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How do I do this question: Prove that \int_{0}^{\frac{\pi }{2}}\frac{cos5\theta sin\theta }{cos\theta }d\theta =\frac{23}{15} thanks in advance.

If in one year everyone doing the HSC does extremely well is it possible to get more than 50 99.95's? Only the top 50 students get 99.95, afaik, so if 100 people get full marks in their exams do they all get 99.95?

If a student is ranked 1 in every single subject at a low ranked school and does very well in the externals is there anything preventing him from achieving 99.95?

I noticed that almost all the more difficult maths extension 2 questions are either analysis or proving so how can I effectively improve at those? Maths extension 2 textbooks don't really cover those topics* very well so which textbooks are good? Should I consider buying university level...

I am aiming for about 94 in English Advanced so can someone please give me some study tips. At the moment I am neglecting English and concentrating heavily on maths and science but I typed some numbers in the ATAR calculator and looks like English is really important, I can get 90 in maths ext2...

Hi, Is doing very well in maths ext2 enough preparation for BSc if I want to major in maths/physics? Many people told me that maths at uni is all about understanding and proving things so they suggested that I go through the velleman book which is a proving book, others suggested that I go...