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Yeah I would love to see something like this in the HSC this year. Without the hint to multiply by e^nt (this might be taking it too far though), I think something similar could be a really nice, challenging last question, much better than something like the geo question from last year.

I would laugh if they did something insane like 2015 q16 c of the BOS trial. Mean mark 1%.

I'm willing to bet it will be geometrical apps of calculus. There hasn't been one of those since 2015.

The equation in y doesn't need an integrating factor, its just seperable, but when you subsitute v + nx back into it you get dx/dt + nx = y0exp(-nt), which does need an integrating factor.

Here is the question: I remembered it slightly wrong, it basically involves making a substitution of y=v + nx to make it a first order seperable equation and then solving the remaining first order differential equation in x using an integrating factor, which it basically gives to you. I guess...

I do kind of want to do the BOS trial this year, but I am unfortunately outside of Sydney so it is a hassle to go up to do it. The past papers I have done from it have been quite a good challenge though (I think I've done 2018, 2017, 2015).

Oh yeah I forgot about mechanics and volumes lol. Volumes is fun but my problem with it is that almost every question is the same. When there is a hard one though its really good. Mechanics is also fun but I generally only like the circular motion bit, the reaisted motion is literally the same...

Yeah conics is mostly garbage, although there have been a few decent questions, such as the 2000 one near the end of the paper (7b iirc), as well as the 2005 one, but even that was convoluted, it just required more mathematical reasoning than algebra. I honestly think the nicest topic in 4u is...

Lol completely forgot about that. What a ridiculous question. It wasn't even difficult, just a standard de moivrre's theorem identity, but god it took ages just because of all the algebra. 2018 in general had a lot of really stupid convoluted questions.

Yeah thats probably true. I personally enjoy the algebraic manipulations, I find the problem solving aspect quite interesting but yeah they aren't very good mathematically. When you have stupid stuff like the geometry question last year though it wouldn't be surprising for the last question to...

I think we could possibly have an integral similar to one of the ones we see in the integration marathons here, but that may be too hard for most 4u students. 2014 one was hilarious.

I = \int_\pi^{3\pi/2}\frac{\sin x}{\sqrt{1+2\sin x\cos x}}\,dx =\int_\pi^{3\pi/2}\frac{\sin x}{\sqrt{\sin^2 x +2\sin x\cos x + \cos^2 x}}\,dx =\int_\pi^{3\pi/2}\frac{\sin x}{\pm \left( \sin x + \cos x \right)}\,dx \frac{\sin x}{\sqrt{1 + \sin 2x}} < 0 \: \text{for} \: \pi < x < 3\pi/2 \text{...

Again, my scanner cropped a bit of the solutions, pretty much just dus and dxs. These were really good questions though

\int_{\frac{\pi}{6}}^{\frac{2019\pi}{2}}\frac{\sin x+\ln\left(x^{x\cos x}\right)}{x^{1+\sin x}}dx =\int_{\frac{\pi}{6}}^{\frac{2019\pi}{2}}\frac{\sin x+\ln\left(e^{x\cos x\ln x}\right)}{xe^{\sin x\ln x}}dx =\int_{\frac{\pi}{6}}^{\frac{2019\pi}{2}}\frac{\sin x+x\cos x\ln x}{xe^{\sin x\ln x}}dx...

God, \int{\frac{u^2}{1+u^4}} is a trek to integrate (Sorry for the sides cropped off, my scanner actually sucks, pretty much only the dus were cropped on the right, and at the bottom I was just saying that the square root of 3+2√2 was 1+√2)

People should also post their chem trials here, so we all have more practice papers for the new syllabus (I'd post mine but it is independent, which I believe is not allowed to be shared here)

Lol I feel like such a dick arguing about maths, especially on a public forum haha. Fun nonetheless, and definitely worth it if you end up proving a question wrong.

Yeah I hated that geometry question. It shows how bad some recent years have gotten in ext 2, either having easy Q16s (2014, 2017) or artificially difficult ones (2018). If you compare to like 2001 or even 2010, which had some really genuinely difficult questions, it is obvious how uninspired...

But if they flip the same number of heads, then Ben will flip more tails, since he flips n+1 coins and Amy only flips n, therefore putting it in the 2nd case of Ben flipping more tails than Amy.