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The 2012 STEP Results Discussion Thread

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    I just had a mare on 2008, hopefully a blip. It was still a 2 but not good at this point
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    (Original post by desijut)
    I just had a mare on 2008, hopefully a blip. It was still a 2 but not good at this point
    I got a low 3 on that paper. (though it was the first SIII paper I ever did)
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    If you're doing a question and you make one little stupid mistake somewhere in the middle or beginning (for example, I forgot the + c integration constant in the easy part of the question, and since it was a logarithm it ended up being crucial to the answer), but you still do the next bit with correct logic (so if you hadn't made the mistake you would be right), how many marks do you lose. Would you even get any method marks at all? I've just done 4 step questions and 3 of those I did something totally retarded, like forgetting a term, or not seeing the - sign, forgetting to square something at the start etc...
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    (Original post by desijut)
    I just had a mare on 2008, hopefully a blip. It was still a 2 but not good at this point

    (Original post by Xero Xenith)
    I got a low 3 on that paper. (though it was the first SIII paper I ever did)
    Did you guys not like Q2? The only part that requires a bit of 'thought' was the very last part, but

    Spoiler:
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    that part falls out easily when you consider S_k(1).


    It was a rather long question though - finding S_4(n) explicitly is just tedious.

    I also thought Q5 was similarly just a slog of finding the right expressions. (The examiner's report did say people responded to both questions in much the same way so maybe it doesn't suit your strong points?) I would've also picked questions 6 and 8. This exam has few 'interesting' questions, with Q13 and potentially Q2 being the exceptions.
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    (Original post by shamika)
    Did you guys not like Q2? The only part that requires a bit of 'thought' was the very last part, but

    Spoiler:
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    that part falls out easily when you consider S_k(1).


    It was a rather long question though - finding S_4(n) explicitly is just tedious.

    I also thought Q5 was similarly just a slog of finding the right expressions. (The examiner's report did say people responded to both questions in much the same way so maybe it doesn't suit your strong points?)
    I did all 3 mechanics on that paper. They were nice but I doubt many did them.
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    (Original post by ben-smith)
    I did all 3 mechanics on that paper. They were nice but I doubt many did them.
    According to the examiner's report:

    - a quarter tried Q9
    - a fifth tried Q10
    - under a twelfth tried Q11

    Having tried Q1, I also realized why this is in STEP III
    Spoiler:
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    How do you find x and y given xy and (x+y)? I assume relations between the roots of polynomials is a further maths topic only?


    I thought 2008 wasn't bad at all... :confused:
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    (Original post by shamika)
    According to the examiner's report:

    - a quarter tried Q9
    - a fifth tried Q10
    - under a twelfth tried Q11

    Having tried Q1, I also realized why this is in STEP III
    Spoiler:
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    How do you find x and y given xy and (x+y)? I assume relations between the roots of polynomials is a further maths topic only?


    I thought 2008 wasn't bad at all... :confused:
    in reply to the spoiler; I wouldn't consider that a further maths topic as it's easy enough to do just substituting them into each other and solving a quadratic.
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    (Original post by matt2k8)
    in reply to the spoiler; I wouldn't consider that a further maths topic as it's easy enough to do just substituting them into each other and solving a quadratic.
    Good point. I was wondering why that was a STEP III question rather than STEP II, although if II and III are supposed to be the same difficulty, questions are interchangeable.
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    For STEP III 2010 Q3, the TSR solution (by "Unbounded" I think, its in the solution thread) of finding the general formula seems a bit overkill (in terms of proving a stronger results) for part (iii) of the question. I tried it using groups/ lagrange's theorem, and want to check whether it is totally correct:

    Spoiler:
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    We want to find an expression for C_p(x) where p is a prime.
    Let  \omega = e^{i\frac{2 \pi}{p}} , so the pth roots of unity form the cyclic group with elements (1, \omega , \omega ^2, ... ,\omega ^{p-1}) . By definition, every element order p in this group must be a "primitive" pth root of unity. Lagrange's theorem gives that every non-identity (i.e. all elements excluding 1) element here must have order p, and hence are all the primitive roots.
    So C_p(x)=\frac{x^p-1}{x-1}=x^{p-1}+x^{p-2}+...+x+1

    Never used groups outside of an a-level q before, so i could be wrong. But i liked how (if correct) the primitive nth roots are bascially the generators for the group of complex roots nth of unity under multiplication. Seemed like a nice link.
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    (Original post by twig)
    For STEP III 2010 Q3, the TSR solution.. seems a bit overkill...
    I don't see how using Lagrange, and unproven results about Groups, is less overkill. Otherwise, it is true and it is nice, yes.

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    Starting with x^p = 1, you could find that all p-th roots of unity are given by \displaystyle \omega = e^{i2\pi n/p}.


    The definition of a primitive root, as given in the question, asserts that there is no integer m such that w^m = 1 for 0 < m < p.
    Hence, since for every integer k we have e^{i 2\pi k} = 1, it suffices to argue that p \mid nm implies that at least one of m and n is a multiple of p.

    If n is not a multiple of p, then no such positive integer m exists (less than p).
    Therefore, the only non-primitive root of the equation is 1.

    By writing x^p - 1 \equiv (x - 1)C_p(x) one easily obtains the result.
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    (Original post by jack.hadamard)
    I don't see how using Lagrange, and unproven results about Groups, is less overkill. Otherwise, it is true and it is nice, yes.

