**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!

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

**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: http://4unitmaths.com/nc-y11-12shelved.pdf

**December 8, 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: http://users.tpg.com.au/nanahcub/yosemite.html

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

Project Academy's solutions to the 2 HSC unit paper is also available at http://www.projectacademy.com.au/2014_HSC_Maths2UAdv_Solutions.pdf

Itute.com also have General 2 solutions at http://www.itute.com/wp-content/uploads/2014-nsw-bos-mathematics-general-2-solutions.pdf

**October 12, 2014**

Review of National Curriculum Final Report

**October 8, 2014**

Version 7.2 of the Australian Curriculum was released today:

http://www.australiancurriculum.edu.au/Download/F10 (for F-10)

http://www.australiancurriculum.edu.au/Download/SeniorSecondary (for Senior)

**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 ( https://www.surveymonkey.com/s/bostesstage6 ) (closing date Sept. 21) or via written submission to the Board Inspector, Peter Osland (email: peter.osland@bostes.nsw.edu.au )

Here are the proposed changes in content for the calculus-based courses on page 22 of http://www.boardofstudies.nsw.edu.au/australian-curriculum/pdf_doc/senior-secondary-evaluation-2014-08.pdf

**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:

link: https://www.youtube.com/watch?v=9ZIZumhAiss

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:

http://www.scientificamerican.com/article/with-awards-like-the-breakthrough-prize-who-needs-a-nobel/

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)

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^{57,885,161}-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 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 ; ScribTeX

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/Forum/index.php

**Other websites**

Higher School Certificate Online

The American Mathematical Society

Last modified on December 20, 2014 by

Derek Buchanan

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Copyleft: Derek Buchanan, 2001