Well, that is a good question! I am sure you have heard horror stories about the kinds of questions which they ask you! They might seem random, but they are actually designed that way for two main reasons. Firstly, they try to avoid topics which you might have done at school to level the playing field between other candidates. Secondly, and relatedly, they are trying to make you think outside of your comfort zone. In an Oxbridge interview, it is not about demonstrating what you know, but demonstrating how you think. Therefore, it is vital that when you are thinking through a problem you say your thought process outloud. They are unlikely to mind whether you get the right answer, in fact there might not be one! For example, in my interview they asked me to interpret a graph about income inequality and then determine what I thought of it. Of course there is no right answer to this question, but they want to see that you can think critically and present a (reasonably) coherent point of view.
While you can never know what they are going to ask you, it might be helpful to look at the expertise of the tutors at the college you are applying to. It is likely they will ask you at least some questions about their field. However, please do not worry about reading loads of books on their work! The most important thing for you to do with your time is to practice thinking on the spot about topics outside of your comfort zone. We can practice this together if you like, by doing a mock tutorial? I would also recommend asking your friends and family to ask you questions about things like the news and what is motivating you to study your subject. As important as the above is, you still need to keep in mind what you wrote in your personal statement and why you are applying to your chosen degree. They want students who are able to motivate themselevs, as well as think critically. Does that answer your question?
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