Where would I find such a thing?
Either International or otherwise Australian Standards would be preferred.
I ask this question because my friend answered every question in his test correctly and only received a 50% mark due to 'incorrect notation'(at Melbourne University).
Thank you for reading! ^_^
On
Although it may seem a bit obvious, the wikipedia "List of mathematical symbols" (https://en.wikipedia.org/wiki/List_of_mathematical_symbols) is quite useful if you are in need of a reference; be sure to check the external links as well. Similarly, for the sake of whatever specific course this took place in, I would refer to the textbook used in the course. Generally speaking, a textbook used by a reputable university should use notation which is up to the university's level of rigor.
The goal of mathematical notation is to clearly convey your ideas in a way which is easily understandable. To that end, unless your friend was using a completely indecipherable (or misleading) notation, I find it extremely difficult to understand that someone would lose 50% of their grade for what ultimately amounts to obfuscating their ideas. Hopefully, this helps in some way, though.
As someone who does a lot of marking, I assume it was a combination of two related things:
The first thing to do is make sure that you always know what you're writing. If you write something like $$\forall x\in \mathbb{R}, \int f(x) \mathrm{d}x = 0$$ don't do it blindly. Make sure you know what "$\mathbb{R}$, $\forall$, $\int$, $\mathrm{d}x$" etc. all mean. You should always be thinking about the exact words you're writing down.
A big problem that maths students have when they haven't had much experience is trying to turn everything into symbols without realising that words are actually better. A single word can contain so much information and it's also a lot easier to read. For example, the sentence "if $n$ is prime and greater than 2, then $n$ is odd". This is completely rigorous and easy to understand. But if you turn it into symbols: $$((n > 2 )\wedge (\forall a,b\in \mathbb{N}: ab = n \implies a = 1 \wedge b = 1))\implies (\exists k \in \mathbb{N}: n = 2k+1)$$ This completely obfuscates the statement (and I probably made some mistakes.) So what your friend should try to do is embrace words and only use notation that has been introduced in the classroom. That means you have a definition (in your coursenotes or whatever) about what the notation means, and you can also understand exactly what you're writing. Words are a mathematician's best friend.