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  1. C

    HSC 2013 MX2 Marathon (archive)

    Re: HSC 2013 4U Marathon Maybe you can use the fact that |z|^2 = z zbar...
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    HSC 2013 MX2 Marathon (archive)

    Re: HSC 2013 4U Marathon Long time no see. Out of the closet?
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    Bad cohort

    Apparently Bio is all memorising and can be picked up very easily later if needed.
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    HSC 2013 MX2 Marathon (archive)

    Re: HSC 2013 4U Marathon Are you using LaTeX?
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    HSC 2013 MX2 Marathon (archive)

    Re: HSC 2013 4U Marathon There's another way to do this problem using mappings in complex analysis. It's WAY more elegant. EDIT: Here is my sketch solution: Let 'c' be the complex number representing centre of the circle. Then the equation of the circle is |z-c| = |c| (since the circle...
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    HSC 2013 MX2 Marathon (archive)

    Re: HSC 2013 4U Marathon I think an 'elegant' approach to this is setting one of the points to 0, finding a condition and then using a change of coordinates.
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    HSC 2013 MX2 Marathon (archive)

    Re: HSC 2013 4U Marathon Yeah. Typo haha. And I think I fixed the formatting now.
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    HSC 2013 MX2 Marathon (archive)

    Re: HSC 2013 4U Marathon In most cases yes. But for my example, geometrically speaking, |z-i| + |z+i| is the sum of the distances from any point z to the points i and -i. So the minimum value its minimum value will be 2. So, if I'm correct, then the locus of |z-i| + |z+i| = 2 will be the...
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    HSC 2013 MX2 Marathon (archive)

    Re: HSC 2013 4U Marathon If I'm not mistaken, it is not an elllipse, but a line...
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    HSC 2013 MX2 Marathon (archive)

    Re: HSC 2013 4U Marathon Spiral!!! :P
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    HSC 2013 MX2 Marathon (archive)

    Re: HSC 2013 4U Marathon Find the Cartesian equation of the locus for all points z such that |z+i|+|z-i| = 2. Hint: Think before performing "mindless algebra".
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    Induction Question-types

    3U inequality induction questions are alright. Most of the time you "fudge" the answer to the next step and then justify it in the previous step. There are 4 main types of induction: 1. Summation 2. Divisibility 3. Inequality 4. Miscellaneous (mostly 4U)
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    Deduce questions

    Yes they are. They're basically the range of the sin and cos functions.
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    BOS MX2 Trials discussion thread.

    I think MathType would've been way slower for me :|
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    BOS MX2 Trials discussion thread.

    Carrot, you should try and learn LaTeX. I believe the HSC paper is written in LaTeX as well (using a package that changes the default font to something that looks like Times New Roman - it isn't exactly that though, since that exact font is patented or something...)
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    Record of completing Q1-Q4 of any HSC trial

    I remember for my actual Ext 1 HSC trial the exam started 8:55am and when I had finished Q1 the time was 9:00am, and I got full marks for Q1.
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    Multiple Choice questions

    Nice, but some of the questions seem a bit too long for a MC question.
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    Cool Things.

    Lol, yeah that is cool. There's two ways of actually doing that. Method 1: Use the fact that sin z = [e^(iz)-e^(-iz)]/(2i) and solve the resultant quadratic Method 2: Use sin(x+iy)=sinx cosh y + i cosx sinh y. But this method only works if the imaginary or real part is zero.
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    HSC 2012-14 MX2 Integration Marathon (archive)

    Re: MX2 Integration Marathon Lol, wallis product... nice :P
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    HSC 2012-14 MX2 Integration Marathon (archive)

    Re: MX2 Integration Marathon Haha, complex analysis is really really nice. How's Peter Brown? Gotta love how he personifies maths :P
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