I will chime back in with on the maths/economics issue.
If your aspiration is to undertake graduate study in economics at a relatively reputable university then you will probably need to write the GRE in maths. I am not sure if this is an absolute necessity for Australian universities (although if you want to do serious graduate work you should consider going overseas) but it certainly is for most American unis and top European ones as well. This tests undergraduate maths. It will extremely difficult to do well if you have to teach all this to yourself. Nothing but a maths major will prepare you fully for that.
In general, you can go from an undergraduate maths major to a lot more graduate fields than the other way around. Same for statistics.
Whilst the UNSW pre-honours program is not stratified as Sydney is, the actual honours year has a great reputation. There is a small cohort (15 or so) and a lot of resources go into it. The bull pen first year subjects effectively subsidise the really top-notch honours year.
What is it you have enjoyed about Extension 2 maths?
If your aspiration is to undertake graduate study in economics at a relatively reputable university then you will probably need to write the GRE in maths. I am not sure if this is an absolute necessity for Australian universities (although if you want to do serious graduate work you should consider going overseas) but it certainly is for most American unis and top European ones as well. This tests undergraduate maths. It will extremely difficult to do well if you have to teach all this to yourself. Nothing but a maths major will prepare you fully for that.
In general, you can go from an undergraduate maths major to a lot more graduate fields than the other way around. Same for statistics.
Whilst the UNSW pre-honours program is not stratified as Sydney is, the actual honours year has a great reputation. There is a small cohort (15 or so) and a lot of resources go into it. The bull pen first year subjects effectively subsidise the really top-notch honours year.
Regarding university mathematics, I would say that an interest and ability to do well in competitions like the UNSW high school maths comp (the one with 6 questions in 3 hours) is probably as good a reflection - perhaps better- of your capacity to enjoy (and succeed) in university mathematics as the HSC is. Sure, first year maths courses are often huge and are pretty much studying to the test like the HSC is, but as you progress further, unless you really enjoy seeing and grappling with proofs and high levels of abstraction, (pure) maths will get the better of you.What were your experiences in university mathematics? Did you enjoy it? Were you particularly strong in mathematics prior to university? And finally, in your perspective, is a major in econometrics or mathematics more beneficial to the further pursuit of economics?
What is it you have enjoyed about Extension 2 maths?