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!