STEP; Trinity at-interview maths test; 1x interviews
Interview: subject-related problems
Practice papers - STEP, MAT and BMO1
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Discuss subject-related problems with teachers and classmates
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.
Tests taken:
Number of interviews: 1
Skype interview: no
Time between interviews: N/A
Length of interview: 45 minutes, after a 1 hour test
The test had 10 questions from a variety of topics.
I brought my solutions with me into the interview where one interview read and checked them while the other asked me for my favourite problem, which I then described my solution to verbally. We went fairly quickly through the questions I'd solved, then came to those I had only managed part-way. After a few hints I was able to make my way to the final answer.
The interviewers definitely put in an effort to make me feel at ease and to make it seem I was just discussing a problem as an equal rather than being interrogated. I came out mentally exhausted but from what I heard that's very normal and if anything
I did the 3 public specimen at-intervew test papers as practice, then also did
STEP has has over 30 years' worth of past papers; stepdatabase.maths.org has every STEP question ever grouped by topic. The MAT is useful as a "stepping-stone" to doing the harder STEP papers, and both are useful for the at-interview test. BMO1 papers are also helpful.
Discussing problems verbally with teachers and students was very useful as it got me used to conveying my ideas clearly in words.