1. In reality, I didn't pass the exam. 2. The fact is that I didn't pass the exam. 1 is grammatically correct, but number 2 is more common and sounds more natural. You can use this to bring conversation back to the *facts*, if you think that you or your partner have been talking too much about ideas or dreams. I do not think there are any other ways to say exactly this in English. Also: In English you "take an exam". When you take an exam you may "pass" or "fail". For example: "I've taken the exam three times, but I failed each time" "I took the exam and passed" "I've taken the exam, but I will only know next week if I passed or failed" So you could use 1. Past Simple tense or 2. Present Perfect tense 1) The fact is that I didn't pass the exam 2) The fact is that I haven't passed the exam 1 means that you took the exam but failed. 2 means that you have never taken the exam, perhaps you hope to take it in the future.

Both are correct uses, though I dont necessarily think people speak in that way. You could say something like: 2+2 is a fact. I should be asleep right now, that is a fact. In reality, I will be up all night doing homework. You think what you are saying is a fact, in reality you are wrong. History books are full of facts.

I think, a fact refers more to things or experiences whereas reality is a state of being.

You can contrast the two words nicely if you add "in" at the beginning. 1. in fact – often used to emphasize a point e.g. It's been very rainy lately. It fact, I think it's rained every day for the last 2 weeks. 2. in reality – often used to contrast reality with an unreal situation e.g. I have perfect attendance at school. In reality, I've only been to half the classes.