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many books use this kind of abbreviations, which looks fine to me as long as you don't get a fussy teacher marking your assessments, or in the HSC I'd use the abbreviations in practice ,but remember what the full version is and use that in real exams

you may be able to get away with shortening the theorem, but how brief is too brief ? I think it's too hard to say, so I'd probably write down the whole thing

what would you get when you integrate both sides ?

it's an even function ,i.e. f(alpha)=f(-alpha) if alpha is a real zero, so is -alpha there is only one real solution -----> then it must be x=0, substitue and we get k^2-1=0 , k= 1 or -1 these two values of k would give x^4 - x^2=0 and x^4 + 3x^2=0 respectively the 1st eqn has 3 real...

but it only accounts for 1/5 of your aggregate, which is then converted to ATAR

+1

i think OP thought your method was 'complicated' , probably due to this?

rep >> everything else btw, is there any particular reason that you're using that partial differentiation 'd' , instead of just dy/dx kind of d?

repped

yeah but how do we know that the derivative of arctany= 1/(1+y^2)?

how did you get da/dy= 1/(1+y^2) ?

nice

you get sec^2 when you differentiate tan hence you get tan when you integrate sec^2

I think this is actually quite sad because not only would they lose the ability to speak another language(and/or appreciating their cultural heritage), nor would they be able to communicate to their parents well enough when they grow up (just guessing, I could be totally wrong about this part )...

these may help? http://en.wikipedia.org/wiki/Rydberg_formula http://en.wikipedia.org/wiki/Quantum_number besides, they must be in your lecture notes somewhere

you could probably borrow one from school library or your teacher, and see how you find it then decide whether or not it's gonna be a good investment

yeah, since it can shown the line xx0/a^2+yy0/b^2=1 (where x0 and y0 are constants) pass through both P (since x1x0/a^2+y1y0/b^2=1) and Q (since x2x0/a^2+y2y0/b^2=1) and two points determine a unique line

???

^this is how I'd do it, and it may not be totally correct

assuming you know how to derive : t(1/2)= ln(2)/lambda , from the N(t)=N0 * exp(-lambda*t) and N(t(1/2))= half of N0 and the rate of dacay(disintegrations per second) is proportional to the number of nuclei, by computing dN/dt i.e. Activity= lambda*N so you can get lambda from the 1st eqn...