Question

1. My math exam is tomorrow.
2. Tomorrow is my math exam.
3. Tomorrow I have a math exam.
4. I take a math exam tomorrow.
(Are all the same and grammatical?)

5. What did you do over the summer vacation?

6. What did you do during the summer vacation?

7. What did you do on the summer vacation?

8. What did you do through the summer vacation?

9. What did you do over the summer vacation?

10. What did you do during summer vacation?

(Which preposition do we have to use? Can we omit 'the'? Are they all grammatical?)

Answer 1

1 - 4 are all fine and all mean the same thing.

5 and 6 are fine and mean the same thing. 7 and 8 are OK, but not as smooth or clear as 5 and 6. 9 and 10 are the same as 5 and 6. And, yes, the word "the" can be omitted.