If the subject is not changing, native speakers will use the infinitive.
In your second example, your listener will not hear "I hope I pass my exam." They will instead understand "I hope he/she passes his/her exam," unless you were NOT recently talking about another individual. If you weren't already talking about a third person, they would wonder why you didn't use the infinitive. It isn't grammatically wrong, but will be ambiguous for your listener.
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