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I posted the solutions on another thread a while ago. One sec, I will try to find it Edit - bottom of this thread https://boredofstudies.org/threads/maths-practice-papers-new-syllabus.389146/page-2#post-7321108

Could be, I haven't thought about it too hard, but generally with questions like this a recurrence relation is the way to go. I haven't done anything like olympiad tutoring or much olympiad maths in general though so maybe there's a nicer way to do them with combinations.

Here is a diagram that will hopefully help with the explanation for b)

This is not the answer I get, and I don't see how combinatorial techniques could help with this question, but feel free to explain how you've done it. I have come up with a nice solution for b). Let f_n denote the number of ways of filling a 3×2n rectangle. First of all, consider the 3×0...

Yeah you are right, edited original post.

With the first one, you are given that 3 of the sides are perpendicular, so obviously the solid is a section of a rectangular prism. Now each face of these 3 perpendicular sides is a triangle, i.e. half of a rectangle, meaning you effectively have (1/2)*(1/3)=1/6of a rectangular prism. Also...

Ah ok, thanks for the clarification

What are the Go8 universities? I'm either going to be going to ANU or USyd for maths and I heard they both are internationally recognised. I won't be able to afford to do undergrad at an Ivy league uni though and I also have no olymiad experience so as silly as it is I would have no chance...

I got my results back and did better than expected, getting guaranteed entry into USyd BSci/MMathSci, supposedly with Daylell Scholars, but I don't know if this is better than the Mathematical Sciences/Science degree at ANU. In terms of location, I would have to move away from home for both unis...

I cannot afford a foreign undergrad degree, but just wondering, how difficult is it to get into a well ranked US university for a pHD/graduate program, coming from an Australian university? I am considering the possibility of pursuing a pHD in maths, if my uni marks are good enough.

Ok nvm, found the email about that lol. I'd assume that means we are eligible, it says on the website 98+ and a Daylell eligible course.

I can't really answer your question sorry, but just wondering, did they already offer the Dayllel Scholars Program to you? I preferenced the BSci/MMathSc at syd and got a 98+ atar but they haven't said anything about it to me yet.

If I were you I would definitely do it. Self learning the maths courses is possibly the best way to get a solid understanding on the content, since you are learning at your own pace, and doing it fast allows for more time to actually practice the content, which is how you do well in advanced...

A bit of a different topic, but the work environments at all those top schools sound horrible, specifically the selective schools. Doing 10+ hours of tutoring a week would completely kill any social life you may have, as well as the ridiculous testing conditions some have. I'm glad to have...

This is why the system for school ranking should be changed. It can be so easily abused like this with just percentage of b6s. Imo the factor should be median atar

I literally cannot believe this right now. As someone who goes to a pretty low ranked school I didn't even think it was possible. Thank you everyone for your help over this year!

NSW HSC 2019: Chem 93 6 EngAd 85 5 MathsX1 99 E4 MathsX2 98 E4 Phys 94 6 JapnB 77 4 Stoked with my marks, but looks like no state rank for 4u. Also japanese is lower than expected, but I didn't study much for it tbh

Haha thank you, good to hear. Good luck to you too

Ok cool, I was just worried they did it differently this year, but the consensus seems to be that its not the case

Thanks for the encouragement. Its just me catastrophising lol. I'm praying the phone call thing isn't true, thinking about it now they would have no reason to do that, since there is no ceremony for 2nd to 5th, and that is like 400+ phone calls, seems a bit weird.