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Using your equation, the cubic formula yields \tan10^\circ=\sqrt{{8\sqrt3\over3}\cos130^\circ+3} However, it might be better to say it is a solution to x^3-\sqrt3x^2-3x+{1\over\sqrt3}=0 in which case the cubic formula yields \tan10^\circ={4\sqrt3\over3}\cos260^\circ+{\sqrt3\over3} (noting...

Do they work from my attachments?

The 1999 and 2000 ones are on the resources section. Don't know about the 1998 though. They seem to be working so I don't know what your problem is. Anyway, I've attached them here.

Sampson Wong was in the SMH today: (The support family... maths gold medallist Sampson Wong, 16, with his parents, Cecilia and Jimmy, and his older sister Samantha. Photo: Domino Postiglione) All that effort adds up to a gold medal Heath Gilmore The Sydney Morning Herald, August 24, 2009...

Correct answer to Int. Q30 is 174 (same as Sen. Q29) not 180. Thanks PC for reuploading corrected version. I made a pdf of the solution provided by 3unitz:

Here are Sampson and Andrew with their Golds.

Here is Terry Tao's lecture he gave at the IMO: http://terrytao.files.wordpress.com/2009/07/primes.pdf

Questions 4-6: Question 4. $ Let $ABC$ be a triangle with $AB = AC$ . The angle bisectors of $\angle C AB$ and $\angle AB C$ meet the sides $B C$ and $C A$ at $D$ and $E$ , respectively. Let $K$ be the incentre of triangle $ADC$. Suppose that $\angle B E K = 45^\circ$ . Find all possible...

Ta. Yeah. / not \ I also made a pdf. I'll put Q4-6 up later today.

Here are Questions 1-3. Question 1. $ Let $n$ be a positive integer and let $a_1,a_2,a_3,\ldots,a_k$ $\left( k\ge 2\right)$ be distinct integers in the set $\left\{ 1,2,\ldots,n\right\}$ such that $n$ divides $a_i(a_{i + 1} - 1)$ for $i = 1,2,\ldots,k - 1$. Prove that $n$ does not divide...

The International Mathematical Olympiad 2009 was held on July 15-16 at Jacobs University, Bremen, Germany. Website: http://www.imo2009.de Australian Team: Aaron Chong, Doncaster Secondary College Andrew Elvey Price, Brunswick Secondary College Stacey Law, James Ruse Agricultural High School...

Again, your example y=x⁶ is easy by the successive derivative test. f'(0)=f''(0)=f'''(0)=f''''(0)=f'''''(0)=0 but f''''''(0)=720 > 0 hence (0,0) is a local minimum. Nevertheless I think the point you are trying to make is what if it's more complicated, like a quotient? The...

Quite often the example y=x⁴ is used to show the second derivative test is sufficient but not necessary and fails for this example. However, the successive derivative test still works. f(0)=f'(0)=f''(0)=f'''(0)=0 but f''''(0)=24 > 0 so (0,0) is a local minimum. Likewise the third...

Terry Tao is coming to Australia for a lecture tour. He'll be giving a public lecture "Structure and randomness in the prime numbers" at UNSW in Leighton Hall, Scientia Building on Sept. 16, 6pm. Details: 1-day meetings & lectures : Clay–Mahler lectures, University of NSW : Wed, September...

The new Mathematics Subject Classification 2010 (MSC2010) will be implemented soon. This is an update to MSC2000. I've attached the final version.

And this is from the Chief Examiner of the HSC: The concluding statements for inductions provided by many candidates show that they incorrectly think that a proof by induction is actually an iterative proof, in which you imagine that the recipe should be repeated as many times as necessary in...

jm01, tell your teacher he is wrong. The following is from the HSC exam committee: --------------------------- I would like to comment on the induction part of the question. It has come to my attention that many teachers are training their students to write some form of the following...

No snooping required. the website is www.coroneos.com.au You can order the solutions from this website for 1990-2008

There are past papers at: http://www.angelfire.com/ab7/fourunit http://au.geocities.com/ext2papers http://www.geocities.com/fourunitmaths

Here's a list of 4 unit texts: http://users.tpg.com.au/nanahcub/texts.pdf We can now add to that the new books by Bob Aus called "The Leading Edge HSC Mathematics Extension 2"