復習してきました。って英語でなんて言うの？

You do not always have to use revision or review. You could also state that you studied. These synonyms can be used interchangeably!

I reviewed. / I did a review. - Review means to go over or look over something for a second, third, forth, etc. time. Re means again. View means to look at something. You can also use the phrase to "brush up (something)". This means to renew old knowledge by going over it once or twice or thrice, etc. more times.

Thanks. I have been brushing up on my English before this class. -When you brush up on something it means you are improving your existing knowledge on something. Thanks. I reviewed the stuff we covered last class. - The 'stuff' used in this phrase could be changed to make it more formal, for example, the material we covered, or the vocabulary

Cheers! - In the UK, this is used informally to mean "thank you": "I've bought you some new curtains for your bedroom." "Cheers, mum!." Actually = we use this word when we want to stress that we did something in person and that there is something unusual about the activity. "I actually had to go to town on my bike in the rain as my car did not start this morning!"

example "i revised what we covered last lesson". or i recapped what we had learned last lesson". or "i did some homework and reviewed what we did last week".

When you want to tell your teacher that you reviewed the lesson material from a past lesson you had with them; then you can say: -Thank you. I reviewed our last lesson before this one. -Thank you. I prepared for this lesson by looking over the one we had before. -Thanks. I think it helped that I went over our last lesson.

"I actually went over the vocabulary/material/lesson before the class." states that before class you looked over the words/material beforehand.