Re: MX2 Integration Marathon
Sorry everyone, this question can't be done using MX2 integration techniques.
You can sub u=sinx and get \int \: \frac{\sin{u}}{\sqrt{1-u^2}}du but can't do anything else :(
Yeah, it doesn't have to prepare student for undergrad maths but I think there are many topics other than conics that are more interesting and more useful in uni. If students know basic coordinate geometry, calculus, and algebra they can definitely do conics so it isn't really teaching you...
If by useless you mean it doesn't have applications in real life then it is not useless but I can think of better topics to study instead of it such as topics that prepare students for university maths and have more applications (linear algebra, differential equations, etc.).
Re: HSC 2013 4U Marathon
Nice work but I don't know how we can prove that the limit goes to 0. There is a more rigorous method to prove this, will post it sometime next week.
I found this question in a book called \pi $Unleashed$.
What is so difficult about circle geometry? I know a lot of students who struggle with it but I think it is very easy. If you have done enough questions and know what to look for you can do even the most difficult questions in a few minutes.