A selection of past HSC papers.
Tuesday, 29 April 2014
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.
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.
Sunday, 13 April 2014
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!
Wednesday, 2 April 2014
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!
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!
Saturday, 15 March 2014
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!
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!
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