Hiya, just about to finish year 13 of maths a-level, here's some of my advice.
Firstly, yes you should do transition work, and I would highly recommend either a revision guide (depends on your exam board, see if you can get one for that). I would recommend just reading through the AS content and seeing how much of it you recognise. When i started my alevel, there was a huge amount of year 12 that I'd already done at GCSE, so it's really useful to be able to remember all of it instead of having to relearn it. It'll make your revision and class work so much easier. Find the topics you'll need that you already know and just do little bits of practice of them - particularly algebra and trigonometry, those are the big ones. Find questions online, do little bits of practice of them, and just make sure you can remember how to do them. If you fancy, you can even try and take on some a-level ones.
Mechanics and stats are a bit trickier. All depends on your exam board, mine wasn't very common so I doubt you're doing that, but for me they weren't worth as much as pure so don't need as much focus, but they're also something you probably won't have seen much before. Some of mechanics you might have seen in physics GCSE, so again, look through the revision guide, see what you recognise. You probably won't have seen much, if any, of statistics before starting year 12, except for bits of probability.
Go into maths ready to work hard. It really isn't an easy alevel, except for very few people. It's a subject where rewriting out your notes is gonna be completely useless, so make your notes in lessons and keep them. Little and often is the best way to keep maths in your head. Aside from homework, do a couple of hours of maths a week, just doing questions, go back over the topics you learned a while ago, practice the topics you've only just done so that they don't leave your head as soon as you walk out the classroom. I'm partly saying this becuase I didn't do it and I regret it.
I know this has gone far beyond what you originally asked, but I hope it's still helpful! Well done on finishing GCSEs and good luck next year.