New South Wales Higher School Certificate Mathematics Extension 2

(Online since January 1, 2001)

Theme song - Spem in alium

Ext. 2 Practice papers: 200 papers ; 158 papers

New

November 5, 2013

The new CASIO fx 82AU PLUS II calculator has new functions to find the first and third quartiles, median and also a new VERIFY mode. New videos are available on youtube on how to use these which was made possible by use of the new calculator emulator version 4:

VERIFY:

Median and first and third quartiles:

October 23, 2013

Apple has released Mavericks to the public today for free at the Mac App Store. It is a good improvement on Mountain Lion because with airplay mirroring, we can now 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.

But there is one slight complication in the installation. Previously with Lion and Mountain Lion you could make a bootable USB by restoring the InstallESD.dmg to the USB via Disk Utilities. This does not work with Mavericks.

Instead one should proceed this way:

Your 8 GB USB drive should be called Untitled and formatted as Mac OS Extended (Journaled). The installer should be called Install OS X Mavericks.app and should be in your Applications folder.

sudo /Applications/Install\ OS\ X\ Mavericks.app/Contents/Resources/createinstallmedia --volume /Volumes/Untitled --applicationpath /Applications/Install\ OS\ X\ Mavericks.app --nointeraction

You should see something like this:

Erasing Disk: 0%... 10%... 20%... 100%...
Copying installer files to disk...
Copy complete.
Making disk bootable...
Copying boot files...
Copy complete.
Done.

You can then boot up from the USB by holding down the option key, then install Mavericks from the USB.

Note that this will also install a recovery partition.

But some people prefer a DVD installer instead of a USB.

If you want such a DVD, then after downloading the Install OS X Mavericks.app file from the Mac App Store, run these 12 commands in Terminal to create a Mavericks.iso file and then burn it to a dual layer DVD with Disk Utility. You may then boot up from it by holding the option key down and then install mavericks. This will not install a recovery partition. To do that, uncompress and run the script file https://dl.dropboxusercontent.com/u/13872235/Musings/Recovery%20Partition%20Creator%203.7.zip

hdiutil attach /Applications/Install\ OS\ X\ Mavericks.app/Contents/SharedSupport/InstallESD.dmg -noverify -nobrowse -mountpoint /Volumes/install_app

hdiutil convert /Volumes/install_app/BaseSystem.dmg -format UDSP -o /tmp/Mavericks

hdiutil resize -size 8g /tmp/Mavericks.sparseimage

hdiutil attach /tmp/Mavericks.sparseimage -noverify -nobrowse -mountpoint /Volumes/install_build

rm /Volumes/install_build/System/Installation/Packages

cp -rp /Volumes/install_app/Packages /Volumes/install_build/System/Installation/

hdiutil detach /Volumes/install_app

hdiutil detach /Volumes/install_build

hdiutil resize -size hdiutil resize -limits /tmp/Mavericks.sparseimage | tail -n 1 | awk '{ print $1 }'b /tmp/Mavericks.sparseimage hdiutil convert /tmp/Mavericks.sparseimage -format UDTO -o /tmp/Mavericks rm /tmp/Mavericks.sparseimage mv /tmp/Mavericks.cdr ~/Desktop/Mavericks.iso September 30, 2013 September 21, 2013 25 trials from 2013 available for 2 unit, 3 unit and 4 unit at http://users.tpg.com.au/nanahcub/otherpapers.html (10 for 2 unit, 7 for 3 unit, 8 for 4 unit) August 5, 2013 Version 5.1 of the Australian Curriculum released at http://www.australiancurriculum.edu.au July 24, 2013 July 16, 2013 Kenneth Wiltshire argues in The Australian newspaper that "the national school curriculum is no longer national, with states opting out of many aspects; the content of the curriculum itself is poor and patchy and has been condemned by experts in just about every discipline.": June 3, 2013 The Beal Prize has been increased to$1,000,000: http://www.ams.org/news?news_id=1910.

This is 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

January 25, 2013

Today, 257,885,161-1 was discovered to be the largest known prime by Curtis Cooper.

It has 17,425,170 digits which you can get here

December 1, 2012

Teaching Resources

4 unit Syllabus (from boardofstudies server)

2 and 3 unit Syllabus (from boardofstudies server)

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

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

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

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 http://www.mersenne.org

Also, on December 25, 2011 the largest known twin primes were found by Timothy D. Winslow. They are 3756801695685x2666669±1 both of which have 200,700 digits.

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

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

Wiles' online lecture

Clay Meeting online

Tate's online lecture

Atiyah's online lecture

2004hsc8bsol.pdf

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

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

Android phone app: VerbTeX_v3.0.3.apk

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

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Other websites

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