fail (in) the exam

[SARDORBEK]

1) I failed my driving test the first time I took it. (no preposition)
2) Sanjar failed in the exam, but his sister got through.
3) He failed maths but passed all his other subjects.(no preposition)
4) I passed in history but failed in chemistry.
5) A lot of people fail their driving test the first time. (no preposition)

Is the preposition in optional after the verb fail?
In general, do we say fail the examor fail in the exam?
Is there a difference between them?

Thanks a lot…

[Alan]

In an academic context, 'fail' is transitive. Otherwise, 'in' is normally required.
I'll leave you to work out which applies in each of your examples!