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$\noindent Expanding the LHS using $\left(1+x\right)^5 = 1 + 5x + 10x^2 + 10x^3 + 5x^4 + x^5$ with $x=\sqrt{3}$, it is $1 + 5 \sqrt{3} + 10\times 3 + 10 \times 3\sqrt{3} + 5 \times 3^2 + 1 \times 3^2 \sqrt{3} = 1 + 5\sqrt{3} + 30 + 30\sqrt{3} + 45 + 9\sqrt{3} = 76 + 44\sqrt{3}$. So the integers...

Yeah it's 3U content (not 2U). It should be a 3U question.

$\noindent Note the angular frequency parameter satisfies $n^2 = 256\Rightarrow n = 16$. Now, clearly the amplitude is $A = 2$ (because we pull the mass down by 2 cm and then just release), so using $v^2 = n^2\left(A^2 -x^2\right)$, the speed at the centre of motion satisfies $v^2 = n^2 A^2$...

How many people doing General Maths plan on doing mathematical things at Uni? One would have thought not many, but it seems quite a lot do. Maybe BOSTES offer Maths General as a subject because they want a "maths" subject for students who don't plan on doing anything mathematical later?

leehuan was probably just joking/jesting.

Re: First Year Uni Calculus Marathon It's probably the first time I've done so for a while. :p

Re: First Year Uni Calculus Marathon 1/3! = 1/6, via Taylor expansion.

Re: HSC 2016 3U Marathon leehuan added a post afterwards, after some discussion on that Q. by others.

Re: HSC 2016 3U Marathon RTP means "required to prove". $\noindent To get from line 4 to line 5, leehuan used the result $ab \leq \frac{a^2+b^2}{2}$. This is true because $\left(a-b\right)^2 \geq 0$, and then expanding and rearranging this gives that result.$

There is (just not in the Games section): http://community.boredofstudies.org/111/lifestyle-interests-social-activities/351741/pokemon-go-thread.html .

$\noindent Let the roots be $\alpha, \alpha, \alpha ^{-1}, \alpha ^{-1}$. From sum of roots: $\alpha + \alpha + \alpha ^{-1} + \alpha ^{-1} = - A \Rightarrow -A = 2 \left(\alpha + \alpha ^{-1}\right) \quad (1)$.$ $\noindent From sum of pairs of roots, $\alpha^2 + 1 + 1 + 1 + 1 + \alpha^{-2} = B...

$\noindent Yes $\textendash$ that exclusion just says that $z\neq 0$, which is clear because $z$ is on the denominator of the given expression.$

Word: SUTHAHARAN. If no two vowels are together, we essentially have: * S * T * H * H * R * N *, where we place the vowels each in one of the "*" spots above. It is easy to see that the configuration will have no two vowels apart if and only if the arrangement is like above. First we arrange...

Maybe BOSTES didn't want to put that formula in twice (one with an absolute value and one without), so decided to put in the absolute value one only (like if you had to choose to put only one, that'd probably be the one to choose).

What do you mean 'puts it out' (haven't got the new Reference Sheet handy)? As in it writes it with absolute value signs? (Edit: OK here's the link to the new Reference Sheet: http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-ref-sheet.pdf .)

Had a look at the HSC's table of Standard Integrals, and what they did for the integral of 1/x was write it as "ln x, x > 0", rather than "ln |x|". (The table can be found at the end of last year's HSC MX2 exam paper, for instance...

Where did it say that in the Syllabus (not saying it didn't, but I had a quick skim through the Integration part of the 4U Syllabus and couldn't see it there. Might've missed it or could be in the 2U/3U Syllabus.)?

It would depend on things like what kind of ATAR you're aiming for.

Re: Why is the ATAR cut off for Medicine so low in UOS compared to other universities Which university are you referring to by "UOS"? (As others have said here, University of Sydney is 99.95 ATAR, so did you mean something else?)

You can go directly to working (just write the question number like "a) ii)" or whatever of course before writing your answer for each question).