*** I also liked (sarcastic) how you used implicit differentiationn which is not even in 3U course for Q13(b)(ii)
*** Q13 (b)(iii) - you assume the reflective property without proving it. I did it a similar way without making that assumption.
I let t=0, t=1 to get the points O and S both of which are part of the locus. I used the distance formula to prove that SQ is a.
My other method is to find the centre S by again letting t=0, t=1. And then finding
x^2 and (y-a)^2 using the substitution t=tan theta/2.
***Also your method for Q12(c) is very ugly/shifty but still gets the same answer. I tend to write
as 1/2 v^2 = 2x+2e^-x/2 + c then evaluate the constant by plugging in v=4, x=0. I know Terry Lee uses that same method sometimes as well.
***Liked your visual methods for Q10
***There was an easier way to Q14(a)(ii)
Note it is a right angle isosceles triangle
i.e. x=-y. Therefore, Vt cos(th) = -1/2gt^2 +Vt sin(th) (t cannot be equal to 0 at D)
Divide by t, make t the subject
then subsitute back in to find x.
Then use trig ratios in right angle triangle. A lot easier.
I like your second method, it is a lot nicer, for Q14(b)(ii)