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!

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Ext. 2 Practice papers: 200 papers ; 192 papers

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



New

November 18, 2014

Apple released OS X Yosemite 10.10.1 update today at http://support.apple.com/kb/DL1779 which has build number 14B25. A full installer is also available on the mac app store and the bootable usb and dvd methods for 10.10 build 14A389 also work for this too.

Updating the recovery partition via USB installer

Just updating 10.10 to 10.10.1 with the delta update via apple's software update website, or the mac app store will not update the yosemite recovery partition.

But if you make a bootable usb installer for 10.10.1 with the full installer from the mac app store, you can use it to update the recovery partition too. Just run it over 10.10 or even 10.10.1 if you already have it installed, and the recovery partition will be updated to a 10.10.1 version.

Just beware that if you previously reverted a core storage logical volume created by a previous yosemite installer, this method will convert it back to core storage, so another revert will be necessary if you want to be able to edit your partitions again.

So here is the reverting method again if you deem it necessary:

Run these 2 commands in terminal.

diskutil cs list

and then

diskutil coreStorage revert lvUUID

where lvUUID is the last lvUUID reported by the previous Terminal command.

Then restart for everything to get back to normal after you have run these commands in Terminal.

November 12, 2014

Apple released Yosemite 10.10.1 build 14B23 to public beta testers today.

November 5, 2014

Apple released Yosemite 10.10.1 build 14B17 to public beta testers today.

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

October 17, 2014

Apple released Yosemite today on the mac app store. It has build number 14A389.

Here is how to make a bootable usb of the Yosemite installer.

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

Run this in terminal and wait about 20 minutes:

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

You can boot up from it by selecting it from the startup manager you get when starting your computer and holding down the option key.

If you prefer to make a bootable dvd, you can do it this way:

After downloading the full Yosemite installer app from the Mac App Store, run these 14 commands in Terminal to create a Yosemite.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 Yosemite.

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

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

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

hdiutil attach /tmp/Yosemite.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/

cp -rp /Volumes/install_app/BaseSystem.chunklist /Volumes/install_build

cp -rp /Volumes/install_app/BaseSystem.dmg /Volumes/install_build

hdiutil detach /Volumes/install_app

hdiutil detach /Volumes/install_build

hdiutil resize -size `hdiutil resize -limits /tmp/Yosemite.sparseimage | tail -n 1 | awk '{ print $1 }'`b /tmp/Yosemite.sparseimage

hdiutil convert /tmp/Yosemite.sparseimage -format UDTO -o /tmp/Yosemite

rm /tmp/Yosemite.sparseimage

mv /tmp/Yosemite.cdr ~/Desktop/Yosemite.iso

If the yosemite installation creates a core storage logical volume you can revert it to get partitions back to normal by running these 2 commands in terminal.

diskutil cs list

and then

diskutil coreStorage revert lvUUID

where lvUUID is the last lvUUID reported by the previous Terminal command.

Then restart for everything to get back to normal after you have run these commands in Terminal.

October 14, 2014

Apple released Yosemite Public Beta 6 (also called PB6) today as an update to PB5. The build number is 14A388b.

October 12, 2014

Review of National Curriculum Final Report

October 8, 2014

Apple released Yosemite Public Beta 5 (also called PB5) today as an update to PB4. The build number is 14A386b.

Also, 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)

October 1, 2014

Apple released Yosemite Public Beta 4 (also called PB4) today as an update to PB3, but also as a full installer. The build number is 14A379b. The commands to make bootable usbs or dvds from the full installer are the same as for PB1, PB2 and PB3.

September 27, 2014

http://www.angelfire.com/ab7/fourunit is up again, but the mirror created yesterday will be kept online because angelfire downtime has happened before and is likely to occur again in the future.

September 26, 2014

http://www.angelfire.com/ab7/fourunit seems to be down at the moment, so a mirror site has been created with all the same resources that were there yesterday at http://4unitmaths.com/angelfiremirror.html except that 164 trials have been bundled together as 2 zip files instead of individual pdf files. Some files on the other sites also had to be moved so some of the links have changed there too.

September 18, 2014

Apple released OS X Mavericks 10.9.5 build 13F34 today.

Delta: http://support.apple.com/kb/DL1761

Combo: http://support.apple.com/kb/DL1760

A full installer is also available on the mac app store which you can use to make a bootable usb with the method explained at http://users.tpg.com.au/nanahcub/mavericks.html

September 16, 2014

Apple released Yosemite Public Beta 3 (also called PB3) today as an update to PB2, but also as a full installer. The build number is 14A361p. The commands to make bootable usbs or dvds from the full installer are the same as for PB1 and PB2.

