Interview for pure math graduate program
My grad school interview for math was a bit different. It was more about determining whether I would accept an offer if they gave me one, because they didn't want to offer places to people who would not take them. I did however interview for my undergrad, and there the questions were on mathematical understanding. A question I was asked was "derive x^x". This is something that most high school students haven't seen, but should be able to figure out with some guidance. I would expect a grad school interview question to follow a similar pattern: ask about something you probably haven't seen before, but that you can figure out with some guidance from the interviewer. They will be looking for how you try to tackle problems you haven't seen and how you justify each step you take.