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Thread: HSC 2017 MX1 Marathon

  1. #26
    Ancient Orator leehuan's Avatar
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by Drsoccerball View Post
    This is even going beyond the course of MX2... It's evil to leave them wandering...

    Hint: Instead of counting up count the ways you can finish.
    Eh, true I guess.

    You can answer after 7 days if you still want to.
    Quote Originally Posted by pikachu975 View Post
    What about Integrand
    InteGrand probably will leave it alone haha

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    Member jathu123's Avatar
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by leehuan View Post
    This is going well beyond the scope of MX1 now but...





    Drsoccerball and Paradoxica are not allowed to post their solutions


    not 100% sure though
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by jathu123 View Post


    not 100% sure though
    Yep. So the basic idea is which steps can I be on as I take my last step:



    Extra question: Write a recurrence for the amount of ways I can climb n stairs using 1,2,3... or n step(s).

    Should be easy now...

  4. #29
    -insert title here- Paradoxica's Avatar
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by leehuan View Post
    This is going well beyond the scope of MX1 now but...





    Drsoccerball and Paradoxica are not allowed to post their solutions
    I just constructed a diagonal line along the rows of Pascal's Triangle and proceeded to count which cells represent a set of possible paths, then sum them all together. Which is basically what si1236 did.

    No complicated enumeration required.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  5. #30
    -insert title here- Paradoxica's Avatar
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by Drsoccerball View Post
    Yep. So the basic idea is which steps can I be on as I take my last step:



    Extra question: Write a recurrence for the amount of ways I can climb n stairs using 1,2,3... or n step(s).

    Should be easy now...
    Hence, express the general solution as the powers of the roots of the recurrence's characteristic polynomial.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    Re: HSC 2017 MX1 Marathon

    General question. Are you allowed to start on the RHS for Trig Identities? I never have done that before.
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by si2136 View Post
    General question. Are you allowed to start on the RHS for Trig Identities? I never have done that before.
    yes
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    Re: HSC 2017 MX1 Marathon

    Are you allowed to use MX2 techniques in MX1?

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by frog1944 View Post
    Are you allowed to use MX2 techniques in MX1?
    No.
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by frog1944 View Post
    Are you allowed to use MX2 techniques in MX1?
    Yes
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by si2136 View Post
    No.
    Quote Originally Posted by pikachu975 View Post
    Yes
    What?

  12. #37
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by eyeseeyou View Post
    What?
    There's like barely any 4 unit techniques applicable to 3 unit anyway so doesn't matter
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by si2136 View Post
    No.
    Yes you can... But if you do generally the questions become harder.

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by Drsoccerball View Post
    Yes you can... But if you do generally the questions become harder.
    I actually didn't know that o.O
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by pikachu975 View Post


    This took years to type and the answer is probably wrong lol
    I think you used internal division in the ratio 2:1 instead of 1:2.

  16. #41
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by si2136 View Post
    I actually didn't know that o.O
    Yeah the question was about inverses and areas so i thought I could just use Integration by Parts since I knew how to integrate the integral... 3 pages later gave up on the algebra and just went for the way they wanted...

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    Re: HSC 2017 MX1 Marathon

    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  18. #43
    Member jathu123's Avatar
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by Paradoxica View Post


    not sure esp part c
    Last edited by jathu123; 22 Oct 2016 at 9:04 PM.
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by Drsoccerball View Post
    Yep. So the basic idea is which steps can I be on as I take my last step:



    Extra question: Write a recurrence for the amount of ways I can climb n stairs using 1,2,3... or n step(s).

    Should be easy now...

  20. #45
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    Re: HSC 2017 MX1 Marathon

    Last edited by InteGrand; 23 Oct 2016 at 3:42 PM.

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by InteGrand View Post
    P(total) = P(H) + P(TH) + P(TTH) + P(TTTH) + ...
    = p + (1-p)kp + ((1-p)^2)(k^2)p + ((1-p)^3)(k^3)p + ((1-p)^4))(k^4)p + ...
    = p(1/(1-k(1-p)) (as k and (1-p) are less than one, the ratio is less than one and hence this is true)
    = p/(1-k(1-p))

    You can check if k=1 then the chance is 1 which makes sense, as eventually she will toss a heads no matter the probability if it is unchanging, and if k=0 then the probability is p, as she can only win if she tosses a head initially, as if she doesn't she can never win.
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by calamebe View Post
    P(total) = P(H) + P(TH) + P(TTH) + P(TTTH) + ...
    = p + (1-p)kp + ((1-p)^2)(k^2)p + ((1-p)^3)(k^3)p + ((1-p)^4))(k^4)p + ...
    = p(1/(1-k(1-p)) (as k and (1-p) are less than one, the ratio is less than one and hence this is true)
    = p/(1-k(1-p))

    You can check if k=1 then the chance is 1 which makes sense, as eventually she will toss a heads no matter the probability if it is unchanging, and if k=0 then the probability is p, as she can only win if she tosses a head initially, as if she doesn't she can never win.
    Well done! (And good job on testing the answer, a lot of students don't seem to think to do these kinds of checks (maybe because teachers don't appear to emphasise it).)
    calamebe likes this.

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    Re: HSC 2017 MX1 Marathon

    2017
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  24. #49
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by jathu123 View Post
    What's f(x) ?

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by Drsoccerball View Post
    What's f(x) ?
    That part was just a general statement.

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