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It would be serious overkill to remove thousands of trials from the internet just because of that one paper!

Sharing trials has been around a long time - even before the internet - and even before the HSC. Even back in the 1950s and 1960s Coroneos was sharing leaving certificate trials from Fort Street and Homebush Boys'. Internet just made it easier to do. The focus of the article was coaching...

It is not really necessary to use equations of line segments, but in that format we may proceed thusly: \text{Line segment }RS:\vec r_1=\overrightarrow{OR}+\lambda\overrightarrow{RS},\lambda\in[0,1] \text{At midpoint of }RS,\ \vec r_1=\textstyle\frac{1}{2}\vec a+\frac{1}{2}(\frac{1}{2}\vec...

First consider the MIF Yr 12 Ext 1 Example 7 pages 445-455 Now we can do this: \text{Let }M_1=\text{midpoint of }RS,\ M_2=\text{midpoint of }PQ\text{ and }M_3=\text{midpoint of }TU \text{Then the bimedians }RS,PQ\text{ and }TU\text{ of the tetrahedron }OABC\text{ are concurrent \text{and...

Watching Einstein and the Bomb now. A very unkind review is on imdb but I think it is undeserving. It seems to be quite good.

Here is a more efficient solution to 1. \begin{aligned}(1+\cos\alpha+i\sin\alpha)^k+(1+\cos\alpha-i\sin\alpha)^k&=(1+e^{i\alpha})^k+(1+e^{-i\alpha})^k\\ &=\textstyle\sum_{j=0}^k{k\choose j}(e^{i\alpha j}+e^{-i\alpha j})\\ &=\textstyle\sum_{j=0}^k{k\choose j}(e^{i\alpha...

Here is a more efficient method to solve 3a. \text{If }T_n\text{ is the }n\text{-th Chebychev polynomial of the first kind so that} T_n(\cos\theta)=\cos(n\theta)\text{ then using the }{}_2F_1\text{ hypergeometric we have that} T_n(x)=\textstyle{}_2F_1(-n,n;\frac{1}{2};\frac{1-x}{2}) \text{and...

The AMC past papers are available for free download at https://shop.amt.edu.au/collections/amc-past-papers/products/amc-past-papers-pdf and the new ones usually come out mid-January the following year. For some reason the 2023 ones are not there yet. There is a Thailand dude Dr. Chatawut...

2023 answer key attached

16b can be done backwards without any integration whatsoever. The question involved beta functions and expected integration methods to be used instead of properties of beta functions because such properties are not in the syllabus. The question can however be done in reverse order by use of...

Integrals aside, at 80 Spivak broke his hip and died in 2020.

One can improve upon Spivak's solution by combining the 2 substitutions: \text{Let }u=\textstyle\left(\frac{x^2-1}{x^2+1}\right)^2.\text{ Then }du=\frac{8x(x^2-1)}{(x^2+1)^3}\ \!dx Hence \begin{aligned}\textstyle\int\frac{x^2-1}{x^2+1}\cdot\frac{1}{\sqrt{1+x^4}}\...

The one I put there is Michael Spivak's own solution. It comes from the Combined Answer Book For Calculus Third and Fourth Editions - Chapter 19 Q8v. The Calculus book and Combined Answer Book are both available as ebooks.

Of course there is:

So apart from the proof chapters in textbooks and past paper questions, what other resources might be useful for proofs? 24 bilibili videos on proofs: https://www.bilibili.com/video/BV1ig411a7kd . This is The Great Courses course Prove It: The Art of Mathematical Argument If you are not...

Still not 100% sure, but I was told that an audio recording will probably be made available afterwards for those unable to attend.

I found out it is at the same place as last year, but not whether the recordings will be video/audio only. Last year it was audio only and views were expressed that it would have been better to do videos. UTS - Guthrie Theatre Building 6, 702 Harris Street Ultimo 9am-10:30am: Extension 2...

So in the 2023 Ext 1 HSC Q14ci it says "or otherwise" So would you say the following gets 3 marks? It is 100% correct by the way: \text{Area of triangle spanned by } \overrightarrow{OA},\overrightarrow{OB}\text{ is}...

You can do c too like how liamkk112 used complementary angles in d. \begin{aligned}\textstyle\cos\frac{\pi}{12}\cdot\cos\frac{5\pi}{12}&=\textstyle\cos\frac{\pi}{12}\sin(\frac{\pi}{2}-\frac{5\pi}{12})\\ &=\textstyle\cos\frac{\pi}{12}\sin\frac{\pi}{12}\\...

https://www.msn.com/en-au/money/markets/a-13-year-old-has-managed-to-beat-tetris-up-until-recently-the-feat-was-thought-impossible-for-a-human/ar-AA1mqCvl good explanatory video here: actual video by blue scuti: which you might want to start at the last few minutes to watch him get the kill...