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1. Best Lcm calculator for students

You can also easily find LCM and GCD on a calculator that doesn't have a specific button for it, like so: .
2. Seriously - why the hell is English compulsory?

Couldn't they just as easily make (say) Maths the compulsory subject that ATAR is based on (if there is a need to have one common subject)? In other words, saying we need a common subject doesn't explain why English (or any particular subject) needs to be the compulsory one.
3. Nice proof

$\noindent It also works for non-integer but \textbf{constant} multiples of$x$, e.g.$ \begin{align*} \frac{d}{dx}(\pi x) &= \frac{d}{dx}(\underbrace{x + x + x + \cdots + x}_{\pi \text{ times}}) \\ &= \underbrace{ \frac{d}{dx}(x) + \frac{d}{dx}(x) + \frac{d}{dx}(x) + \cdots +...
4. How do you know when to use u-substitution for integration and what u is? (example included)

$\noindent$\int f(\sin x)\, d(\sin x)$essentially just means$\int f(u)\, du$where$u=\sin x$. If you don't like using$d(\sin x)$, just write it using a$u$-substitution, integrate with respect to$u$, and then write the answer in terms of$x$.$ $\noindent For example, to find$\int e^{\sin...

8. HSC 2019 NSW School Ranking

The ranking really should be based on ATAR; maybe the Sydney Morning Herald doesn't get access to the ATAR scores, so doesn't rank based on that.
9. Do they allow you to use “reversing the step” in the HSC? (Nature of proof)

$\noindent You could in theory add the$\color{blue}\Leftrightarrow$(or even$\color{blue}\Leftarrow$) symbol before each line after the first line to make the proof valid. However, I'm not sure if the HSC markers would accept it.$
10. pigeon hole principle help!

You can show that if there are 7 stamps placed, then there must be a row of 3 stamps as follows: Suppose 7 stamps are placed, then consider the "blank" squares (squares that don't have a stamp in them). There are 2 blank squares (because there are 7 stamps placed in 9 squares). Since there are...
11. Mathematics Extension 1 Exam Predictions/Thoughts

Depends what you said exactly I think.
12. Mathematics Extension 1 Exam Predictions/Thoughts

$\noindent Note that it is not generally true that if$\cos A = \cos B$, then$\cos \left(\frac{\pi }{2}-A\right) = \cos\left(\frac{\pi}{2}-B\right)$.$
13. My solutions to the 2019 Mathematics Extension 2 Paper

$\noinent Do you mean whether you needed to express your answer in radians? I would be very surprised if they penalised you for expressing the answer in degrees.$
14. Maths Extension 2 predictions/thoughts?

I would be very surprised if they penalised you for expressing the answer in degrees.
15. Help on Past Paper questions

$\noindent As long as you can show that$\alpha_{k}$is a root for all$k =1,\ldots, m$and can explain why the$\alpha_{k}$are all different (i.e. if$k\neq j$, then$\alpha_{k} \neq \alpha_{j}$), then you are done, no need to use$p'$.$
16. Help on Past Paper questions

Q7(b)(i) is a special case of the rational root theorem. For a proof of this, you can see https://en.wikipedia.org/wiki/Rational_root_theorem#Proofs.

20. What course in which uni do most Ruse graduates go to?

Is that for a specific university, or altogether? And is the limit only for James Ruse, or do all schools have such a limit?