He did well in / on the exam.

An American would most likely write "on the exam." Personally, i've never seen "in the exam" used, although there's no telling what those silly Saxons will get up to. When speaking of an examination as an event, though, it would not be unusual for an American to use "in." So, for example:

"Where's Bill, he was just here a moment ago?"

"The lecture hall over there, he's in an examination."

Uk & Commonwealth use is "in"

Failure in an examination may have uncomfortable consequences but the situation can be retrieved (Brighton, UK)

The LPAB recognises that disability, illness or other circumstances may affect your performance in an examination (Australia)

In the case of failure in an examination, the Head of Department will decide whether the student shall be required to withdraw from the College. (Imperial College, UK)

A pass in an examination taken after completing a training programme will not be acceptable for a CCT (General Medical Council, UK)

An examination irregularity occurs when a student seeks to improve their performance in an examination by accessing, or attempting to access, material not listed on the front of the question paper (Birmingham, UK)

Oddly, I would say someone did will in English. I would also say he did well on an exam.

That is odd, Roger, exceedingly so.

But you are an odd duck.

US only - "well on the exam"
About 2,410,000 results

US only - "well in the exam"
About 3,230,000 results

=====================

UK only - "well in the exam"
About 242,000 results

UK only - "well on the exam"
About 1,490,000 results

Using the unrefined number of google to determine correctness seems, well, decidedly odd.

It does, doesn't it, Roger? I'll go back there and change where I said that.

Is your little ignore hole too cold and damp for you?