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The solution considers x<0 and x>0 to ensure that the constant value is the same as the function is not continuous. It doesn't imply you need to consider these cases separately for an alternate proof. If you look at other proofs of tan(arccosx) they don't consider the x<0 case because its...

where x<0 y=arccosx has pi/2<y<pi therefore f(x)=tany<0 which matches with g(x). Does this case really need to be considered? x<0 is accounted for its just misleading that an acute angle is drawn.

This is true from looking at the sine / cosine graph. I think it should also be true whether the particle initially moving left or if B is to the left of O.

yeah it works for ii) Probably use a different variable to replace y like theta or something for clarity.

Usually the best approach is to ignore that it's flawed. \int_1^2 \frac{\ln x^2+2}{(x \ln x-1)^2}dx This is a question I found in the Ascham paper, its clearly flawed once you get it negative answer but then its a bit harder to realise in the exam that its undefined rather than you just made...

that sucks man, your parents sound like assholes. hope you do well either way

If you want to prepare for year 12 in the break I'd just start on the year 12 content, whatever your first task is gonna be on. Skim through the textbook to learn it then go through trial papers from thsc on that topic. That's what I did anyway. For extension, combinatorics is not revisited at...

how would you find the volume if it wasn't restricted by y=x?

Maybe I'm missing something but that solution does not seem to be correct. (tany)^2-y^2 should be correct

If you look at the syllabus it doesn't mention equations of planes anywhere. So no, it won't appear in the HSC if that's what you mean.

if you're solving for cos(a) then it should be 4 roots, its degree 4 for a polynomial where x=cosa but if you're solving for alpha it should be different

I guess I need to revise algebraic inequalities :( stuff like that is very hard to see if you haven't done something similar. I mean that was the only thing I couldn't do so its not that bad. Do you also have q11d) answer? My thing is probably right but the wording (of the question) is kinda weird.

you go to ruse right? did anyone actually get this in the test?

notes and resources

(a^3+1)(b^3+1)(c^3+1) \geq (\frac{ab+bc+ca+1}{2})^3 I found this question in the JRHS 2023 paper that was upload here recently. I skipped it when I did the practise test, but when I went over it again I still couldn't get it. I asked my teacher and she hasn't gotten it as of yet. Could anyone...

well if you prove first then yea they couldn't mark you down for it

I was the dude, cool solution but ofc its outside the syllabus. I saw 2sqrt(5) in my solution so I just thought it would be correct without considering any logic before posting.

pick c=-1/2n , this is clearly larger than -1 as n>=2, on RHS the n cancels out so its just 1-1/2=1/2

can you send them to me as well? Thanks

I just wrote questions on onenote and had the answers on another page. highlight the ones you keep getting wrong in red. I have tried the notion slip box thing but I don't like it, idk why. For specific notes I use word, I prefer it over google docs. For random notes / unstructured notes...