August 29, 2014

Apple released Mavericks 10.9.5 build 13F25 to public beta testers today.

August 22, 2014

Apple released Yosemite Public Beta 2 (also called PB2) today as an update to PB1, but also as a full installer. The build number is 14A329r. The commands to make bootable usbs or dvds from the full installer are the same as for PB1.

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.

August 10, 2014

Yosemite DVD

To make a bootable DVD of Yosemite:

After downloading the full Yosemite Public Beta installer app from the Mac App Store, run these 14 commands in Terminal to create a Yosemite.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 Yosemite.

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

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

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

hdiutil attach /tmp/Yosemite.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/

cp -rp /Volumes/install_app/BaseSystem.chunklist /Volumes/install_build

cp -rp /Volumes/install_app/BaseSystem.dmg /Volumes/install_build

hdiutil detach /Volumes/install_app

hdiutil detach /Volumes/install_build

hdiutil resize -size `hdiutil resize -limits /tmp/Yosemite.sparseimage | tail -n 1 | awk '{ print $1 }'`b /tmp/Yosemite.sparseimage

hdiutil convert /tmp/Yosemite.sparseimage -format UDTO -o /tmp/Yosemite

rm /tmp/Yosemite.sparseimage

mv /tmp/Yosemite.cdr ~/Desktop/Yosemite.iso

This may not create a recovery partition. If not you can make one by first reverting core storage logical volume (if one is created) and then follow the steps to make the recovery partition:

To revert the logical volume:

Run these 2 commands in terminal.

diskutil cs list

and then

diskutil coreStorage revert lvUUID

where lvUUID is the last lvUUID reported by the previous Terminal command.

Then restart for everything to get back to normal after you have run these commands in Terminal.

To make the recovery partition:

1. Download the Lion Recovery Update from http://support.apple.com/kb/dl1464. Make sure it is in your downloads folder. If you still happen to have the yosemite installer app somewhere, right click on it and click Show Package Contents. Go to Contents/SharedSupport/. Copy the InstallESD.dmg file into your Downloads folder. If you don't still have the installer, you can get it again by redownloading from your purchases tab in your mac app store.

2. Download and decompress the file recovery.sh.zip from http://4unitmaths.com/recovery.sh.zip and move recovery.sh into your Downloads folder if it's not there already.

3. Open Terminal and type the following commands:

chmod +x ~/Downloads/recovery.sh

sudo ~/Downloads/recovery.sh

4. Wait a few minutes for it to finish and return back to a prompt. Reboot with holding down the option key to test your 10.10 recovery partition.

July 25, 2014

Yosemite USB

Apple released the OS X 10.10 Yosemite public beta 1 today. It has build number 14A299l. You can get it at https://appleseed.apple.com/sp/betaprogram/

Here is how to make a bootable usb of the Yosemite public beta 1 installer.

Format an 8 GB USB drive which should be called Untitled and formatted as Mac OS Extended (Journaled). The installer should be called Install OS X Yosemite Beta.app and should be in your Applications folder.

Run this in terminal and wait about 20 minutes:

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

You can boot up from it by selecting it from the startup manager you get when starting your computer and holding down the option key.

If the yosemite installation creates a core storage logical volume you can revert it to get partitions back to normal by running these 2 commands in terminal.

diskutil cs list

and then

diskutil coreStorage revert lvUUID

where lvUUID is the last lvUUID reported by the previous Terminal command.

Then restart for everything to get back to normal after you have run these commands in Terminal.

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

July 1, 2014

Mavericks 10.9.4 build 13E28 was released today:

Delta update: http://support.apple.com/kb/DL1754

Combo update: http://support.apple.com/kb/DL1755

A full installer is also on the mac app store, which you will need if you want to make a bootable usb for 10.9.4.

More info on mavericks is at http://users.tpg.com.au/nanahcub/mavericks.html

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)

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 Mavericks

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

DON'T BAN YOUTUBE!

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

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 http://www.mersenne.org

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 http://4unitmaths.com/tp1.pdf and http://4unitmaths.com/tp2.pdf.

Summary of the proof of Fermat's Last Theorem

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

Bill Pender's Harder 3 unit inservice

pisquaredonsix.pdf

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

Assignments

International Mathematical Olympiads

AIS Maths Focus Day summary

1916 LC, 1989 HSC and 2001 HSC

Another proof of the irrationality of e

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

History

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): MonkeyTeX ; Verbosus ; ScribTeX

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

Forums

http://community.boredofstudies.org/forumdisplay.php?f=14

http://www.artofproblemsolving.com/Forum/index.php

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 November 18, 2014 by

Derek Buchanan

drbuchanan@tpg.com.au

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Copyleft: Derek Buchanan, 2001