You can find past papers and information linked below. The official TMUA website is here.
The specification for November 2021 onwards can be found here and some notes on the logic and proof questions here.
I used to have playlists here working through questions from TMUA papers – these have now been replaced with a free online course where you can work through past TMUA questions with my video solutions:
I also occasionally run some online small group classes (not free) to prepare for these papers – see the schedule and sign up here.

Past Papers and Solutions
If you are preparing for TMUA you might also find my MAT content useful – the syllabus is similar and the short answer questions from the MAT are particularly good practice for the TMUA too.
Also, here’s a video about writing amazing personal statements, particularly aimed at maths: