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itute solutions, but I think their 16c is wrong: https://www.itute.com/wp-content/uploads/2023-NSW-ESA-Mathematics-Extension-2-Solutions.pdf

itute solutions: https://www.itute.com/wp-content/uploads/2023-NSW-ESA-Mathematics-Extension-2-Solutions.pdf

This might help for 16c too. It's a bit neater than Xu's.

\text{We can't have }m=1\text{ because then }\theta=\pi \textstyle\text{ and the question had }\frac{\pi}{2}<\theta<\pi I like your desmos though. I don't think it's as hard as has been reported in the media. I just reduces down to an exercise in inequalities.

You can just say the gradient is greater than 1 like this:

I made a workaround for the 10000 character limit. I reduced post #7 to 100 papers and moved all the English to post #11 I will use post #11 as a continuation of post #7 in case I get more 2023 trials

Sydney Grammar English 2023 Paper 1 is here: https://community.boredofstudies.org/resources/sydney-grammar-english-advanced-paper-1-2023.20366/ Maybe too late for class of '23 but not for class of '24. post #7 is now so big I can't fit any more in there. It got to 104. To put this Sydney...

Sydney Grammar English Advanced Paper 1 2023

One might wonder why on earth would one want to do 15aiii like that. Well it actually removes integration entirely as well as algebraic gymnastics required to relate it back to Jn from 15ai. It turns it purely into a manipulation of factorials. And as Kennedy didn't say, we don't do it...

Here are alternative solutions to 15aii and 15aiii using beta and gamma functions

These are essentially the same diagram rotated. So you can do it a similar way - but with just 1 diagram Fix the solitary student for which there are 5 possiblilities. Then there are 3! ways for the teachers and 4! ways for the other students Answer is therefore 3!4!x5=3!5! .......... B

Roch solutions are here: https://community.boredofstudies.org/threads/mathematics-extension-1-predictions-thoughts.405500/post-7515646 These ones are typed up

roch solutions

Here is a pdf of mindyourdecisions youtube so can see it in 9 seconds instead of 9 minutes

MindYourDecisions made a youtube of 16c solution

Check this out dude https://community.boredofstudies.org/threads/mathematics-advanced-predictions-thoughts.405498/post-7511884 In there you will find solutions by 2xq and 187

Here is a modification of Âmîňńñ's method which is a bit easier (again "do it not because it's hard but because it's easy") \text{Area}(\triangle OAB)=|\text{Area}(\triangle OAC)+\text{Area}(\text{trapezium }ACDB)-\text{Area}(\triangle OBD)|...

Here is yet another otherwise method by Âmîňńñ

Well in maths I like what Kennedy didn’t say. He didn’t say “We don’t do it because it hard. We do it because it’s easy”

Here is yet another "otherwise" approach. \text{Area of triangle spanned by } \overrightarrow{OA},\overrightarrow{OB}\text{ is} \textstyle\frac{1}{2}|\overrightarrow{OA}\times\overrightarrow{OB}|=\frac{1}{2}\left|\begin{vmatrix}\bold i&\bold j&\bold...