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Yrs 10 & 11: Explanations

posted Oct 1, 2009, 2:20 PM by Eddie Woo   [ updated Oct 1, 2009, 4:41 PM ]
The long-awaited last day of term is here! (I know I've been waiting.) I've saved the 'best' for last: two write-ups where I spend some time explaining new concepts & ideas. These are the most fun and interesting for me to compose, but they also take the longest time. Often, I put them together specifically because they represent me coming to a new and deeper understanding of something I never fully grasped when I learnt it the first time going through school (or university).

The first file is for year 10, and it's a derivation of Viète's formulas for quadratic and cubic equations. These little nuggets give the results for the sum and product of roots for polynomials of any order, and their simplicity is what makes them attractive.

To this day I still haven't found an immediately practical application of this piece of knowledge, but as I say (and think I need to say again soon, since it's been a while): practicality is an exceedingly poor measure of the worthiness of a topic to be studied. Some of the most glorious things in the world have no 'practical' value whatsoever, but by virtue of what they are, they are eminently worthy to be studied. But that's a topic for another expanded post. 8-)

The second file is for year 11, which I've pointed out that I don't teach this year. I've titled it Differentiating 'Unnatural' Exponentials, because it's a derivation of the derivative (seriously!) for exponential functions with arbitrary base. That is, it demonstrates the result for dy/dx when y = ax, and a is a constant (but a ≠ e). I realise this sounds like total nonsense to someone who hasn't learnt about exponentials and the number e yet. Trust me, you'll get there eventually!

And with that, I'm done for the term. Next term is set to be very different in tone to the rest of the year. Year 12s are gone, so there will be a real change in pace; but there are other changes afoot too, and we'll have to wait and see to find out how they'll pan out. Keep your eyes peeled for updates. Have a good break, and I'll see you all in two weeks!
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