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I'd have to disagree with buchanan. Even for those who can do every question, having the answers is very important in finding silly mistakes (which can often occur in similar places) or knowing where you have to be more rigourous or less rigorous in your proofs. And for those who can't do...

This is probably a bit late for most people but this page has all the 4u hsc papers going back to 1967 (as well as catholic back to 1982 and plenty of trials) so that should suffice for anyone who has run out of papers to do. http://au.geocities.com/ext2papers/

Check in the resources sections for some of them. (I think back a few years til about 2002). Here are 99 and 01.

Just stay at High - its a better school than ruse anyway ;)

In answer to buchanan's question, we did do the AMC (along with nz, malaysia and singapore) on the thursday afternoon after the second day of the IMO. I (along with a few other aussies) turned up about 10 minutes late to the test cos we were out shopping in Hanoi.

I went yesterday (well friday) and it was unallocated. I dont think they'll be moving to allocated seating any time soon.

The photos are a bit unnecessary i reckon ;).

Just as additional information, the Australian team will be officially announced on the 21st of June in Canberra. For more information specifically about Australia-related involvement in the IMO see the Australian Maths Trust website at http://www.amt.canberra.edu.au/

I'm quite sure its impossible to find an exact solution to that equation with elementary functions (that is exponential, logarithm, trig & inverse trig, algebraic.

Happy Feet's question is quite nice use the cosine rule and the area of the triangle with sine thingamy. We get: RTP: a^2 + b^2 + a^2 + b^2 - 2abcosC >= 2*rt(3)*absinC RTP: a^2 + b^2 >= abcosC + rt(3)*absinC RTP: a^2 + b^2 >= ab(cosC + rt(3)*sinC) but we know by AM-GM a^2 +...

Undalay, I don't want to sound elitist anything (lets face high isn't all that good at sport either compared to the GPS) but I don't think the GPS would be looking for another school to join, let alone a public school. Most of the schools already look down on High because we're public and the...

I never knew I had such a reputation. I am honoured (sincerely - I don't want to come off as too much of an arrogant prick). And I accept your apology. I would have to agree with simonloo's suggestion that Ruse is a better school than Fort Street in most respects. Academically I would...

Way to destroy the lovely argument we had going Stone Monkey, yet ironically in your chastising of me for being "snarky", "wanton" and "offensive", you seem to have committed the same sins. Now to answer your two questions of me (I will take the bait) - I attend Sydney Boys High School...

Oh excellent. Just clarifying the bold bit: 5 actually has degree 0 (just like how the constant polynomial has degree 0) Possibly one way to think about this is that 5a^3/b could be written a^3/b + a^3/b + a^3/b + a^3/b + a^3/b. and now its clear that each term has degree 2. I don't have...

If you can't work out which school she goes to when all it takes is one click then obviously you're not going to have much chance when it comes to the Physics Olympiad. Anyway - she's achieved far more than you ever have (and most likely more than you will) so you really shouldn't be talking...

Don't worry about it all kagrawal. These sort of questions require vry different sort of thinking to those that you would get in 3u. And the mathematics required to solve this problem (modular arithmetic) is completely unneccessary for the 3u (or any nsw hsc) syllabus. I don't think theres...

Umm - this is quite tricky to understand and even harder to explain over a forum but i think that if i just gave you the factorisation that would be quite useless so i will try to continue explaining. lets start of with something easier first to explain the factor theorem. let f(n) = n^2 -...

I don't see that as working because this is only really valid when the exponents are a specific set of numbers. These questions are very different to the 3u questions where you asked to prove the divisibility by induction and they require far stronger techniques. And kagrawal - where did u...

This is quite tricky - its especially hard to show a motivation for finding the solution but heres some ideas on how i got the factorisation. Notice firstly that c is special variable in a sense that the expression is symmetric in a and b (ie you can swap them around and get exactly the same...

I'm guessing that this is from the Polya Enrichment Series? (sounds like one of those questions) So with this question you have to use modular arithmetic and also notice the prime factorisation of 174 = 2*3*29 so basically the problem reduces to three sub problems of proving the expression...