North Shore may use teachers, but most of them are NOT GOOD, and the material is shithouse (maths is ok i suppose). good uni students who have experience of the hsc are in many cases better.
for 1), other reasons why NaOH is not a good primary standard:
it has a low molecular mass, so weighing errors will be amplified
it reacts with carbon dioxide in the air:
NaOH + CO2 ---> Na2CO3 + H2O
for the first one, split sinⁿx into sinⁿֿ¹x.sinx and then apply integration by parts.
similarly split secⁿx into secⁿֿ²x and sec^2x and do likewise.
wat kfunk just did :)
for the locus,
y = a(p^2 + q^2)/2
x = a(p+q)
now 3x^2 = 3a(p^2 + q^2 + 2pq)
from the result in b, 2pq = -(p^2 + q^2)/3
so 3x^2 = 3a(p^2 + q^2-(p^2 + q^2)/3)
= 2/3*3*a(p^2 + q^2)
= 2a(p^2 + q^2)
= 4ay