Syllabus of Trinity Maths entrance exam?

Trinity can't guarantee that all their applicants for maths will be studying A-level further maths (it isn't an option at some schools), so I imagine that the test will mainly be on A-level maths, specifically the modules C1, C2, C3 and C4. Obviously, the questions will be much harder than standard A-level ones, as they are aimed at the best few percent of mathematicians. I strongly doubt that FP3 would appear on the test - even people studying further maths won't necessarily cover it. I remember reading that maths tests at interview were similar to STEP I papers in difficulty (although the questions will be much shorter, as you have less time). You could also try looking at Oxford MAT past papers.

The vast majority of applicants for places at Trinity will be taking two Mathematics A-levels. While this certainly provides a good preparation for the Tripos, and is a course we recommend potential candidates to follow, wherever possible, we recognise that in some schools this may not be the case. AS Further Maths is now a necessary requirement.

AS Further Maths is now a necessary requirement, whether your school offers it or not. But if you do not study A-Level Further Maths, whether your school offers it or not, you would be unlikely to secure a place/offer at Trinity due to the high level of intense competition.

Perhaps he is talking about the need to know FM for the STEP II/III exam?

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(I was replying to the person I quoted, not the OP, I haven't addressed the OP yet)

But, as for the OP's query:

Nopes, they don't - the questions are based on strictly general mathematics and whilst further maths topics like hyperbolic functions comes in useful every now and then, Trinity does not expect you to do all the questions, so you can easily do the test without FM knowledge. Some people have done 2-3 questions on the test and gotten offers, others have done 9-10 on the test (there are 10 question) and gotten offers, Trinity isn't very fussed about the number of questions, so you should be fine!

Although, once it comes to STEP III - the OP is going to be in trouble.

(I was replying to the person I quoted, not the OP, I haven't addressed the OP yet)

But, as for the OP's query:

Nopes, they don't - the questions are based on strictly general mathematics and whilst further maths topics like hyperbolic functions comes in useful every now and then, Trinity does not expect you to do all the questions, so you can easily do the test without FM knowledge. Some people have done 2-3 questions on the test and gotten offers, others have done 9-10 on the test (there are 10 question) and gotten offers, Trinity isn't very fussed about the number of questions, so you should be fine!

Although, once it comes to STEP III - the OP is going to be in trouble.

I have taken a STEP III exam and I was able to solve 9 questions in the time limit of 3 hours. I know differential/integral/vector calculus, probability, and mechanics, which is basically the content on STEP.

However I don't know linear algebra or group theory or differential equations. But looking at the previous STEP exams, this doesn't appear to be a problem.

If you managed to do nine questions on STEP III (the hardest STEP exam, by a fair distance) within the time limit (and got them right!) you'll be completely fine with the interview test. I'm impressed that you managed to do that well without knowing about differential equations, as I was under the impression that they formed quite a big part of both the pure and mechanics questions.