grammar - Is 'Maybe I can help?' correct?

Two weeks ago I did an English test.
I was asked the following question:
(or something like this, I don't remember the exact question)

A classmate is trying to do his homework, but he doesn't know how to do it. You do know how to do it. How can you say you can help him?

My answer:

"Maybe I can help you?"

This was not the correct answer. The correct answer was:

"Perhaps I can help you?"

I asked my teacher why my answer wasn't correct. She said: 'I don't exactly know how to explain that, but it has something to do with being polite. I'll come up with a better example next time.'

Is there really a difference between 'Maybe' and 'Perhaps'? And was my answer a valid alternative?

Answer

If your teacher can't explain why one word is better than another, then she didn't teach you; and so has no right to expect the correct answer. The nuance between 'maybe' and 'perhaps' is too fine to make one 'incorrect'.