fail in the exam vs. fail the exam

[Foreigner]

Here are the sentences that have always caused 'trouble' for me

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)

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

Thanks a lot…

[Esl_Expert]

Hi Foreigner,

I would normally NOT use 'in' to simply state that I did not pass a test or exam.
Thus, I would not use 'in' for sentence 2.

I would use 'in' as you have used it in sentence 4 (i.e. in a subject). You will also see that sort of a sentence without 'in'. In my opinion, the omission of 'in' in such a sentence would tend to put more focus on (failing) the exam and less on the subject.