New South Wales Higher School Certificate Mathematics Extension 2

(Online since January 1, 2001)

Mediocrity is something you can buy. Excellence is something you can download from the internet for free!

Theme song - Spem in alium

Ext. 2 Practice papers: 200 papers ; 160 papers

668 other papers (general, 2 unit, 3 unit)


July 25, 2014


Apple released the OS X 10.10 Yosemite public beta 1 today. It has build number 14A299l. You can get it at

Here is how to make a bootable usb of the Yosemite public beta 1 installer.

Format an 8 GB USB drive which should be called Untitled and formatted as Mac OS Extended (Journaled). The installer should be called Install OS X Yosemite and should be in your Applications folder.

Run this in terminal and wait about 20 minutes:

sudo /Applications/Install\ OS\ X\ Yosemite\ --volume /Volumes/Untitled --applicationpath /Applications/Install\ OS\ X\ Yosemite\ --nointeraction

You can boot up from it by selecting it from the startup manager you get when starting your computer and holding down the option key.

July 18, 2014

Youtube of Alex Gunning talking about the 2014 IMO:


Note there is a mistake in the video. The woman at the start says he is in year 12. He isn't. He is in year 11. The mistake is repeated in the caption.

July 17, 2014

The Age article on Alex Gunning

July 12, 2014

55th IMO Results

An Australian (Alexander Gunning) is one of only 3 out of 560 contestants to get a perfect score in the 55th International Mathematical Olympiad held a few days ago. It is the first time ever that an Australian has got a perfect score! Results are out today.

People's Republic of China had overall country rank 1 with 5 gold medals and 1 silver medal, (which USA also got), but total points were 201 (and USA got 193 and country rank 2).

There were 3 perfect scorers, one of whom was from Australia! (individually ranked equal 1st out of 560):

Alexander Gunning (Australia), Jijang Gao (People's Republic of China), Po-Sheng Wu (Taiwan)

Medal cutoffs: Gold=29, Silver=22, Bronze=16

Results for Australian Team: rank=11 out of 101, total=156 out of 252:

Alexander Gunning: 7+7+7+7+7+7=42=Gold Medal (and perfect score!) (rank=1)

Seyoon Ragavan: 7+2+0+7+1+0=17=Bronze Medal (rank=256)

Mel Shu: 7+7+0+7+2+0=23=Silver Medal (rank=109)

Yang Song: 7+3+0+7+3+0=20=Bronze Medal (rank=200)

Praveen Wilerathna: 7+7+0+7+7+0=28=Silver Medal (rank=50)

Damon Zhong: 7+5+0+7+7+0=26=Silver Medal (rank=83)

July 9, 2014

International Mathematical Olympiad 2014

July 1, 2014

Mavericks 10.9.4 build 13E28 was released today:

Delta update:

Combo update:

A full installer is also on the mac app store, which you will need if you want to make a bootable usb for 10.9.4.

More info on mavericks is at

June 23, 2014

Terry Tao has won one of the $3m breakthrough prizes:

That's worth more than a Nobel Prize!

February 28, 2014

Response to Inquiry into the Australian Curriculum

February 18, 2014

Version 6.0 of the Australian Curriculum was released today: (for F-10) (for Senior)

January 10, 2014

Today the government announced a review of the national curriculum.

Teaching Resources

4 unit Syllabus (from boardofstudies server)

2 and 3 unit Syllabus (from boardofstudies server)

Syllabus Issues

Terry Lee's HSC Solutions website

Youtube video for finding the Median and First and Third Quartiles on the CASIO fx-82AU PLUS II calculator

Youtube video for the new VERIFY function on the CASIO fx-82AU PLUS II calculator

OS X Mavericks

Vectors summary ; Matrices summary

Alternative solution to James Ruse 2011 Trial Question 8b

Solution to 2010 Mathematics Extension 2 HSC exam Question 8

Link Between 1995 and 2010 HSC Exams Leads To Generalised Wallis Product (preprint) - another version appeared in MANSW's Reflections, Vol. 36, No. 4, 2011, pp. 22-23

Parabola Magazine Online

Barbarians at the Helm, by Derek Buchanan

How NOT to find the surface area of revolution, by Derek Buchanan

Johan Wastlund's Elementary Proof of the Wallis Product Formula for pi

Yet another proof of the irrationality of e


Three Unit Notes 1

Three Unit Notes 2

Alf van der Poorten's 28 online Number Theory lectures (28 mp4's)

Professional mathematics versus amateur mathematics

Sixty 4 unit lectures

257,885,161-1 was discovered on January 25, 2013 to be the largest known prime by Curtis Cooper. It has 17,425,170 digits which you can get here. More info on this discovery is at

Also, on December 25, 2011 the largest known twin primes were found by Timothy D. Winslow. They are 3756801695685x26666691 both of which have 200,700 digits.

They are at and

Summary of the proof of Fermat's Last Theorem

Online videos on Fermat's Last Theorem: youtube ; msri

Bill Pender's Harder 3 unit inservice


Wiles' online lecture

Clay Meeting online

Tate's online lecture

Atiyah's online lecture

David Hilbert's radio address

English translation of Hilbert's radio address

SMH HSC Survival Guide 2009


International Mathematical Olympiads

AIS Maths Focus Day summary

1916 LC, 1989 HSC and 2001 HSC

Another proof of the irrationality of e


Alternative solution to 2003 HSC Q3(a)(iv)

Have your pi and e it too.

The General Conic and Dandelin Spheres

The Cubic Formula

The Quartic Formula

Proof of the Fundamental Theorem of Algebra

University Mathematics

The Putnam Competition

Harvard University's notes


More history

Euclid's elements

Proof of Fermat's Last Theorem

Proof of the Taniyama-Shimura-Weil Conjecture

Beal Prize for $1,000,000 for proving (or disproving) the Beal Conjecture, i.e., that the only solutions to the equation \(A^x + B^{\ y} = C^{\ z}\), when \(A\), \(B\), \(C\), are positive integers, and \(x\), \(y\) and \(z\) are positive integers greater than 2, are those in which \(A\), \(B\) and \(C\) have a common factor

Poincare conjecture

Proof of Poincare conjecture - part 1

Proof of Poincare conjecture - part 2

Proof of Poincare conjecture - part 3

Perelman on YouTube

The Riemann Hypothesis - Part 1

The Riemann Hypothesis - Part 2

Lagarias Equivalence to the Riemann Hypothesis

Birch and Swinnerton-Dyer conjecture

Hodge conjecture

Navier-Stokes equations

Yang-Mills theory - part 1

Yang-Mills theory - part 2

P vs NP

The ABC Conjecture and Mochizuki's proposed proof

Online LaTeX editors

Too many philistines are using Word. They should stop being philistines and start using LaTeX.

For web browsers (nothing needs to be installed): MonkeyTeX ; Verbosus ; ScribTeX

iPad app: TeX Touch. Files created in this app can be compiled via the TeX Cloud.


Other websites

Fields medallists

Terry Tao on YouTube

Number Theory Website

Clay Mathematical Institute

Enoch Lau

Wolfram Alpha

Integrals online

Higher School Certificate Online

The American Mathematical Society

Last modified on July 25, 2014 by

Derek Buchanan


Copyleft: Derek Buchanan, 2001