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People of different race have difference in their genetic makeup too. Does this justify giving different legal rights to couples of differing race, or interracial couples?

Re: HSC 2017 MX2 Marathon ADVANCED Haha not even bashy, once you spot you can parallel project / affine transform the circle to an ellipse, there are no calculations to do, you just need to prove that the cevians meeting the incircle contact points are concurrent. This is within the scope of...

Re: HSC 2017 MX2 Marathon ADVANCED Bump to move the unanswered question to the front. This one is a bit harder (in a certain sense) than the previous problem, unless there is a shortcut other than my intended method. Good to see some thread activity!

Re: HSC 2017-2018 MX2 Marathon ADVANCED My meaning was that "angle of contact" means "acute angle of contact", otherwise the two circles that meet the ellipse tangentially give you the maximal angle (pi) and the problem is boring. Your new answer seems correct with absolute values. My...

Re: HSC 2017 MX2 Marathon ADVANCED I don't think that is quite correct, but it is close. (Perhaps an erroneous trig manipulation?) As a test, if b\approx 1, then we expect the maximal angle of contact to be close to 0, because the circle and the ellipse are basically identical. Also, the...

Hadn't come across the Demidovich book before omegadot, thanks for that! (Good to have lots of sources to mine for assignment/exam questions for my calculus students haha. Some of these older texts are great for this purpose.)

No worries at all man, hope they are helpful for your particular interests :).

So this answer assumes that you are just interested in getting better at integration itself, rather than HSC integration in particular. If you are already on top of the integrals in past papers and the standard HSC textbooks, you will be absolutely fine for HSC integration. If you want to...

Re: HSC 2017 MX2 Marathon ADVANCED Also, a new problem in the meantime of a different flavour: An ellipse is inscribed in the triangle ABC, with points of contact X,Y,Z on the triangle sides opposite A,B,C respectively. Prove that AX,BY,CZ are concurrent. (That is, prove that there exists a...

Re: HSC 2017 MX2 Marathon ADVANCED Honestly can't remember, but will check this afternoon. (It's just a simple calculation of course.)

Just a couple of minor comments on Q16 to the examiners: 1. You introduce the notion of a prime, but none of its properties besides its definition. In several steps of the proof, we prove that integers are indivisible by p essentially because they are the product of integers indivisible by p...

Haha good choice of Q16 :).

Re: HSC 2017 MX2 Marathon This is what I had in mind. On the topic of a more geometric solution, I suspect there is a way to kill it quicker using nonsyllabus techniques (inversive geometry perhaps), but it is not immediately apparent to me, I might have a crack later this week.

Ah well, I'll be in Sydney at least a couple more times before I leave Aus.

Someone post/PM the paper plz :)

Had to leave Sydney because of a meeting unfortunately, still look forward to seeing the paper :).

Every 10 minutes, the water volume is halved. After one hour (=60mins), you have halved the volume 6 times. So the answer is (1/2)^6=1/64.

I am in Sydney that weekend for a wedding, might come by.

Can you post some examples of the sort of questions you are struggling with and your current thought process with these questions? This would make it much easier to help :).

Here is an interesting problem. If you are not comfortable with higher dimensional spaces, replace "affine hyperplane" with "line" (not necessarily through the origin), and fix n=2 in the below. Suppose we have finitely many affine hyperplanes \mathcal{H}_1,\mathcal{H}_2,\ldots,\mathcal{H}_m...