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So the exam is tomorrow but I can't afford a calculator. Do I really need one? Most of the mathematics in the course does not require a calculator as they are proof based/involve pronumerals rather than actual numbers. For example, graphing would not require much use of a calculator, and conics...

Reminds me of https://www.research.ibm.com/haifa/ponderthis/challenges/May2001.html and https://www.research.ibm.com/haifa/ponderthis/solutions/May2001.html (spoiler alert - solutions are in the second link)

I just checked the textbook and I typed the question wrong. There should be a square in the denominator but not inside the log. This might be what OP is asking?

There is a similar question in a Sydney Grammar textbook: \int_0^1\frac{\log(1+x)}{1+x^2}. It also appeared in a Putnam a long time ago. Use the substitution x=\tan\theta so I= \int_0^{\frac{\pi}{4}} \log(1+\tan\theta) \, d\theta Use the fact that \int_0^a f(x) =\int_0^a f(a-x) so I =...

I did all four. Anyone is allowed to participate in the olympiad, but only year 10 and 11 (and I think year 9 if they are old enough) are eligible for the summer school. Also offers have been sent out for quite a while now (since last week).

\int x^2 e^x \,dx and \int x^2\cos x \,dx and \int (\log x)^2\,dx are also examples. Whether they have been asked before, I'm not too sure. I can't be bothered checking through all the past papers.

Isn't that called reduction formula?

I got the question from David Monk, who wrote a book with geometry questions. I decided to chuck it in the trial, without solutions. Alternate solutions involving other parametrisations or complex numbers or just euclidean geometry would be interesting as well.

Actually it was EES 5% and it wasn't even a serious attempt. Just writing random answers and leaving half the exam blank. For all those 8 markers, I wrote 3 sentences.

You'll have to find out from your school - so ask your teacher/head teacher/olympiad coordinator.

I got a call this morning offering me a place at the summer school. But I had to decline because I'm in year 12.

Hello, I keep getting stuck on this question. It gets a bit messy. I already did part (a) - the point A (and hence B,C,D) all lie on the circle given... just parts b, c, d I need.

median was like 87 or something

Most people got like 90+ We also didn't cover mechanics and volumes at the time of the exam rip

spud is that you?

The answers to the multiple choice are on my instagram though

Most of us had to gamble question 9 because we forgot which one was the transverse axis ._. Also follow me on instagram https://instagram.com/jonathanlam13/ and you can find this https://instagram.com/p/7Z6hr4hU1Z/?taken-by=jonathanlam13 //shameless advertising

Sorry for the late reply. Like you said, it varies from year to year. It is quite difficult to determine cut offs and stuff because you're never given ranks, percentiles, marks or other details on your performance. The best you know is from your award (distinction, credit, medal etc). I got a...

I'm interested in doing it.