2009 Extension 2 HSC, Question 6(b)

Some of the later questions in the Extension paper allow for some cross-fertilisation between topics.  This question links some of the basics from complex numbers and polynomials.

2010 Extension 2 HSC - Ordinary Differential Equations

It appears that over the last few years, there is a trend towards ordinary differential equations (ode's) in the Extension 2 HSC.  They could probably be considered as an extension on the two and three unit problems involving growth and decay.

Here is the 2010 HSC, Question 5

2010 Extension 2 HSC - A question on Banked Tracks

2012 Extension 2 HSC - Question 16(b)

Harder 3U - 1994 HSC, Question 8

2013 James Ruse Extension 2 Trial

2013 Normanhurst Boys High Extension 2 Trial

2013 Penrith High School 4U Trial

2013 St George Girls High School

2014 Extension II Assessment III with Marking Scheme

Here is the last assessment, with the marking scheme included.

2009 HSC, Question 4(b)

Another question on the conical pendulum, this time with a minor variation that has it constrained to the surface of a cone.  The message is still the same - set your question up clearly, finding components in the horizontal  and vertical (or in some cases, radially and tangentially), the use Newton's Second Law. 
If you can successfully find the components, most of the subsequent parts following relatively easily.

2014 Sydney Morning Herald HSC Study Guide

As they have been doing for a good number of years, the Sydney Morning Herald have again published their HSC Study Guide.  Here is the link for this years guide.  It contains a lot of very useful advice.

http://www.smh.com.au/national/education/hsc-study-guide-2014--mathematics-20140519-38kf4.html

2006 HSC - The Conical Pendulum

Another question on the conical pendulum.  Notice how they are similar?

1999 HSC - The Conical Pendulum

Questions on conical pendulums are quite common in the HSC, albeit with minor variations.  Most start with having you finding components of the forces acting on the bob, so this is something you need to be able to do.

Circular Motion

As we continue our discussion of Mechanics, here are some notes on circular motion. 
Just remember that the centripetal acceleration is always directed towards the centre.

Resisted Motion Worksheet

Here are some resisted motion questions.  I am not sure where they came from, as they were hand written.  If the original owner sees these here and contacts me, I will acknowledge them on the blog!

2012 HSC - Resisted Motion

Resisted motion is a relatively common feature of HSC mechanics questions, be they in a straight line, or projectile motion questions.  The important point is to use Newton's Second Law, $$\sum F=m\ddot{x}$$  Make sure you always define you directions at the start!

Extension II Mechanics Syllabus

Here is an interactive form for you to check off each part of the syllabus as we work through mechanics.
There seems to be a lot here, but don't let it put you off!  Most the of mechanics hinges on the ability to write components  of vectors and make sure the signs are correct.

Past HSC Questions

A selection of past HSC papers.

A Cautionary Tale from Volumes

Quite often in an Extension 2 volumes question, the student will be asked to use a particular method to complete the problem, viz. shells or discs.

Every so often, a question will appear that gives a student complete liberty to choose the method of solution.
In such cases, be careful!

While some of the integration in the presentation below can be streamlined, it is still interesting to see how each method differs, and the length of time it would take to solve the problem under exam conditions.