For university preparation, begin with the course: why it interests you, what you have studied and what you want to explore next. UCAS interview guidance suggests discussing these questions with a teacher or adviser.
Oxford describes its undergraduate interviews as academic conversations. Explaining an idea, testing it and responding to a new suggestion matter. Cambridge’s preparation guidance distinguishes critical discussion of wider reading in the humanities from explaining working and solving problems in maths and science.
Here is a constructed maths warm-up, not an official interview question: a rectangle has a perimeter of 20 metres. What is its greatest possible area? A first response might be, “A square seems best.” Testing a 4-by-6 rectangle gives 24 square metres; a 5-by-5 square gives 25. That suggests an answer, but two examples do not prove it.
Let one side be x metres. The other is 10 − x because all four sides total 20. The area is x(10 − x) = 25 − (x − 5)². A squared number cannot be negative, so the area cannot exceed 25 square metres; it reaches 25 when x = 5. This explains why the square works.
Now change the question: what if the perimeter doubles? The largest square has sides of 10 metres and an area of 100 square metres. Doubling the lengths makes the area four times as large. In practice, the tutor can ask you to explain that change before offering a hint.
For a humanities exercise, imagine a factory owner’s speech saying, “Everyone welcomed the new factory.” A careful response is, “This shows what the owner publicly claimed; it does not establish every resident’s opinion.” A resident’s diary describing objections would then give a reason to qualify the claim. The practice is in explaining what the evidence supports and revising your view.