don't you think?..
Original post by zuzia.kru
Do you know how it works with part points? ..with solutions there should be amount of points given for each step, don't you think?..


I emailed the STEP guys about this:

Dear Sir / Madam,

I am a candidate due to take STEP papers this summer, but I'm having difficulty marking my work even with full solutions available. Each question is marked out of 20, but I haven't been able to find any guidelines for what any particular answer is worth.

Are there any such guidelines available, or sample marked questions? I understand that these materials may not be made public, but it's difficult to prepare without some idea of what is required.

As it stands, I cannot ascertain whether a partially complete answer is worth 5 marks or 15. I must admit that as I have no means of getting this information through professional STEP tuition, I feel a little disadvantaged.

Any guidance or materials would be hugely appreciated!

Many thanks,

[me]

-----------------------------------------

Dear [me]

Other than the comments posted in the 'Final STEP solutions', the 'Final Examiner's Report' and other information on the website at http://www.admissionstests.cambridgeassessment.org.uk/adt/step, there is no published guideline on the potential value of each partially completed STEP question; each candidate's answer, whether or not complete, would be unique.

There are past papers downloadable from the website; we would suggest that thoroughly revising all topics within your A level syllabus and completing these past papers to the best of your ability under timed conditions will help you to prepare for the tests in June.

You would also find useful information at http://meikleriggs.org.uk/ and https://nrich.maths.org/.

best wishes,
Sandi Spence
Admissions Tests Team
Cambridge Assessment www.atsts.org.uk/


(This term went out with a bang! Finished my notes on A-level Economics, and my teacher guess-marked my STEP III 2004 as 72 - an S was 75 :smile: So happy I'm starting to do papers to a good standard... I've been doing them long enough :tongue:)
(edited 11 years ago)
Original post by Xero Xenith
I emailed the STEP guys about this:



(This term went out with a bang! Finished my notes on A-level Economics, and my teacher guess-marked my STEP III 2004 as 72 - an S was 75 :smile: So happy I'm starting to do papers to a good standard... I've been doing them long enough :tongue:)


Wow! Congrats!! I wish I was doing that well too :P
And It's not nice of them not telling us about those points...;P
because "Little credit will be given for fragmentary answer" doesn't sound good ...
Original post by zuzia.kru
Wow! Congrats!! I wish I was doing that well too :P
And It's not nice of them not telling us about those points...;P
because "Little credit will be given for fragmentary answer" doesn't sound good ...


Don't worry too much about it. I think the general consensus is that these days, if you answered around half a question, expect to get around 10/20 (with the rule generalising for how much of a question you answer). We know this because of several years of people here getting 1's with 'fragmented' answers. I'm sure we discussed this earlier in quite a lot of depth if you want to take a look in this thread.
(edited 11 years ago)
Original post by shamika
Don't worry too much about it. I think the general consensus is that these days, if you answered around half a question, expect to get around 10/20 (with the rule generalising for how much of a question you answer). We know this because of several years of people here getting 1's with 'fragmented' answers. I'm sure we discussed this earlier in quite a lot of depth if you want to take a look in this thread.


That sounds good :smile: Thanks for the information
Original post by zuzia.kru
Wow! Congrats!! I wish I was doing that well too :P
And It's not nice of them not telling us about those points...;P
because "Little credit will be given for fragmentary answer" doesn't sound good ...


As shamika said. But that's assuming that the parts of the question you answer require half the effort that a full answer did.

Sometimes a question will have part i) as very easy then part ii) much more difficult, or vice versa. In those cases, despite having completed half the instructions, you haven't done half the question. It's often difficult to tell.

I think "little credit will be given for fragmentary solutions" really means "if you start a question but don't get anywhere, don't expect much".

(And thanks :smile:)
I'd reckon that you'll lose a *little* by if you did exactly half of two questions instead of one full one. But something like 18/20 v.s. 20/20, not a huge difference.
Original post by Xero Xenith
As shamika said. But that's assuming that the parts of the question you answer require half the effort that a full answer did.


I think XX hit the nail on the head. Determining whether something takes effort or not isn't as easy as you'd think. Plenty of times (in fact, pretty much on every paper) some part of a question turns out to be harder than expected by the examiners.

