I have start tutoring a student in Pre-Calculus. Since I don't have the text I am largely guessing what I'll have to be teaching. I find myself deriving equations that I haven't thought about in years. At about 3 AM this morning I found my self coming up with an alternate derivation of the quadratic equation.
Last week I wasted a couple of hours deriving trig relations for added angles. I don't look any of this up because I keep telling the student that while I am not sure he will find the equations for translated parabolas of any use in later life, figuring out the logic behind the procedures is valuable exercise for developing analytical thinking, and I need to get some of that exercise for myself.
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