STEP Mathematics is a set of examinations in the UK. Cambridge University uses it as an admissions test. The best way to prepare for an examination is to practise, but when I took the paper in 2007 you had to get copies of past papers. Since then, the exam board Cambridge Assessment have published the past papers freely on the web. This is a good thing for fair admissions.

However it happens that the exam board have published the past papers inside zip archives. This makes it hard to find specific questions using a search engine. The web site also keep changing its urls!

For posperity, I’ve republished the papers at document publishing website Scribd: STEP Mathematics past papers 1998-2011. Since the exam board have already published the papers online, this seems fair use.

One memorable problem, that I’d like to write a post about.

If k people are in the room, what is the probability p that at least two of them share a birthday? What is the least k such that p is at least one half?