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Thread: HSC 2017-2018 MX2 Marathon ADVANCED

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    HSC 2017-2018 MX2 Marathon ADVANCED

    Post any questions within the scope and level of Mathematics Extension 2 mainly targeting Q16 difficulty in the HSC.

    Any questions beyond the scope of the HSC syllabus should be posted in the Extracurricular Topics forum:
    http://community.boredofstudies.org/...icular-topics/

    Once a question is posted, it needs to be answered before the next question is raised.

    I encourage all current students in particular to participate in this marathon.

    To get the ball-rolling

    Question:
    Using MX2 methods & complex numbers, find an expression for (degrees)


    Edit 6/3/17: I have moved some of the advanced questions to this forum...
    Last edited by dan964; 10 Oct 2017 at 11:23 AM.
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    HSC 2017 MX2 Marathon ADVANCED

    A nice question
    Attached Images Attached Images
    Last edited by dan964; 6 Mar 2017 at 5:23 PM. Reason: question moved out of normal marathon to here

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by Kingom View Post
    A nice question
    What paper is that from? Looks interesting

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by wu345 View Post
    What paper is that from? Looks interesting
    It's a surprise!

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by Kingom View Post
    A nice question

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by seanieg89 View Post
    IMO Longlist 1988

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    Re: HSC 2017 MX2 Marathon

    Haha that was my suspicion.

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    Re: HSC 2017 MX2 Marathon

    I believe it's accessible to the extension 2 student so i put it on the marathon

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    Supreme Member seanieg89's Avatar
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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by Kingom View Post
    I believe it's accessible to the extension 2 student so i put it on the marathon
    Yeah fair enough, they were a lot easier back in the day.

    Still should probably put questions like it in the advanced thread (Dan only created it today I believe, but for the last couple of years we have usually split the questions into two marathons, one for routine stuff and one for questions at HSC Q16 difficulty or above. As long as it is still within syllabus of course).

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by seanieg89 View Post
    Yeah fair enough, they were a lot easier back in the day.

    Still should probably put questions like it in the advanced thread (Dan only created it today I believe, but for the last couple of years we have usually split the questions into two marathons, one for routine stuff and one for questions at HSC Q16 difficulty or above. As long as it is still within syllabus of course).
    Yeh i wanted to put this in the advanced marathon, but none existed at the time it was posted so

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    Re: HSC 2017 MX2 Marathon ADVANCED

    Quote Originally Posted by dan964 View Post
    Post any questions within the scope and level of Mathematics Extension 2 mainly targeting Q16 difficulty in the HSC.

    Any questions beyond the scope of the HSC syllabus should be posted in the Extracurricular Topics forum:
    http://community.boredofstudies.org/...icular-topics/

    Once a question is posted, it needs to be answered before the next question is raised.

    I encourage all current students in particular to participate in this marathon.

    To get the ball-rolling

    Question:
    Using MX2 methods & complex numbers, find an expression for the cos 36.
    Note that . Consider whose roots are . Thus the roots of are . Note that are the conjugates of respectively.

    By comparison of coefficients for we get:
    and
    These are the sum of roots and product of roots of the quadratic equation; .
    , but . Thus
    Mathematics Extension 2 - Physics - Chemistry - Economics - English Advanced

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    Re: HSC 2017 MX2 Marathon


    Mahan Ghobadi

    Maths Tutor- ESL (80)| 2 Unit maths (96)(2013) | 3 Unit maths (99)| 4 Unit maths(95)| Physics (88)| music1(93)

    Get more answers for your questions, as well as weekly tips and blog posts, from my friends and I at:
    HSC http://bit.ly/HSC-Help
    VCE* http://bit.ly/VCE-Help

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by Mahan1 View Post

    Lagrange multipliers because why not

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

    Quote Originally Posted by Mahan1 View Post

    By inspection, the limit is -∞
    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 ADVANCED







    Last edited by dan964; 1 Apr 2017 at 2:57 PM.
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    Re: HSC 2017 MX2 Marathon ADVANCED

    Quote Originally Posted by dan964 View Post






    For Q1 instead of (n-1) at the top it should just be n-i.



    Last edited by calamebe; 31 Mar 2017 at 9:50 PM.
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    Re: HSC 2017 MX2 Marathon ADVANCED

    fixed sorry.
    calamebe likes this.
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    Re: HSC 2017 MX2 Marathon ADVANCED

    Quote Originally Posted by calamebe View Post
    For Q1 instead of (n-1) at the top it should just be n-i.



    Q2 is correct. Split it into (x+1)(x-1)
    calamebe likes this.
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    Re: HSC 2017 MX2 Marathon ADVANCED

    Quote Originally Posted by frog0101 View Post
    Find the Cartesian coordinates of a complex number that has a modulus of 3 and argument pi/8
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    Re: HSC 2017 MX2 Marathon ADVANCED

    A square pyramid has height exactly half it's base side length, a. Find the volume of the pyramid.
    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 ADVANCED

    Quote Originally Posted by Paradoxica View Post
    A square pyramid has height exactly half it's base side length, a. Find the volume of the pyramid.
    It's just .
    Consider a cube with side length a. If you cut along its diagonals u get 6 identical pyramids with height half the base.
    Paradoxica and pikachu975 like this.

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    Re: HSC 2017 MX2 Marathon ADVANCED

    why can the standard V=1/3Ah be using used
    where A is the area of the base = a^2
    and h = a/2
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    Re: HSC 2017 MX2 Marathon ADVANCED

    Quote Originally Posted by dan964 View Post
    why can the standard V=1/3Ah be using used
    where A is the area of the base = a^2
    and h = a/2
    ewwww formula pleb jkjk

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    Re: HSC 2017 MX2 Marathon ADVANCED

    Find the maximal possible angle that a circle centred at the origin can meet the ellipse x^2/a^2 + y^2/b^2 = 1.

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    Re: HSC 2017 MX2 Marathon ADVANCED

    (The above Q isn't too hard, just something to get this thread rolling again .)

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