Not publishing the mark scheme in the questions (or with the solutions) is probably a good thing, since it allows the examiners to make a retrospective adjustment to the marks if a question turns out not to work as expected. Besides, university maths exams typically don't give you a mark distribution on the paper, so you might as well get used to it now :smile:

@XX: Congrats on doing so well on that paper!
Original post by shamika
I think XX hit the nail on the head. Determining whether something takes effort or not isn't as easy as you'd think. Plenty of times (in fact, pretty much on every paper) some part of a question turns out to be harder than expected by the examiners.

Not publishing the mark scheme in the questions (or with the solutions) is probably a good thing, since it allows the examiners to make a retrospective adjustment to the marks if a question turns out not to work as expected. Besides, university maths exams typically don't give you a mark distribution on the paper, so you might as well get used to it now :smile:

@XX: Congrats on doing so well on that paper!


You're probably right...Oh, I wish it was already August and everything was clear.. :P
Question I just thought up - someone might find it interesting. You may like the result at the end. :smile:

Spoiler



If you'd prefer, here it is in a "show that" form. (Also my answer to the above!) I can't guarantee that the formula given is the best, but it's not too hard to get, and gets the above result with an error of 0.00005% :smile:

Spoiler



The more I think about the final result the more it just makes sense :tongue:
On 2007 STEP III the last part how can you find the sum of roots? I assume the previous part of the question is intended to give you an idea of what to do but if you do say cos(sum of roots) it will give you an expression of cosines, not the actual roots. Can anybody help, i do not want to look at the answers.
Thanks
Original post by oh_1993
On 2007 STEP III the last part how can you find the sum of roots? I assume the previous part of the question is intended to give you an idea of what to do but if you do say cos(sum of roots) it will give you an expression of cosines, not the actual roots. Can anybody help, i do not want to look at the answers.
Thanks

If you expand all the cosines using the compound angle formulae so the things you have involving theta are cos(theta), sin(theta) and tan(theta), you should be able to re arrange to something of the form at^4 + bt^3 + ct^2 + dt + e = 0 and then apply the previous part.
Original post by matt2k8
If you expand all the cosines using the compound angle formulae so the things you have involving theta are cos(theta), sin(theta) and tan(theta), you should be able to re arrange to something of the form at^4 + bt^3 + ct^2 + dt + e = 0 and then apply the previous part.


cos(A+B+C+D) does not give anything in terms of tan

I have expanded it out and it has product of cosines of the roots and also of sines but i see no way of simplifying it further, i cannot prove anything about the relationships between the roots from the equation.

since sum of roots = npi i guess i could try to show that cos(sum of roots) = 1 or -1 but still i do not know where to go from here. :frown:
Reply 1356
Original post by oh_1993
cos(A+B+C+D) does not give anything in terms of tan

I have expanded it out and it has product of cosines of the roots and also of sines but i see no way of simplifying it further, i cannot prove anything about the relationships between the roots from the equation.

since sum of roots = npi i guess i could try to show that cos(sum of roots) = 1 or -1 but still i do not know where to go from here. :frown:


That's not what he meant, he meant that first you expand the given equation, the pcos2theta one, then you'll have to square both sides to obtain a quartic. When you obtain the quartic you'll see how to use the previous part, to obtain the final answer. Don't forget that p and alpha are constants, when you obtain the quartic it'll be hard for you to see what a,b,c,d,e are if you forget that p and alpha are constants.
(edited 11 years ago)
You need to write the expression they give in terms of tan theta rather than cos theta and cos 2theta. A bit of rearranging should finish things off.
Original post by Xero Xenith
Question I just thought up - someone might find it interesting. You may like the result at the end. :smile:

Spoiler



If you'd prefer, here it is in a "show that" form. (Also my answer to the above!) I can't guarantee that the formula given is the best, but it's not too hard to get, and gets the above result with an error of 0.00005% :smile:



The more I think about the final result the more it just makes sense :tongue:


The 'obvious' way of doing this seems to be to derive stirling's approximation (not a difficult task) and log 10 it

Spoiler

(edited 11 years ago)
I tried some of STEP III 2007:

- Q7 is a nice easy question. Recommend you try it because its a godsend given most STEP questions

Spoiler



- Q3 looks easy, but I don't see a good way of knowing which substitutions to make to get the quoted results. I just tried different things until it worked. I would've been one of those the examiners labelled 'rambling'. Perseverance is the key here. I think I missed something because I couldn't get it out for a while.

- I found Q2 even easier than Q7, but only because I knew that

Spoiler



This paper also proves DFranklin's point - its one thing trying to do these questions without a time limit, and quite another when you've only got 3 hours.

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