Thanks for your answers. I made a mistake in #3, I hadn't noticed it before.
I know how the future tenses work (in theory), but I wanted a more detailed explanation regarding those sentences (the concept of taking an exam tomorrow). It would help me if you could add some more information to each sentence so I could see in which context and how exactly they can be used. Thanks.
Actually, those sentences are identical in meaning and would not make any difference to English native speakers.
The forms going to and will are interchangeable, whereas the present simple form must be used only when you are fixed up to do something [an arrangement, a plan].
Of course, #4 is a variation of the form will. It just differs to the normal form because you are specifying the time of the action.
The first sentence is the least formal.
The second one, according to me, is the best one.
The third sentence is wrong. It ought to be - I'm going to take this exam tomorrow.
The four sentence is a variation of the form will, which is written out in the fifth sentence.
In any case, in my opinion, I would say I have got this exam tomorrow.