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Are you sick and tired of testing either side of the point, when verifying inflections? Do you remember that there's a second derivative test for classifying turning points, which is usually faster than testing either side of the point? Well there's also a faster method for verifying...

You're not dumb! Here's another way to explain the solution to your problem. Since you've spent some time trying to understand my previous solution, I think this time you will find this one easier to understand. Consider the convex polygon...

Thanks for that A l. Those mantras are precisely what the HSC Exam committee are objecting to. They would prefer it to be concluded simply with "Hence the statement is true for all positive integers n≥1, by induction". Some teachers however, insist that it be done the way...

That's right. Some teachers have stated their opposition to the HSC Exam Committee's stance. I am more sympatetic to their cause. An explanation of a proof is not the same as a proof. They were likewise pleased with my Darth Vader comment.

The contentious issue is whether or not to include the mantra in the proof itself. It's fine as an aid to explain the proof. But the mantra isn't actually part of the proof itself. It is this explicit distinction which was the substance of my Darth Vader comment above. I am pleased that your...

I certainly have. I have already put a link to my solutions to the 2005 HSC exam in the biki (which contains the Darth Vader comment) However, I have chosen NOT to edit Slide Rule's contribution, because it now leads to open discussion (hopefully, non-abusive).

On the new boredofstudies wiki (the biki), the following comment appeared today, regarding what to do at the end of an induction: 4) You've done all the hard work. Now you must make a summary paragraph to explain it. These vary from person to person, but something to the effect of "Thus, if...

My link seems to work now but Oakhill_Phreak's still doesn't.

Don't buy any book. They are all rubbish. My website is better: www.fourunitmaths.cjb.net and it's all free.

Yes they do. I solved the problem in 1 line using hyperbolic tangent: I bet you $50 that wasn't in your crummy out-of-date book!

And if you do as the syllabus says and actually solve those equations, you get

I get paid to do it.

That link doesn't work anymore. <a href="http://www4.tpgi.com.au/nanahcub/oakhill2004.pdf">Click here instead</a>.

Aren't these papers Tony van Ravenstein's from http://www.geocities.com/mathematicsplus/resources.html ?

I made a website for 4 unit. It's www.fourunitmaths.cjb.net

It's up at http://www.boredofstudies.org/mirror/4u/cath2004.pdf

I'd say you have to do really, really, really, REALLY well in 4-unit to match a decent 4-unit mark. lol

No. That link doesn't work. It's actually at http://www.boredofstudies.org/courses/maths/4u/1124324074_2004_Mathematics_Extension_2_Trial_Paper_CSSA.pdf

Html code is OK for some small mathematical expressions, but for big ones it's much better to use latex. The nature of the Extension 2 forums are such that big ones are often needed. So clearly there is a need for a latex renderer on the Extension 2 forum. It's great to see there's a latex...

Here's a question on circle geometry using complex numbers: Given any 3 non-collinear points, there is 1 and only 1 circle through those points. You can prove it by proving that for any 3 non-collinear complex numbers z₁, z₂, z₃, the locus of points in the...