Basically the difference, as pointed out, is in the Pure Maths
section
In fact, H1 Maths Stats section may be harder in some years than
H2 Maths
One example: For H1, there is a lot of explanation type of
questions , like explain what is the meaning of unbiased estimator
of population variance (the full one is if A is an estimator of
variance of population B, A is an unbiased estimator if E(A) equals
to sigma squared) (????? to me as a H2 student as we do more
calculation and less explanation generally in A levels - exception
2012 H2 Maths Paper).
For the issue of B3 in A maths, I am a person in Sec 3 my A
maths is F9, after a lot of pushing I finally managed to get an A1
for my O levels, however, my prelims in school for H2 maths is an A
thankfully. Hope my experience can tell you that A maths, although
absolutely important as a stepping stone, but is not all for H2
maths. Topics that you must master from A maths are Partial
fractions by CUR (As you won't have time to expand all and compare
coefficients), differentiation and integration as well as maybe
indices, surds and logarithms. Recently the ability to prove trigo
identities is key as recent A level papers (e.g. 2011 P1 on
Mathematical Induction and 2012 P1 last question part (iv)) and
also your sine / cosine rule (in E maths)
Most if not all courses in Uni requires H2 maths exceptions are
law, FASS as well as business , education (arts), sports science -
NTU and etc so decide carefully ...