English question: Is there any difference between the following two sentences.?

A slight difference. With the first sentence they are giving you information that it's possible that
there could be a math test tomorrow, it sounds more trustworthy and authoritative.
The second one sounds like a student is just thinking out loud, but really has know
idea what would happen.

Yes there is a difference. But the most common way to say what I think you mean is "The teacher MIGHT give a test tomorrow", not may or maybe.

"Maybe...", as you've used it here, suggests a hopeful possibility. If the teacher giving a test would be a good thing for you, then it would make sense to say "maybe". "might" just means it's possible.

"may" is formal and doesn't really fit here in my opinion.