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    (Original post by Palette)
    UK Senior Mathematics Challenge held annually to Year 12 and Year 13 students.
    Oh, it's not really talked about much on here so I've never seen it abbreviated. I'm not really sure what you're expected to know and what you're not tbh.
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    (Original post by Ano123)
    I'll get the ball rolling. If anyone is out there who has done some trigonometry and want to put their knowledge to the test, here's a tough question they can try if they want to. (Probably not many for another few months at least). I made it up a while ago.
    Attachment 557673
    For the solving the equation the question should really state that 0<x<90.
    :eek::eek::eek:
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    (Original post by ODES_PDES)
    :eek::eek::eek:
    Nice question?
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    (Original post by Ano123)
    Nice question?
    Looks very hard
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    (Original post by Ano123)
    Nice question?
    Might want to spoiler it. Might make the new Y13's run away from the thread
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    (Original post by ODES_PDES)
    Looks very hard
    It's alright actually. Plenty of guidance. I did that so people wouldn't just lose interest when seeing an expression like that.
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    (Original post by Palette)
    This is an SMC problem which I solved, but I want to know if there is a way of solving it non-manually:

    Let  f(x)= \frac{x-1}{x+1}. Calculate  f^6(x).
    I think actually that they are using the notation that  \displaystyle f^n= \underbrace{ fff\cdots f}_{n} . So it would just be composing the function with itself 5 times for  f^6 .
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    (Original post by B_9710)
    I think actually that they are using the notation that  \displaystyle f^n= \underbrace{ fff\cdots f}_{n} . So it would just be composing the function with itself 5 times for  f^6 .
    Is there any rigorous shortcut that enables one to solve the question quickly? I deduced manually that for  f^n(x) from n=1 to n=4, f^{n+2}(x)=-\frac{1}{f^n(x)} but I can't actually prove it for all n.
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    (Original post by Palette)
    Is there any rigorous shortcut that enables one to solve the question quickly? I deduced manually that for  f^n(x) from n=1 to n=4, f^{n+2}(x)=-\frac{1}{f^n(x)} but I can't actually prove it for all n.
    I'll have a proper look later, but perhaps it may be useful to see if this pattern holds for a few more and if it does use induction to prove the result (if it is true). Can be much easier than a direct proof, maybe so in this case.
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    (Original post by Palette)
    Is there any rigorous shortcut that enables one to solve the question quickly? I deduced manually that for  f^n(x) from n=1 to n=4, f^{n+2}(x)=-\frac{1}{f^n(x)} but I can't actually prove it for all n.
    If you consider  f^5(x) it will become very clear that you can write a general expression for  f^n(x) explicitly, and it's very easy to just define  f^n(x) in more than 1 way.
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    (Original post by Palette)
    This is an SMC problem which I solved, but I want to know if there is a way of solving it non-manually:

    Let  f(x)= \frac{x-1}{x+1}. Calculate  f^6(x).
    Sure.

    f(x) = \frac{x-1}{x+1} \Rightarrow f^2(x) = \frac{-1}{x} \Rightarrow f^3(x) = -\frac{1}{f(x)} \Rightarrow f^5(x) = f(x) \Rightarrow f^6(x) = f^2(x) = -\frac{1}{x}
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    Hello, friends. I'm just curious! Have you ever used online homework help services like https://assignment.essayshark.com/math-help.html to do your math assignments? Did they work fine for you? I'm considering giving it a try.
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    (Original post by jessback)
    Hello, friends. I'm just curious! Have you ever used online homework help services like https://assignment.essayshark.com/math-help.html to do your math assignments? Did they work fine for you? I'm considering giving it a try.
    Homework help services? I've never went to lengths of that for homework lol. Just post some problems, or ideas you dont understand, here.
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    (Original post by SeanFM)
    My D2 textbook has arrived :excited: I feel like a 6th former again. :moon:
    Reminds me - I should buy M4 and M5.
    Spoiler:
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    ...or "download" them.
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    I'll be working on M3, D2 and S3 this year. Perhaps M4, 5 and S4 depending on whether I find them too insane.
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    (Original post by Ayman!)
    Reminds me - I should buy M4 and M5.
    Spoiler:
    Show
    ...or "download" them.
    Spoiler:
    Show
    Links pl0x :laugh:
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    Silly question but is this thread for maths alone or can FM students use it as well?
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    (Original post by Imperion)
    Silly question but is this thread for maths alone or can FM students use it as well?
    FM as well.
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    (Original post by Imperion)
    Spoiler:
    Show
    Links pl0x :laugh:
    Better not post it here - the TSR police will arrest me. :mob:

    Check your PM soon, I'm looking for the link :lol:
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    (Original post by Ayman!)
    Better not post it here - the TSR police will arrest me. :mob:

    Check your PM soon, I'm looking for the link :lol:
    I wouldn't mind...the links.. You know !
 
 
 
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