2x interviews
Interview 1: technical questions; Interview 2: reasons for applying
Consolidated knowledge of Maths syllabus
Treat the interview as a chance to learn
Remember this advice isn't official. There is no guarantee it will reflect your experience because university applications can change between years. Check the official Cambridge and Oxford websites for more accurate information on this year's application format and the required tests.
Also, someone else's experience may not reflect your own. Most interviews are more like conversations than tests and like, any conversation, they are quite interactive.
Test taken: None
Number of interviews: 2
Time between interviews: 1-2 hours
Length of interviews: 30-40 minutes
Online interview: No
I had one technical and one non-technical interview. The first was working through a few questions with pen and paper, as well as a few questions about general areas of interests and ideas about different topics. The second was more about why I had picked Engineering, what I hoped to achieve, what was important to me about the course, etc.
I prepared for my interview mainly by making sure that I knew the basics well. For an Engineering interview that meant that my basic maths was solid - integration/differentiation/graphs/trigonometry and that I had enough of a grounding in electronics and mechanics to be able to approach questions there.
The key point is that I did not focus on anything beyond the syllabus, and that I had been told previously that the whole point of the interview was to see how you respond to new material, not how much you already knew. Knowing this meant that I didn't get too flustered when I was presented with ideas that I hadn't seen before, and I could work towards answers with the prompts that were given to me.
I also prepared by general reading about areas that interested me and staying up to date with the wide trends (electric vehicles, fracking, green energy). More cynically, as we were told who would be interviewing us,
My advice would firstly be to make sure that this course is the right one for you and that you're only picking it out of genuine passion and interest. After that, read as much as you can in the areas that interest you, focus on getting good grades, and don't think that you have to be the finished article on interview day. Treat the interview as a chance to learn (ask questions!) and be as well rested and relaxed as you can.