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.

Volume Syllabus Form

2010 HSC - Volumes

A volumes question from the 1020 HSC.

2014 John Paul College Half Yearly

Here it is! The 2014 John Paul College Extension 2 Half Yearly paper, with solutions and the marking scheme!

2005 Extension 2 HSC Volumes Question

The 2005 Extension 2 HSC contains a nice volume by cylindrical shells question.
What makes it even more interesting is the resulting answer.  The volume is finite.  All well and good, but this is a variation of the famous question often seen in a multi-variable calculus course, known as Gabriel's Trumpet  or the Infinite Paint Can.  Such a shape would have a finite volume, but an infinite surface area.  It wouldn't be able to hold enought paint to paint the outside of the can!

2011 HSC Integration Questions

The 2011 HSC has some nice integration questions;  They start out fairly basic in question 1, progressing to a good one in Question 7.
Both of these questions are included here for completeness, but don't worry too much about Question 7 - it contains a property of integrals we haven't studied yet.  That being said, it won't hurt to have a look at it!

100 Integrals from Coroneos

One of the good 4 unit books around is the one by Jim Coroneos.  It was published years ago, and still contains some really good questions.  In particular, at the end of the integration chapter, there are 100 integrals.  If you can do these, then you are well on your way to a good understanding.
I've simply re-typeset them, and you can get them below.

Partial Fractions

Partial fractions plays a major role in the theory of integration, and is examined in all HSC papers.  You should be able to identify the way to decompose your function, but there has been a trend over the years to give you the decomposition and ask you to find the missing numbers.  The second part usually involves the integration.

Here are two questions on partial fractions from past HSC papers.

Reduction Formulae

As we move into the integration topic, one application of integration by parts is to reduction (or recurrence) formulae.  The two presentations are from past HSC papers.

It should also be noted that while most reduction formulae are completed using integration by parts, there are some that are achieved through use of the Pythagorean Identities...I'll post some more on this later!

2001 Trial HSC - International Grammar

Below is question 4 from the 2001 International Grammar Trial HSC. It has some good questions on polynomials.

A nice question from the latter stages of the Extension 2 paper.It shows how seamlessly complex numbers and polynomials go together!

Polynomials Outline

Betty & John's Journey Into Complex Numbers

Another little gem, written in a similar vein to children's books you may have used when you were learning to read.

Betty & John's Journey Into Complex Numbers

Complex Numbers Video

I came across this on You Tube over the break.  Whilst he does provide a brief discussion to complex numbers, I thought it was quite clever the way he interacted with himself! A nice little way to ease yourselves back into 2014!

 (This self-interaction has echoes of some fantastic science fiction time travel stories!)