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 ; 225 papers

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


January 22, 2015

Beta build 14C106a for OS X 10.10.2 was released today to public beta testers.

January 8, 2015

Beta build 14C94b for OS X 10.10.2 has just been released to public beta testers.

January 5, 2015

Version 7.3 of the Australian Curriculum was released today: (for F-10) (for Senior)

December 20, 2014

Beta build 14C81h for OS X 10.10.2 has just been released to public beta testers.

December 13, 2014

National curriculum for Years 11 and 12 is now shelved. Here is The Australian article:

December 8, 2014

Putnam Competition 2014

November 18, 2014

Apple released OS X Yosemite 10.10.1 update for macs today. With airplay mirroring, we can have Extend Desktop which lets you use full screen apps on one screen whilst working on something different on another. This is very useful for classrooms where for example a class is working on some questions on an interactive whiteboard connected to an apple tv, and at the same time, the teacher could be recording a roll online without interrupting the student activity.

Here is my yosemite page with more details on it:

If on the other hand you have a pc, you could get Airparrot instead which does a similar thing - but the major difference is apple's airplay mirroring runs off the processor, whereas airparrot is a less efficient software-based version of airplay mirroring.

October 28, 2014

Terry Lee has published his solutions to the 2014 Extension 1 and 2 HSC papers at his website

Project Academy's solutions to the 2 HSC unit paper is also available at also have General 2 solutions at

October 12, 2014

Review of National Curriculum Final Report

October 8, 2014

Version 7.2 of the Australian Curriculum was released today.

August 13, 2014

The 2014 Fields medals have been announced today.

The recipients are Artur Avila, Manjul Bhargava, Martin Hairer, Maryam Mirzakhani.

Maryam Mirzakhani is also the first woman to ever receive it.

August 11, 2014

Proposed changes to the NSW Calculus-based courses

BOSTES has announced proposed changes to the NSW Calculus-based courses today and are calling for feedback via the online survey ( ) (closing date Sept. 21) or via written submission to the Board Inspector, Peter Osland (email: )

Here are the proposed changes in content for the calculus-based courses on page 22 of

Preliminary Mathematics 2 Unit

Approximately six topics focusing on areas of Mathematics such as real numbers, algebra, functions, graphs, geometry, trigonometry, differential calculus, sequences and series, and descriptive statistics.

A number of modelling topics focusing on applications of Mathematics from other topics in the Preliminary course and utilising techniques from other topics in the course and earlier courses, such as applications involving real functions and applications of series to finance.

HSC Mathematics 2 Unit

Approximately six topics focusing on areas of Mathematics such as differential calculus, integral calculus, probability, trigonometry, exponential and logarithmic functions, descriptive statistics, and random variables.

A number of modelling topics focusing on applications of Mathematics from other topics in the HSC course, and utilising techniques from other topics in the course and earlier courses, such as applications involving probability and finance, applications to the natural environment.

Preliminary Mathematics Extension 1

Approximately six topics focusing on areas of Mathematics such as circle geometry, further algebra, polynomials, functions, graphs, trigonometry, series, elementary difference equations, random variables, and the normal distribution.

HSC Mathematics Extension 1

Approximately six topics focusing on areas of Mathematics such as mathematical induction, binomial theorem, methods and applications of integration, further trigonometry, inverse functions and the inverse trigonometric functions, and further applications of calculus.

Mathematics Extension 2

Approximately eight topics focusing on areas of Mathematics such as further inequalities, complex numbers, polynomials, functions, graphs, vectors, integration techniques, volumes, modelling with functions and derivatives, mechanics, difference equations, and statistical inference.

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

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

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 Yosemite

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

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 video on Fermat's Last Theorem: 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): 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 January 22, 2015 by

Derek Buchanan


Copyleft: Derek Buchanan, 2001