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Also question 8 has more than one possible answer. If you assume that z can be neither purely real nor purely imaginary, only one valid answer remains (I think anyway), but it's not the answer they gave. Classic school trial paper :|

Exactly - I'll just clarify further but I think you got it. Because (p-1)! = (p-1)(p-2)...(a+1)(a)(a-1)...(3)(2)(1), which has a factor of a

well first off the question is wrong (p = 1 is a counterexample) but if we be generous and change ‘prime’ to ‘not composite’ then yes SadCeliac is right go by contrapositive: p is composite => p does not divide that thing so p is composite, we can write it as p=ab, where 1<a<p so (p-1)! is a...

Honestly there’s probably more content for advanced than ext 1 and 2 combined. You’ll be fine on that front. The bigger question is how good are you at tackling really hard questions (not hard content, hard questions)? If you aren’t sure, give it a go but make sure you’ve got room to drop it...

As long as you use the same star for m2 and b2, you'll get the same answer. It's a nice fact about logs that log(\frac{1}{x})=-log(x) so that means it works either way.

I guess where I'm not sure is what we're trying to do with a simulation - you may get unlucky and never earn the maximum profit. Are we just trying to see statistically what's most likely?

Look I'm not sure how you'd simulate it, but the maximum profit for one game would just be the profit that you'd earn if you got a 5 or 6 with every roll.

Thank you

Dunno if you still need help on this … if you don’t just ignore but otherwise here’s what I have to say You said: By way of contradiction assume n^2-3 is rational. The problem here is that the question isn’t asking us to prove it’s irrational. It’s asking us to prove it’s a multiple of 4. So...

Completely agree with what everyone’s said. But also you can often improve a lot more than you think. I know people at my school who got Band 6s comfortably in math Extension 1 last year, despite starting off the year with not-so-great marks (can’t talk for physics as I don’t know many peoples...

Thanks everyone for the helpful replies. seems like I’ll be sticking with math and maybe comp sci

Thank you!

Sorry I know there are already so many threads on this topics but I've got a few questions I can't seem to find clear answers to and would appreciate any thoughts, especially from those taking Actuarial Studies or a similar degree For context, I'm a 2023 HSC student studying maths ext 2 (among...