**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!

**July 20, 2016**

New draft syllabuses released at http://www.boardofstudies.nsw.edu.au/syllabuses/curriculum-development/senior-years.html

Consultation ends August 31, 2016

**July 12, 2016**

**July 4, 2016**

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

\(\frac{1}{1^{2}}+\frac{1}{2^{2}}+\frac{1}{3^{2}}+\dots=\frac{\pi^2}{6}\)

The original question with 4 parts is at http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2002exams/pdf_doc/mathemat_ext2_02.pdf

Here is the solution to the original question my mojako: http://4unitmaths.com/2002-8a-mojako.pdf

Here is the extension with 4 more parts proving the Basel problem as a pdf file: http://4unitmaths.com/2002-8a-extended.pdf

Here is the solution to the extended parts: http://4unitmaths.com/2002-8a-extended-sol.pdf

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.

F-10: http://www.australiancurriculum.edu.au/download/f10

Senior: http://www.australiancurriculum.edu.au/Download/SeniorSecondary

**February 16, 2016**

New writing briefs for senior maths HSC:

**January 7, 2016**

2^{74207281}-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 http://www.mersenne.org

**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:

http://www.acara.edu.au/verve/_resources/Mathematics_-_Sequence_of_content.pdf

http://www.acara.edu.au/verve/_resources/Mathematics_Sequence_of_achievement.pdf

**December 5, 2015**

**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 http://www.amazon.com/Prime-Numbers-Riemann-Hypothesis-Barry/dp/1107101921/ but is available now from one of the author's own websites as a pdf at http://wstein.org/rh/rh.pdf

**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: http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-ref-sheet.pdf. 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: https://www.youtube.com/watch?v=XxuO5W23Z60

Embed:

Daily Mail article: http://www.dailymail.co.uk/news/article-3304802/Meet-boy-geniuses-developed-math-theorem-calculates-problems-faster-computer-despite-high-school.html

Proof of theorem: http://ijgeometry.com/wp-content/uploads/2015/10/1.pdf

**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: http://hsccoaching.com/documents/35.html

The papers themselves are (or will be) available at http://www.boardofstudies.nsw.edu.au/hsc_exams/2015/

**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: http://news.boardofstudies.nsw.edu.au/index.cfm/2015/10/9/Consultation-on-Senior-Years-English-Mathematics-Science-and-History-syllabuses

**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: http://news.boardofstudies.nsw.edu.au/index.cfm/2015/10/2/Development-of-new-reference-sheet-for-HSC-Mathematics-examinations-from-2016

**October 1, 2015**

El Capitan has been released. Here are instructions for making a bootable usb: http://users.tpg.com.au/nanahcub/elcapitan.html

**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: http://www.scseec.edu.au/site/DefaultSite/filesystem/documents/Communiques%20and%20Media%20Releases/2015%20Communiques/Education%20Council%20Communique%20-%2018%20September%202015.pdf

**July 11, 2015**

International Mathematical Olympiad 2015

**March 7, 2015**

New youtube of Terry Tao:

(link: https://www.youtube.com/watch?v=P3dLcTkJRr0)

**Teaching Resources**

4 unit Syllabus (from boardofstudies server)

2 and 3 unit Syllabus (from boardofstudies server)

Terry Lee's HSC Solutions website

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

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

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

Professional mathematics versus amateur mathematics

2^{74207281}-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 http://www.mersenne.org

Also, on December 25, 2011 the largest known twin primes were found by Timothy D. Winslow. They are 3756801695685x2^{666669}±1 both of which have 200,700 digits.

They are at http://4unitmaths.com/tp1.pdf and http://4unitmaths.com/tp2.pdf.

Summary of the proof of Fermat's Last Theorem

Online video on Fermat's Last Theorem: msri

Bill Pender's Harder 3 unit inservice

English translation of Hilbert's radio address

International Mathematical Olympiads

1916 LC, 1989 HSC and 2001 HSC

Another proof of the irrationality of e

Alternative solution to 2003 HSC Q3(a)(iv)The General Conic and Dandelin Spheres

Proof of the Fundamental Theorem of Algebra

**University Mathematics**

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

Proof of Poincare conjecture - part 1

Proof of Poincare conjecture - part 2

Proof of Poincare conjecture - part 3

The Riemann Hypothesis - Part 1

The Riemann Hypothesis - Part 2

Lagarias Equivalence to the Riemann Hypothesis

Birch and Swinnerton-Dyer conjecture

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.

**Forums**

http://community.boredofstudies.org/14/mathematics-extension-2/

http://www.artofproblemsolving.com/community

**Other websites**

Higher School Certificate Online

The American Mathematical Society

Last modified on July 20, 2016 by

Derek Buchanan

Counter:

Copyleft: Derek Buchanan, 2001