Hi,
Based off my experience I considered dropping down to Advanced Maths before Year 11 even started. HOWEVER, after receiving great advice from the fellow BOS members on this website I stuck with it. I'M NOT REGRETTING IT AT ALL! By the way special thanks to all the BOS members who helped me with the decision making process.
It's good to hear you are in 5.3, you will be taught some of the topics that are involved in the Advanced course through Year 10. This includes the Cosine Rule, exact Trigonometric ratios, Hyperbolas, Parabolas, Domain and Range etc. Basically Years 7-10 don't matter in relation to the HSC but you're Year 10 marks can be an indicator of what course you should do. This shouldn't discourage you with your subject selection. In my Extension class a small group of students were receiving marks in the 50s to 70s (based on the difficulty of the exam) and they are giving it a go.
Extension 1 Mathematics is a challenging but fun course. It is completely different to the Advanced course and will be extremely difficult if you don't revise your content on a regular basis. I revise the topics that are covered in class and were previously covered during Term 1 every night. Now I'm not saying you need to give up everything, lock yourself in your bedroom and devote your study time to Extension Mathematics. You need to manage your time and avoid any form of distraction (my biggest weakness is the Internet). Time management is important whether you are doing 12 units with study periods, or 13 units with no study periods. If you don't understand a concept go to your teacher straight away, you will be less stressed in the long run!!
With your marks I can't make an exact judgement. I know 2 students in my class who pulled in 50s to 70s during Year 10 and are currently receiving marks between the 50s to 70s. As I stated above Extension Mathematics is difficult, after the first assessment my class completed our teacher warned us that our marks will most likely drop from Year 10. Our average in Year 10 was in the 80s, it went down to the 60s. A lot of students weren't too happy with their marks in my class. The range of marks went from 31% to 94%, only 2 students in our class got a band 6 - 91% and 94%. Those 2 students studied frequently - not excessively but to the point where they felt confident. They had to balance their other subjects, their social life, exercise and down time. Our teacher didn't expect this either. There were 4 students who got 80% to 89% a band 5. The rest of the marks in the class were between the 30s to 60s. If you are willing to put in the effort and work hard you will be fine. DO expect your results to drop after the first assessment because it is different to Advanced. However, you might have an unexpected surprise with your marks if you work hard - trust me on this.
If your marks do go down THIS IS OKAY! If everyone was pulling in 94% then it wouldn't be an Extension course. Just use it as motivation to work hard and improve.
Your teachers can't specifically deny you of a course - unless you were receiving an average of 30% in 5.3 then Extension wouldn't be the right course. You seem to be doing fine, since you enjoy the subject you will be motivated to work harder which will impact your results positively. DON'T CHOOSE THE SUBJECT FOR SCALING! You have to do WELL in the subject to be scaled, otherwise if you are pulling in 20% in Extension then you won't be scaled up, you will still receive a low mark. The school can't deny you either, you should give it a go if it is too hard you can drop down to Advanced. The positive of dropping down is that Extension and Advanced complement each other - so you will a thorough understanding of the concepts that you were taught in Year 11 and the challenging Advanced Mathematics questions in the exam will be a bit easier to answer. This doesn't mean you will be secure of receiving 100% in Advanced, but you will be a bit further ahead of the Advanced students. In my class we are a whole chapter ahead of the Advanced cohort.
There are no special processes to enter an Extension course either.
Don't be intimidated by the course just because it is more difficult, personally I find it fun and considering the fact you enjoy Mathematics like I do you will be fine with your motivation.
Good luck.