The 2012 STEP Results Discussion Thread

Maths exam discussion - share revision tips in preparation for GCSE, A Level and other maths exams and discuss how they went afterwards.

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  1. gff's Avatar
    2001 15-04-2012  18:51
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    Re: The 2012 STEP Prep Thread!
    Here is another decent integral related to current discussions.
    Spoiler:
    Show

    \displaystyle \int^{\frac{\pi}{2}}_{0} \frac{x}{1 + \sin(x) + \cos(x)}\ dx
  2. Xero Xenith's Avatar
    2002 15-04-2012  19:01
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    Re: The 2012 STEP Prep Thread!
    (Original post by gff)
    Here is another decent integral related to current discussions.
    Spoiler:
    Show

    \displaystyle \int^{\frac{\pi}{2}}_{0} \frac{x}{1 + \sin(x) + \cos(x)}\ dx
    I believe...

    Spoiler:
    Show

    t-substitution, followed by integrating the ln... answer drops out?

    EDIT: it doesn't seem to drop out. Ah well
    Last edited by Xero Xenith; 15-04-2012 at 19:06.
  3. Rahul.S's Avatar
    2003 15-04-2012  19:04
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    Re: The 2012 STEP Prep Thread!
    (Original post by fruktas)
    After STEP School I actually tried to relax for some time knowing that this is the last week until end of June where I can do nothing, so only doing 2 STEP questions a day I successfully relaxed haha. Tomorrow it all begins again, going to start by doing a STEP mock paper in school, STEP 2 2008 and hopefully get atleast a 1. How is everyone else doing ?
    you suggest that doing 2 step questions a day is child's play :lol:

    how many step questions a day is actual work?!
    Post rating:
    1
  4. Dog4444's Avatar
    2004 15-04-2012  19:09
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    Re: The 2012 STEP Prep Thread!
    (Original post by gff)
    Here is another decent integral related to current discussions.
    Spoiler:
    Show

    \displaystyle \int^{\frac{\pi}{2}}_{0} \frac{x}{1 + \sin(x) + \cos(x)}\ dx
    Spoiler:
    Show

    How to represent x in terms of t?
    Maybe tan(x/2)=t, so x=2tan(-1)(t) ?
    But I have no idea how to work with this.
  5. Aurum's Avatar
    2005 15-04-2012  19:14
    • Full Member
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    Re: The 2012 STEP Prep Thread!
    (Original post by Xero Xenith)
    I believe...

    Spoiler:
    Show

    t-substitution, followed by integrating the ln... answer drops out?
    Spoiler:
    Show

    Much simpler is let the integral = I, Apply x = pi/2 - theta. Add the resulting integral and I and then the integral is pretty standard.
  6. fruktas's Avatar
    2006 15-04-2012  19:18
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    Re: The 2012 STEP Prep Thread!
    (Original post by Rahul.S)
    you suggest that doing 2 step questions a day is child's play :lol:

    how many step questions a day is actual work?!
    I just kinda did it to keep my mind interested. I just wanted to relax! I just found the time for 40 minutes, sat down, did the 2 questions and done. After STEP school, pure question are becoming quite straight forward (thank god!)
  7. TSong's Avatar
    2007 15-04-2012  19:25
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    Re: The 2012 STEP Prep Thread!
    (Original post by Aurum)
    Spoiler:
    Show

    Much simpler is let the integral = I, Apply x = pi/2 - theta. Add the resulting integral and I and then the integral is pretty standard.

    I got
    Spoiler:
    Show
    ln2 * (pi/4)


    Quite surprised to know that it's not in A-Levels.
  8. Xero Xenith's Avatar
    2008 15-04-2012  19:28
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    Re: The 2012 STEP Prep Thread!
    (Original post by fruktas)
    I just kinda did it to keep my mind interested. I just wanted to relax! I just found the time for 40 minutes, sat down, did the 2 questions and done. After STEP school, pure question are becoming quite straight forward (thank god!)
    Boo hiss boo.

  9. Aurum's Avatar
    2009 15-04-2012  19:31
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    Re: The 2012 STEP Prep Thread!
    (Original post by TSong)
    I got
    Spoiler:
    Show
    ln2 * (pi/4)


    Quite surprised to know that it's not in A-Levels.
    Just evaluated the integral (before I just suggested the method) and your answer matches mine.
  10. ben-smith's Avatar
    2010 15-04-2012  19:57
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    Re: The 2012 STEP Prep Thread!
    In the 2008 STEP II examiner's report it says:
    the scripts received covered the full range of marks (and beyond!).
    wtfbbq, beyond the full range of marks?
  11. Rahul.S's Avatar
    2011 15-04-2012  20:00
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    Re: The 2012 STEP Prep Thread!
    (Original post by fruktas)
    I just kinda did it to keep my mind interested. I just wanted to relax! I just found the time for 40 minutes, sat down, did the 2 questions and done. After STEP school, pure question are becoming quite straight forward (thank god!)
    :lol:

    who were you btw? you still havent answered that shook?!

