Chances of getting into Trinity college Cambridge

You need to find what interests you and pursue that, for example through self-directed reading, online courses, podcasts, documentaries etc
The books on reading lists will give you a solid foundation in the subject but they are the books at will come up again and again in personal statements and interviews so they will not make you stand out.
You clearly excel academically but your post indicates that this could be due to strong book-learning, the fact that you dont do well on UKMT challenges could mean your problem solving and mathematically reasoning and intuition isnt as strong as your taught a level knowledge. For interviews and the like you really need to develop these qualities, top universities will want to see someone who is able to work logically through unfamiliar problems, not just memorise a textbook.

By never done well, I don't mean like silvers btw. We did a practice paper in class with only half an hour and i got 9 off olympiad score. I just collapsed in the exam for reasons that shouldn't have happened with my access arrangements because my school didn't let me have them

Thats understandable, thanks for the clarification. Hope I didn’t cause any offence 🙂

No it's alright, you're trying to help and I get that. My fault for not making myself clear. What I meant to say was I don't have any good results to prove I have strong intuition for their problems, but I do.

No it's alright, you're trying to help and I get that. My fault for not making myself clear. What I meant to say was I don't have any good results to prove I have strong intuition for their problems, but I do.

My school isn't unfortunately. I've done quite a few NRICH problems but haven't submitted solutions. Thanks for thelink to the lectures. I could read about/learn how to solve PDEs, func eqs, number theory, graph theory, etc. but I don't know exactly how I could work that into my personal statement.

My school isn't unfortunately. I've done quite a few NRICH problems but haven't submitted solutions. Thanks for thelink to the lectures. I could read about/learn how to solve PDEs, func eqs, number theory, graph theory, etc. but I don't know exactly how I could work that into my personal statement.

Hi, I'm currently doing A levels. I'm y12 predicted 5A* (maths fm phys comp sci chem, and yes those predictions will hold, ive already finished maths and fm content and haven't got below a* in a single paper i've done and i've got wayy more time than the 3 months i did maths and fm in for those 3 other subjects + i've finished all physics content and am doing really well in comp sci and chem anyway) + distinction in maths AEA, my GCSEs are 9999998888 + A (but I have multiple extenuating circumstances) and I've started STEP prep and can do some STEP II/III questions pretty comfortably in half an hour as needed but some I can't do. The issue I have is supercurriculars though. I've never really studied for UKMT and therefore never done well in it, and I've started going through their reading list + doing NRICH modules (i have a file with everything i've done but it's on another computer) but I don't really know what I could do to stand out to them beyond that. I've heard a lot of "study higher level maths" but how do I do that? What should I study? That's all more or less besides the point though. Come 2 years, do I stand a good chance of getting into Trinity College?

Tbh very unlikely. trinity maths is arguably one of the best and most competitive courses to get into in the world. i notice u said "come 2 years" but your application will be sent off in less than a year since ur yr12 now. a significant number of trinity maths applicants have reached bmo1 and a lot still bmo2. not studying for ukmt and having extenuating circumstances is not really something they will accept as an excuse to not doing well in maths challenges. it's kind of the bare minimum (esp at trinity, they do look at competitions for maths a bit more than other colleges) to show u are actually good rather than just good at learning from a level books.
obviously this means little but personally i have gotten bmo1 distinction and am applying natsci(chem, not even physics at trinity💀) with very little smc preparation (i did do some more for bmo) and although i have good mathematical intuition i would personally not even think i am anywhere near good enough for trinity maths
i assume u have studied mech and stats for FM so you can also look at add pure content (edexcel and ocr have number theory) for extra learning alongside lectures, videos etc.
since u have said u finished content for 3 a levels and are doing really well in the other two, i assume u have a lot of time this year? start preparing for STEP properly and you can apply to sit it at the end of this school year (usually done alongside a levels). although i don't think they accept it done early, it can be something to include in ur personal statement or reference which will PROVE that u are "good" assuming you can get at least 1,1.
overall i think u are a good candidate for cambridge maths but maybe ask urself why trinity? because your chances at cambridge are still great applying to other colleges. there is a pooling system (but only roughly 1/4 get picked from pool) and u can really test your luck if you want

i'm applying to trinity for the express purpose of competitiveness, and like i said, the reason i did badly (still gold) wasn't inability, it was extenuating circumstances. i get rest breaks for exams for a very good reason. they're allowed in smc. my school didn't give them to me. i'm not going to explain everything wrong with me to you, but that meant i had less than half the actual time needed for the exam, and yet i managed gold and almost olympiad. the issue isn't intuition. i've already got 1,1 in some step past papers, and my goal is ss. why would i sit step early if they don't accept it though?

It is not necessary to be in Trinity for "the purpose of competitiveness". Actually, the highest grades of IA tripos was from another college last year. I understand that most of them are often international competition medallists or hold a BMO2 distinction. This isn't because they actively seek competition; rather, they simply happen to be exceptionally good at it. They often have diverse talents—they might also be an athlete, an artist, or a musician, etc. Overall, you will be disappointed if you want to find a competitive environment in Trinity for maths.

If you think trinity won't be a competitive environment, what will be?

It's university and adult life, not kids at school. There's no 'competitive environment' except what you want to imagine for yourself. You can become the best mathmo you can be at any College. Only apply to Maths at Trinity if you'd rather be at Trinity than Cambridge.

So how is life at trinity other than location different from any other college?

So how is life at trinity other than location different from any other college?

i'm applying to trinity for the express purpose of competitiveness, and like i said, the reason i did badly (still gold) wasn't inability, it was extenuating circumstances. i get rest breaks for exams for a very good reason. they're allowed in smc. my school didn't give them to me. i'm not going to explain everything wrong with me to you, but that meant i had less than half the actual time needed for the exam, and yet i managed gold and almost olympiad. the issue isn't intuition. i've already got 1,1 in some step past papers, and my goal is ss. why would i sit step early if they don't accept it though?