[Vocabulary] make up and do over

Can you tell me if I caught the meaning of these two phrasal verbs in this context, please?

The context is this: Let's picture I'm a student and I'm in the class and my teacher is standing in front of me. I was absent the day before and I ask him if I can do the test I didn't do.

1) Can I make it up tomorrow? I'd like to have a good mark at the end of the semester.

2) Can I do the test over?


In the first, it should mean that I didn't do the test and I want to do for the first time.
In the second, it should mean that I did the test but maybe it is full of errors and I'm asking to do it again.
Is it correct? Are the two verbs used with the correct meaning?
Thanks so much for your help.

Those interpretations are correct.

Instead of "do the test over" you can also "retake the exam."
My daughter's school has a formal retake policy, for example.

Barb_D said:

Instead of "do the test over" you can also "retake the exam."
My daughter's school has a formal retake policy, for example.

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"do the test over" would not be understood by most BrE speakers.

bhaisahab said:

"do the test over" would not be understood by most BrE speakers.

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Really? I had no problem with it. I hear "That's rubbish. Do it over" more and more these days. Admittedly, it has entered the language from AmE and when I was a child it would have been "That's rubbish. Do it again" or "Re-do it", but I have no issue with "to do something over" meaning to repeat the action.

I would add, however, that "to do someone over" in BrE means either to cheat them or, more commonly, to beat them up. It's a very informal (if not slang) term.

I didn't know about that one (do someone over) - another phase to add to the stockpile.