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 ; 299 papers

1073 other papers (general, 2 unit, 3 unit)


January 10, 2017

State maths revamp under attack - incoherent, rushed and appalling, say critics of syllabus:

January 1, 2017

Last year the University of New South Wales held a professional development day for teachers pertaining to new topics from the draft syllabus and set up a publicly accessible moodle page with downloadable resources at

December 16, 2016

Version 8.3 of the Australian curriculum was released today.



December 3, 2016

Putnam 2016

October 20, 2016

The draft syllabus isn't good enough and they need to start again:

But I bet they won't.

August 31, 2016

Draft Syllabus Response

July 20, 2016

New draft syllabuses released at

Consultation ends August 31, 2016

July 12, 2016

IMO 2016

July 4, 2016

Question 8a in the 2002 Extension 2 HSC exam can be extended to prove the "Basel problem"


The original question with 4 parts is at

Here is the solution to the original question my mojako:

Here is the extension with 4 more parts proving the Basel problem as a pdf file:

Here is the solution to the extended parts:

Historical note: This was first proposed in 1644 by Pietro Mengoli and then solved by Euler in 1734. But Euler did not use this method. In fact there are several methods by which it can be proved. The method in this HSC exam together with the extension was first used by Augustin Louis Cauchy in 1821 in a book called Cours d'Analyse.

June 30, 2016

Version 8.2 of the Australian curriculum was released today.

February 16, 2016

New writing briefs for senior maths HSC:

January 7, 2016

274207281-1 was discovered on January 7, 2016 to be the largest known prime by Curtis Cooper. It has 22338618 digits which you can get here. More info on this discovery is at

December 16, 2015

Version 8.1 of the Australian curriculum was released today.

It seems though that only the F-10 was really updated for mathematics. The senior seems to still be a mixture of versions 7.5 and 8.0.

There are 2 new documents for F-10 called Sequence of content and Sequence of achievement:

December 5, 2015

2015 Putnam competition

November 9, 2015

Mysterious calculator exercise

November 8, 2015

New book Prime Numbers and the Riemann Hypothesis to be published in hardcover and paperback at but is available now from one of the author's own websites as a pdf at

November 7, 2015

Polynomials questions from past Leaving Certificate papers 1920-1955

November 6, 2015

The new reference sheet has now been published a few days early: This will be used in next year's HSC exams for 2 unit, Ext. 1 and Ext. 2.

November 5, 2015

Schoolboys Ivan Zelich and Xuming Liang make a new theorem called the Liang-Zelich theorem.

Youtube video:


Daily Mail article:

Proof of theorem:

October 26, 2015

Terry Lee has updated his website today to include solutions to the 2015 Ext. 1 and 2 HSC exams which also concluded today:

The papers themselves are (or will be) available at

October 18, 2015

Version 8.0 of the Australian Curriculum was released today.

October 16, 2015

The draft writing briefs are online now a few days early:

General 1 and 2 draft writing brief

2 unit/ ext. 1 and 2 draft writing brief

October 9, 2015

Draft Writing Briefs for new senior syllabuses will be online for consultation beginning on October 19, 2015:

October 2, 2015

A new reference sheet will be published on the BOSTES website on November 9 following the completion of the 2015 HSC which will be used in HSC exams for calculus courses beginning in 2016:

October 1, 2015

El Capitan has been released. Here are instructions for making a bootable usb:

September 18, 2015

During the Education Council meeting today it was announced that an updated version of the F-10 National curriculum will be published in mid-October:

July 11, 2015

International Mathematical Olympiad 2015

March 7, 2015

New youtube of Terry Tao:


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 El Capitan

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

274207281-1 was discovered on January 7, 2016 to be the largest known prime by Curtis Cooper. It has 22338618 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 ; ShareLaTeX

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 10, 2017 by

Derek Buchanan


Copyleft: Derek Buchanan, 2001