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. fruktas's Avatar
    • Benevolent Member
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    Re: The 2012 STEP Prep Thread!
    Question 2 STEP II 2008

    Can anyone help me with the partial fractions? ( I know, I know).

    I can see very clearly what to do in this question, but my my partial fractions are
    not coming out right
  2. Llewellyn's Avatar
    • Section Moderator
    • Astray anyway
    Re: The 2012 STEP Prep Thread!
    (Original post by fruktas)
    Question 2 STEP II 2008

    Can anyone help me with the partial fractions? ( I know, I know).

    I can see very clearly what to do in this question, but my my partial fractions are
    not coming out right
    Are you setting aX+b for the numerator for the fraction with denominator 1+x^2 ? Remember the numerator must be 1 degree lower.

    If it's not that, I'm assuming it's a trivial sign or division error?
  3. Rahul.S's Avatar
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    Re: The 2012 STEP Prep Thread!
    I know this might seem abit off....but has anyone habits changed whilst doing STEP?

    i use to pump out grime tunes regularly...now Im playing some emosh tunes due to STEP
  4. fruktas's Avatar
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    • Location: London
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    Re: The 2012 STEP Prep Thread!
    (Original post by Llewellyn)
    Are you setting aX+b for the numerator for the fraction with denominator 1+x^2 ? Remember the numerator must be 1 degree lower.

    If it's not that, I'm assuming it's a trivial sign or division error?
    Really!? Sadly, this is the first time I am hearing about this. It works now. thank you!
  5. Rahul.S's Avatar
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    Re: The 2012 STEP Prep Thread!
    (Original post by fruktas)
    Really!? Sadly, this is the first time I am hearing about this. It works now. thank you!
    U SERIOUS!!!!!!

    :lol:
  6. fruktas's Avatar
    • Benevolent Member
    • Location: London
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    Re: The 2012 STEP Prep Thread!
    (Original post by Rahul.S)
    U SERIOUS!!!!!!

    :lol:
    I know, sadly I was never taught that, and I sort of never encountered it before. Wow, I sound like a moron hahaha
  7. Rahul.S's Avatar
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    Re: The 2012 STEP Prep Thread!
    (Original post by fruktas)
    I know, sadly I was never taught that, and I sort of never encountered it before. Wow, I sound like a moron hahaha
    main thing is that now you do
  8. marcus2001's Avatar
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    Re: The 2012 STEP Prep Thread!
    (Original post by mikelbird)
    I hope this explains it......
    Ah yeah that clear's it up - thanks
  9. 8inchestall's Avatar
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    Re: The 2012 STEP Prep Thread!
    cant be bothered to look back for a quote, but I saw some people mention logarithmic differentiation, can someone clarify what this is?

    is it as simple as

    

y = x^x

\ln y = x \ln x

    then differentiate?
  10. Rahul.S's Avatar
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    Re: The 2012 STEP Prep Thread!
    (Original post by 8inchestall)
    cant be bothered to look back for a quote, but I saw some people mention logarithmic differentiation, can someone clarify what this is?

    is it as simple as

    

y = x^x

\ln y = x \ln x

    then differentiate?
    yh implicitly...
  11. Extricated's Avatar
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    Re: The 2012 STEP Prep Thread!
    (Original post by 8inchestall)
    cant be bothered to look back for a quote, but I saw some people mention logarithmic differentiation, can someone clarify what this is?

    is it as simple as

    

y = x^x

\ln y = x \ln x

    then differentiate?
    Alternatively notice that x^x is equivalent to e^xlnx
    Last edited by Extricated; 16-05-2012 at 22:40.
  12. Dog4444's Avatar
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    Re: The 2012 STEP Prep Thread!
    (Original post by Extricated)
    Alternatively notice that x^x is equivalent to e^xlnx
    And what after that?
  13. Rahul.S's Avatar
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    Re: The 2012 STEP Prep Thread!
    (Original post by Dog4444)
    And what after that?
    then differentiate.....as its now an elementary function.
  14. Ree69's Avatar
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    • Location: London
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    Re: The 2012 STEP Prep Thread!
    (Original post by Dog4444)
    And what after that?
     \frac{d}{dx}\ e^{f(x)} = f'(x)e^{f(x)}

    (You learn this in C3/4 I think).
  15. Zuzuzu's Avatar
    • Peer Of The TSR Realm
    • Posts: 1,540
    Re: The 2012 STEP Prep Thread!
    (Original post by 8inchestall)
    cant be bothered to look back for a quote, but I saw some people mention logarithmic differentiation, can someone clarify what this is?

    is it as simple as

    

y = x^x

\ln y = x \ln x

    then differentiate?
    That's one application, yes.

    Another useful one is for differentiating products. ie. y = \prod_{i}^{n} f_i \implies \ln y = \sum_{i}^{n} \ln f_i .
  16. Rahul.S's Avatar
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    Re: The 2012 STEP Prep Thread!
    (Original post by Zuzuzu)
    That's one application, yes.

    Another useful one is for differentiating products. ie. y = \prod_{i}^{n} f_i \implies \ln y = \sum_{i}^{n} \ln f_i .
    for some odd reason or another....even though I know this- Ive never used it I would be interested to see where it can be used effectively :p: :rolleyes:
  17. bananarama2's Avatar
    • TSR Legend
    Re: The 2012 STEP Prep Thread!
    (Original post by Rahul.S)
    for some odd reason or another....even though I know this- Ive never used it I would be interested to see where it can be used effectively :p: :rolleyes:
    Surely it restricts the domain of the function?
  18. voygehr's Avatar
    • Junior Member
    • Posts: 49
    Re: The 2012 STEP Prep Thread!
    Got a 2, 6 points below a 1 on my very first past paper. Could have been better, could have been worse :rolleyes: Now I have exactly one month to up it to a 1. Seems doable..?
  19. ben-smith's Avatar
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    Re: The 2012 STEP Prep Thread!
    (Original post by wcp100)
    Surely it restricts the domain of the function?
    nah, you can do some clever things with branch cuts and effectively give yourself a workable natural log for -ve numbers.
  20. member910132's Avatar
    • Banned
    • Posts: 891
    Re: The 2012 STEP Prep Thread!
    Quick Q:

     (x^2 +y^2)^2 = 2a^2xy

    In polar form will be  r = a\sqrt{\sin 2\theta} not  r = a\sqrt{\sin \theta} right ?
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