How do I tackle questions that seem only vaguely related to the course I've covered?

These questions are particularly stressful, because they seem completely random. But the most important thing to do is relax and think back to your syllabus. Can you make any links to the topic at hand and something you covered in class - if so that is probably what they're aiming at, its all a ploy to get you applying your knowledge. For example, in my A2 exam, I had a question about paracetamol metabolism in the liver at the same time as alcohol. I had no idea even vaguely about how paracetamol is metabolised, so I stuck to basics and talked about enzymes, substrates, competitive and non-competitive inhibition - it worked out alright!