Recent content by InteGrand

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.
14. BoS Maths Trials 2019

Why is it obviously 42C9? $\noindent This answer follows from noting that we need to insert at least one 0 between each 1. If there are$K1$'s and$N-K0$'s, there are$K-1$gaps between$1$'s, so after putting one$0$in each gap, there are now$N-K-(K-1)=N-2K+10\$'s left to place...
15. BoS Maths Trials 2019

I got 42C9 using the method I posted above, so I assumed there was a simpler method. For the equivalence between the method your teacher used and the original question, it is as follows: The bit string of length 50 corresponds to your choice of whether you pick each number from 1-50 or not. A...