This page is devoted to fun ideas you could use for the exploration, personal statement reading, or procrastination.
Go look at the IB Exploration for more ideas for projects and some good past examples of sixth-form projects.
Biology and Maths
"Nature's Raincoats" - a short article about how plants stay dry
Symmetry and Snapdragons
Chemistry and Maths
oscillating reactions book - an interesting and readable guide to the weird reactions behind cheetah spots, heartbeats, and more.
Physics and Maths
The Discovery of the Higgs Boson is a free online course with videos from eminent scientists including Peter Higgs. Some of the maths is a bit too advanced, but the course can still be understood without those bits, and you might be able to collar a maths teacher to explain them.
The what if? blog (and book) by the author of xkcd comics (as seen all around the maths office) has some great physics, such as what would happen to a mole of moles (spoiler - it's pretty gruesome).
Computing and Maths
Singapore's PM has solved sudokus forever! Find the article and get the C++ code here. Let him know if you find bugs.
Try out maths coding problems on project euler here. They start easy but get gradually harder.
The different mathematical techniques behind encryption used by Microsoft can be found here, with some videos and starting points for research.
Maths and more maths
Some weird new shapes to be intrigued by.
History and Maths
Paleodetectives - a short article about how maths can help with archeology
Multiple choice exams - how they could reduce the reward for guessing. You can read more on that here on the xkcd what if? blog.
What can you do next?