"may have done" used for the future

[joham]

Martin Hewings' ADVANCED GRAMMAR IN USE says 'may/might have done' can be used for the future:
His maths may/ might have improved by the time next exam comes around.

One of my Chinese netfriend says that 'may/might have done' can't be used for the future. I feel Hewings's sentence is perfect. But I can't persuade him to accept this sentence.
May I ask native English teachers to explain if it is a good sentence?

Thank you very much.

[riverkid]

Martin Hewings' ADVANCED GRAMMAR IN USE says 'may/might have done' can be used for the future:
His maths may/ might have improved by the time next exam comes around.

One of my Chinese netfriend says that 'may/might have done' can't be used for the future. I feel Hewings's sentence is perfect. But I can't persuade him to accept this sentence.
May I ask native English teachers to explain if it is a good sentence?

Thank you very much.

Hi Joham.

We can say, [at least Brits can ] the 100% level of certainty sentence,

His maths will have improved by the time next exam comes around.

so of course we have to be able to modify that for level of certainty because that is a possible thought/scenario in life.

His maths almost certainly will have improved by the time next exam comes around.

His maths probably will have improved by the time next exam comes around.

His maths may have improved by the time next exam comes around.

His maths might have improved by the time next exam comes around.