Here is a problem from i-want-to-study-engineering.org, the website written by Cambridge University Engineering department that helps you to apply for Engineering courses at top universities.
Jane has 5 pairs of socks. The first pair of socks are both red. The second pair of socks are both blue. The third pair of socks are both green. The fourth pair of socks are both yellow. The fifth pair of socks are both white. One sock from each pair is placed in a bag on the left, and the rest are put in a bag on the right.
In each turn, Jane draws one sock at random from each bag and folds them together to form a pair. After five turns, she has formed 5 pairs of socks. Find the probability that no pair consists of socks of the same colour.
Isaac Physics provides resources to offer support and activities in physics problem-solving to students (and teachers) working from GCSE (Year 11), through sixth form (Years 12 & 13), and to university.
Scrambled Eggs is a series of podcasts aimed at helping Year 11 and 12 students to explore their subjects and think about what they'd like to study at University. These are ten to fifteen minute discussions with university academics, many of them professors from the University of Oxford. Here are just a few:
Dr Ha-Joon Chang, from Cambridge University's Faculty of Economics, interviewed with Owen Wilson recently for The Guardian. Dr Chang discusses the Conservative party's austerity programme, arguing that austerity is a ‘self-defeating strategy’ and an attempt to undermine the welfare state. The Cambridge professor also talks about inequality, asking whether the UK has ‘socialism for the rich and capitalism for the poor’. You can watch the full interview here.