    Spoiler:
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    Starting with x^p = 1, you could find that all p-th roots of unity are given by \displaystyle \omega = e^{i2\pi n/p}.


    The definition of a primitive root, as given in the question, asserts that there is no integer m such that w^m = 1 for 0 < m < p.
    Hence, since for every integer k we have e^{i 2\pi k} = 1, it suffices to argue that p \mid nm implies that at least one of m and n is a multiple of p.

    If n is not a multiple of p, then no such positive integer m exists (less than p).
    Therefore, the only non-primitive root of the equation is 1.

    By writing x^p - 1 \equiv (x - 1)C_p(x) one easily obtains the result.
    Yeah sorry, did not phrase my post properly! I would not have the confidence/ability to try the groups things in exam conditions, but wanted to check whether this was right. My first attempt was very similar to your with considering the exponential, but more messy.
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    Very happy, just got 3 perfect solutions and 2 'mostly' (14+) on III 2010 which is an S

    That paper just suited me all over - surprised by its low boundaries.
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    (Original post by hassi94)
    Very happy, just got 3 perfect solutions and 2 'mostly' (14+) on III 2010 which is an S

    That paper just suited me all over - surprised by its low boundaries.
    I just did that paper too and loved it. I did 2 mechanics 2 stats and a pure question.
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    (Original post by ben-smith)
    I just did that paper too and loved it. I did 2 mechanics 2 stats and a pure question.
    Nice Mine were all pure; 1,3,4 fully and 2 and 7 were the partials
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    I've got 2010 and 2011 left, ive got monday afternoon and tuesday to do them in exam conditions (3 hours) and then knock out any I left that i feel i can do (should get a lot of it done)

    I need to do well in those two to get some sort of a confidence boost for the exam after my dismal 2008 display
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    (Original post by hassi94)
    Very happy, just got 3 perfect solutions and 2 'mostly' (14+) on III 2010 which is an S

    That paper just suited me all over - surprised by its low boundaries.
    I loved that paper! It had just the right questions, which made me wonder why the boundaries were even low?

    Let's hope for something similar wednesday!
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    (Original post by fruktas)
    I loved that paper! It had just the right questions, which made me wonder why the boundaries were even low?

    Let's hope for something similar wednesday!
    I don't understand how one can criticise the boundaries; they're designed to reflect the performance of the majority. The reason they were so low is because, under exam conditions, most of the candidates had a difficult time - given that it's nigh on impossible to recreate an exam atmosphere at home, it's more a case of you failing to judge the difficulty of the paper for yourself.

    For example, this year's STEP II was very straightforward in comparison to last year's (based on my opinion and that of the more experienced STEP folk on here) - yet people were still suggesting that they would have rather done 2011 even though chances are, if one couldn't handle the 2012 paper, the 2011 paper would have chewed them up and spat them out.

    I guess what I'm trying to say is that you almost definitely don't want a paper like 2010 III; the boundaries are low for a reason.
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    (Original post by Exp!)
    I don't understand how one can criticise the boundaries; they're designed to reflect the performance of the majority. The reason they were so low is because, under exam conditions, most of the candidates had a difficult time - given that it's nigh on impossible to recreate an exam atmosphere at home, it's more a case of you failing to judge the difficulty of the paper for yourself.

    For example, this year's STEP II was very straightforward in comparison to last year's (based on my opinion and that of the more experienced STEP folk on here) - yet people were still suggesting that they would have rather done 2011 even though chances are, if one couldn't handle the 2012 paper, the 2011 paper would have chewed them up and spat them out.

    I guess what I'm trying to say is that you almost definitely don't want a paper like 2010 III; the boundaries are low for a reason.
    I sat this years paper, and I thought it was hard for one major reason : the questions did not suit my style. Only one calculus question, no trig, no differential equations or induction. These are the areas I usually pick up marks on and the reason I thought 2010 III paper was approachable was due to the questions, and that is exactly what I mean when I hope that the paper is similar

    I am not saying nerves, and stress under an exam conditions do not do any impact, but success comes from the fact whether you can do the questions, and if the style of questions suits you, it can only help.
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    (Original post by fruktas)
    I sat this years paper, and I thought it was hard for one major reason : the questions did not suit my style. Only one calculus question, no trig, no differential equations or induction. These are the areas I usually pick up marks on and the reason I thought 2010 III paper was approachable was due to the questions, and that is exactly what I mean when I hope that the paper is similar

    I am not saying nerves, and stress under an exam conditions do not do any impact, but success comes from the fact whether you can do the questions, and if the style of questions suits you, it can only help.
    definately on point :cool:
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    (Original post by Exp!)
    I don't understand how one can criticise the boundaries; they're designed to reflect the performance of the majority. The reason they were so low is because, under exam conditions, most of the candidates had a difficult time - given that it's nigh on impossible to recreate an exam atmosphere at home, it's more a case of you failing to judge the difficulty of the paper for yourself.
    Surely its more a case of sadly, your reaction to different STEP papers will be very dependent on the topics the questions test, and that it is entirely possible for someone to love one paper and do extremely well and not get on with another. Thus its entirely possible for the majority to do badly but for individual candidates to outperform the pack when usually this would not happen. At this level, luck is a factor, like it or not.

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