Submitted by Anonymous on Tue, 04/07/2015 - 11:03
Forums:
I've been doing quite a few STEP questions lately and thought it would be nice to have a thread where people can share their favourites. I enjoyed STEP I 2006 question 8 because although I'm not usually fussed about geometry questions, there were some nice ways of thinking about it and as it was a "show that" question, I knew when I'd got the right answer! Anyone else got a favourite to recommend?
traingle
I like that one with the triangle; I'll try to find the question number.
Testing TeX $\cos \theta - \int_0^\theta x \mathrm{d}x$
Osculating Circle
I liked STEP II 2010 Q1 about the osculating circle to a curve. It was a relatively straight-forward question that had a fab concept.
There was a great one where
There was a great one where you had to integrate a function in the form e^(-x^2) by relating it to the normal distribution, and using the probability tables.
STEP II 2000 Q5
STEP II 2000 Q5
STEP III 1998 Q5
STEP I 1999 Q11
STEP III 2010 Q1
Are a few interesting ones that come to mind.
Are some interesting ones.
Stats is cool guys
STEP II 1999 Q13 is one of my favourites just because of how simple it is to explain to friends whilst having a lot of ideas going on in the problem, making it really satisfying to actually solve
"A stick is broken at a point, chosen at random, along its length. Find the probability that the
ratio, R, of the length of the shorter piece to the length of the longer piece is less than r.
Find the probability density function for R, and calculate the mean and variance of R."
Im such an amateur
Measly STEP I 2000 - the problem with the integral of floor(e^x). It is one of a handful that I have attempted since starting last week but I thought it was elegant nonetheless.