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 ; 192 papers

New

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

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 October 8, 2014 Apple released Yosemite Public Beta 5 (also called PB5) today as an update to PB4. The build number is 14A386b. 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. 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 25, 2014 Version 7.1 of the Australian Curriculum was released 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:

3. Open Terminal and type the following commands:

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

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

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

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.

June 23, 2014

Terry Tao has won one of the $3m breakthrough prizes: That's worth more than a Nobel Prize! February 28, 2014 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) 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 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 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 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

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