Question regarding personal statement - Maths

Hello, I am currently writing my personal statement for maths at Cambridge. At the moment, I am finding that I am having to cut out a good amount of stuff I have done, so I wanted some advice about what Cambridge is looking for in a PS for maths, and hence, what should remain, and what should be cut, this is, as far as I can recall, what I have done this last year, and what seems to be relevant to my PS:

- Done a good number of competitions, e.g Ritangle, UKMT, Maths Bombe
- Gone a few lectures at UEA, Cambridge, etc.
- Looked into Galois theory, Complex analysis and number theory
- Read a number of books, some about the history of maths, some about mathematical thinking, etc.
- Invited by Oxford to attend an online maths & physics school (COMPOS)
- Done a lot of STEP prep, and I see this a lot in personal statements
- I have a residential for maths at Lancaster over summer (Also doing MAT for Imperial and TMUA because it looks fun - So could be worth mentioning?)
- DofE (Bronze), Duke of York (Bronze, Silver, now doing gold) awards
-Something not necessarily an advanced topic, but I self taught myself the A level maths content between the y11 and y12 summer, and I also did this online maths thing in y11 that only a few people have done, and it took me about 10 days on the site to complete, so I was curious if that would apply, given it is y11

I know that some of these may not be as relevant to Cambridge to others, so I am looking at removing the bits they care less about, as I am a good way over the limit talking about all of these things, and I also need to make room for my residential after I complete it, so I need to be careful about how I use my words up.