I’ve little more to add – the advice given by Alan is pretty comprehensive. I’ll probably end up covering the same ground, but here is some more general advice:
State the obvious
It’s as much to help yourself as to help the interviewer. Rather than jumping straight to an answer, it’s more instructive and generally safer to talk through your reasoning, even if it does sound too simple to merit an explanation. To start off a conversation, your tutor might ask you what seems like a deceptively simple question. In reality, it’s just a warm-up to make you comfortable and ensure you’re on the same page.
Show your working
In a similar vein, ensure the tutor knows what you’re thinking (as Alan advised). You are ‘marked’ in exactly the same way as in exams – your method and thought process carry far more weight than your reaching an answer. It shows that you have an appreciation of what you’re doing, that you know better than to learn by rote.
Don’t be phased
No matter what happens during or between interviews, try not to let it distract or demoralise you. There’s no harm in learning from experience but you might find yourself thinking too much on what happened during your last interview. Find something to take your mind off it – go to the JCR, wander round town, comfort eat – whatever works.
And now for some subject-specific advice:
Maths questions tend to be a cut-and-dried assessment of whether or not you’re familiar with a particular mathematical topic or technique.
Graph sketching questions seem to be very popular. Often they will be combinations of functions you’re familiar with. It might not be clear how detailed your sketch needs to be but, as Alan advises, if you’re in any doubt then just ask. Common features include intercepts, asymptotes and stationary points, maybe points of inflection if they’re feeling particularly mean.
You can also be sure that calculus is going to pop up in one form or another. Fortunately it’s usually in a rather explicit ‘differentiate this’ or ‘integrate this’ form. You might be asked to find the derivative of a variable nested within several functions, so you need to use the chain rule multiple times to extract it. Integration by substitution may well come up, but it’s also useful to make sure remember standard forms, such as
Physics questions are generally open-ended and form the basis of a discussion between you and the tutor. The answer might not be quantitative.
Some questions will be designed to test your physical intuition. Do you have a feel for how a system is going to act? What happens when I change this parameter? You practice this skill all the time when you ask yourself whether an equation makes good physical sense.
Another typical type of physics question you see quoted in horror stories is so-called ‘Fermi problems’. These involve estimating some bizarre quantity like ‘how many Mars Bars would you need to eat to climb Everest?’. Again, the emphasis is not on giving an answer but on how you try to get there. They’re occasionally fun to answer too.