# Search results

1. ### 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...

5. ### 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.
6. ### 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$) symbol before each line after the first line to make the proof valid. However, I'm not sure if the HSC markers would accept it.$
7. ### 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...
8. ### Mathematics Extension 1 Exam Predictions/Thoughts

Depends what you said exactly I think.
9. ### 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)$.$
10. ### My solutions to the 2019 Mathematics Extension 2 Paper

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

I would be very surprised if they penalised you for expressing the answer in degrees.
12. ### 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'$.$
13. ### 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.

17. ### 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?
18. ### Wrong Intended Answer in HSC 2011

For convenience, here's the link to the paper: https://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2011exams/pdf_doc/2011-hsc-exam-mathematics-ext2.pdf. Here are the Sample Answers...
19. ### HSC 2018-2019 MX2 Marathon

$\noindent The solutions to$\tan x + 2 = 0$for$x$between$0^{\circ}$and$360^{\circ}$are indeed$180^{\circ} + \tan^{-1}(-2)$and$360^{\circ} + \tan^{-1}(-2)$.$ $\noindent To see this, note that if we don't restrict$x$, then$\tan x + 2 = 0 \iff \tan x = -2$has a solution$x =...