    I think the step school was very good in terms of logical thinking :cool:
  12. TheMagicMan's Avatar
    2012 15-04-2012  20:01
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    Re: The 2012 STEP Prep Thread!
    (Original post by ben-smith)
    In the 2008 STEP II examiner's report it says:

    wtfbbq, beyond the full range of marks?
    If you answer more than 6 questions...
  13. Aurum's Avatar
    2013 15-04-2012  20:07
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    Re: The 2012 STEP Prep Thread!
    Since everyone's interested in the integration of trignometric functions here's another one (it's indefinite though), integrate (cos2x)^1^/^2(sinx)^-^1
  14. TheMagicMan's Avatar
    2014 15-04-2012  20:36
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    Re: The 2012 STEP Prep Thread!
    (Original post by Aurum)
    Since everyone's interested in the integration of trignometric functions here's another one (it's indefinite though), integrate (cos2x)^1^/^2(sinx)^-^1
    Another nice on...but reasonably elementary

    This is a good one \displaystyle\int_0^{\infty} sin(x^2) dx

    HINT:

    Spoiler:
    Show
    You won't be able to find\displaystyle\int sin(x^2) dx
  15. safmaster's Avatar
    2015 15-04-2012  20:41
    • Adored and Respected Member
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    Re: The 2012 STEP Prep Thread!
    (Original post by fruktas)
    Tomorrow it all begins again, going to start by doing a STEP mock paper in school, STEP 2 2008 and hopefully get atleast a 1. How is everyone else doing ?
    Hey fruktas, how's it going? I'm planning to do STEP II 2008 next week aswell so let me know how it goes.
  16. Xero Xenith's Avatar
    2016 15-04-2012  20:43
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    Re: The 2012 STEP Prep Thread!
    (Original post by Rahul.S)
    :lol:

    who were you btw? you still havent answered that shook?!

    I think the step school was very good in terms of logical thinking :cool:
    What were the conditions for applying to the STEP School? State school... anything else?

    Kind of regretting not going, though I do have a bit of (unofficial) support at school - one teacher who does know his stuff. (But I think I'd still be the first in anyone's memory to get into Cambridge for Maths... eep!)
  17. fruktas's Avatar
    2017 15-04-2012  20:48
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    Re: The 2012 STEP Prep Thread!
    (Original post by safmaster)
    Hey fruktas, how's it going? I'm planning to do STEP II 2008 next week aswell so let me know how it goes.
    hey man! not too bad, been a bit ill, but serious work has to start tomorrow! what about you? Yeah, the 2008 paper looks quite nice, 4 solutions shouldnt be hard. I will let you know once I done it
  18. Aurum's Avatar
    2018 15-04-2012  20:50
    • Full Member
    • Posts: 127
    Re: The 2012 STEP Prep Thread!
    (Original post by TheMagicMan)
    Another nice on...but reasonably elementary

    This is a good one \displaystyle\int_0^{\infty} sin(x^2) dx

    HINT:

    Spoiler:
    Show
    You won't be able to find\displaystyle\int sin(x^2) dx
    Here's another one
    Given: Integration of sinx/x from 0 to infinity is pi/2.
    Obtain the value of integraiton of (sin^4 x)/x^2 from 0 to infinity
    Last edited by Aurum; 17-04-2012 at 02:48.
  19. TkTk's Avatar
    2019 15-04-2012  20:54
    • Junior Member
    • Location: London
    • Posts: 29
    Re: The 2012 STEP Prep Thread!
    Hey all, joining the thread as I'm in quite a pickle.

    I'm doing STEP1, as part of an offer to study Computer Science (I do not take Further Maths), and need to get a 2. I know for most that'd seem quite manageable, yet I'm struggling and need some advice.

    I currently try and do one question a day (up to 1 hour max), from pre-2000 papers, as I have already worked through 2000-2009. However, on most papers, I have only been able to do 3-4 full questions maximum (needing guidance for some). I've been looking at some of the older papers as I have been running out of material, and I've felt like I have stepped backwards. Is it strange to just look at some questions and feel this brick wall of impossibility?

    I honestly have no idea how I can move forwards when questions in each paper are generally so unpredictable that I can't pick up many transferable skills! Should I try some STEP2 questions to keep fresh material?

    All advice greatly appreciated. TkTk
  20. shamika's Avatar
    2020 15-04-2012  20:55
    • Peer Of The TSR Realm
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    Re: The 2012 STEP Prep Thread!
    (Original post by TheMagicMan)
    Another nice on...but reasonably elementary

    This is a good one \displaystyle\int_0^{\infty} sin(x^2) dx

    HINT:

    Spoiler:
    Show
    You won't be able to find\displaystyle\int sin(x^2) dx
    The graph is pretty!
    Spoiler:
    Show
    There is a ton of stuff I never knew about the Fresnel integrals - like how incredible the Euler spiral is. Lots of fun graphs with these functions!
    Last edited by shamika; 15-04-2012 at 21:15.
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