That depends largely on what state you're in. NSW has HSCs in Year 12, and I think they have some kind of exam in Year 10 as well, but you might want to check that.
QLD doesn't have major exams, because we're awesome. We have QCS (Queensland Core Skill) but it doesn't actually count to anything, it's just a way for the Queensland Board of Education to compare different schools. You have to do a writing task in response to stimulus, two multiple choice exams on English, Maths and Science, and one Short Response task with slightly harder questions on English, Maths and a little bit of Science. These tests are sat over the same two days, usually a Tuesday and a Wednesday, at the same time in every school in QLD. They are very very easy, unless you get a bad topic for your writing task. My year got circles, the year before got essence which is way harder.
I just realised that I'm not entirely right about the no exams thing - I should have said that we have no standarised testing for the entire state - our teachers set the exams.
If I remember correctly, however, your fic isn't actually set in QLD so I'm going to stop now.
Oh, and in primary school they have the Three Five Seven tests, which I think might be nation wide. As you can tell from the name which I don't think is the correct name, they're taken in years 3, 5 and 7.
I highly doubt any of this helped, but whatever.