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Thread: HSC 2017 MX2 Marathon

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by seanieg89 View Post
    Suppose you have n points on a circle such that no three distinct chords coincide at any single point.

    How many regions do the nC2 chords divide the interior of the circle into?

    (You don't have to provide rigorous proof for this question if you can guess the answer correctly).
    2m where m is the number of chords. (2*nC2??)

    Sorry thats not right, hold on.
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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by frog1944 View Post
    A question posted in the 2016 MX2 marathon by Paradoxica that wasn't answered:
    Paradoxica and frog1944 like this.

  3. #78
    This too shall pass Sy123's Avatar
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    Re: HSC 2017 MX2 Marathon

    Part (b) is a little long and requires good understanding of the problem, so keep that in mind






    ---------------------------------









    ---------------------------------

    ---------------------------------
    Last edited by Sy123; 24 Feb 2017 at 4:49 PM.
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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by seanieg89 View Post
    Suppose you have n points on a circle such that no three distinct chords coincide at any single point.

    How many regions do the nC2 chords divide the interior of the circle into?

    (You don't have to provide rigorous proof for this question if you can guess the answer correctly).
    something along the lines of the sum of three binomial coefficients of even lower argument...

    I'll leave the details to the interested reader...
    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 MX2 Marathon

    Just a reminder this thread is mainly for Q1-15 material, and should be accessible to all Ext 2 students, not just the really talented ones.

    I have moved the Lagrange multiplier & IMO question to the Advanced Marathon thread here...
    HSC 2017 MX2 Marathon ADVANCED

    If you have questions for help not related to questions posted here, it is advisable to post a separate thread rather than posting here in the marathon thread thanks. Although feel free to post a question here of course...
    I have moved some of those also out of this thread.

    here is another question to attempt
    abbotsleigh20034u_q7b.PNG
    Last edited by dan964; 7 Mar 2017 at 12:37 AM.
    2014 HSC - E4 in MX1 (90) / 2015 Gap Year (Youthworks) / 2016-2017 UOW - B. Maths Adv. (done math110, 201, 202, 203, 204)

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  6. #81
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    Re: HSC 2017 MX2 Marathon

    Just did my half yearly today... 30% of my internal mark... Calculating that im getting in the 70%'s
    Why am i still in this course

  7. #82
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    Re: HSC 2017 MX2 Marathon

    current question:
    abbotsleigh20034u_q7b.PNG
    2014 HSC - E4 in MX1 (90) / 2015 Gap Year (Youthworks) / 2016-2017 UOW - B. Maths Adv. (done math110, 201, 202, 203, 204)

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  8. #83
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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by dan964 View Post
    current question:
    abbotsleigh20034u_q7b.PNG
    dat quality

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    Re: HSC 2017 MX2 Marathon




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    Re: HSC 2017 MX2 Marathon

    HSC 2016 Q 10. I spent 5 minutes this morning on this question and couldn't work it out.





    Any tips? Advice? Short cuts? I assume 5 minutes would be too long for a question like this .
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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by davidgoes4wce View Post
    HSC 2016 Q 10. I spent 5 minutes this morning on this question and couldn't work it out.





    Any tips? Advice? Short cuts? I assume 5 minutes would be too long for a question like this .
    Just solve the quadratic-in-disguise

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by davidgoes4wce View Post
    HSC 2016 Q 10. I spent 5 minutes this morning on this question and couldn't work it out.





    Any tips? Advice? Short cuts? I assume 5 minutes would be too long for a question like this .

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by davidgoes4wce View Post
    HSC 2016 Q 10. I spent 5 minutes this morning on this question and couldn't work it out.





    Any tips? Advice? Short cuts? I assume 5 minutes would be too long for a question like this .
    we know that x^2+x+1=0. but this means that x is a cube root of unity ie x^3=1
    therefore x^2016=1 and the solution is 2

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    -insert title here- Paradoxica's Avatar
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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by omegadot View Post


    Is this by any chance just you taking a special case of the AMM Problem 11947 of 2016?
    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 MX2 Marathon

    Quote Originally Posted by omegadot View Post


    Quote Originally Posted by Paradoxica View Post
    Is this by any chance just you taking a special case of the AMM Problem 11947 of 2016?
    Why indeed it is! As asked, the question makes for a very nice complex number question (and a bit of algebra) which is more than doable at the MX2 level.

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    Re: HSC 2017 MX2 Marathon

    Hey guys, I have a question that I have never encountered before in 4U, how would I go about solving this? Thanks!
    CodeCogsEqn.gif

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by si2136 View Post
    Hey guys, I have a question that I have never encountered before in 4U, how would I go about solving this? Thanks!
    CodeCogsEqn.gif

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    Re: HSC 2017 MX2 Marathon

    Just a curious question, is there a a faster way to prove the Recursive Integration Formulae without going through the long process?

  19. #94
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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by si2136 View Post
    Just a curious question, is there a a faster way to prove the Recursive Integration Formulae without going through the long process?
    What's the long process? Integration by parts?

    If you mean integration by parts, then almost all questions involve IBPs, but some can be done by manipulating the integrand.
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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by si2136 View Post
    Just a curious question, is there a a faster way to prove the Recursive Integration Formulae without going through the long process?
    When you are asked to prove a given reduction formula, the efficient way is usually by differentiation.

  21. #96
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    Re: HSC 2017 MX2 Marathon

    Given:

    x+y+z = 3a

    xy + yz + zx = 3b

    Where x,y,z are all real, and ab>0, find the greatest and least possible values of any of x,y,z
    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 MX2 Marathon

    leehuan likes this.
    Sxc avatar made by a sxc person: carrotontheground http://community.boredofstudies.org/...otontheground/

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