In what context are "going to" and "supposed to" the same? "Supposed to" merely means that he is expected to go, not that he actually will. See: "He's supposed to take the examination next week, but since I haven't seen him studying at all, I think he's forgotten about it (and thus will end up not going unless someone reminds him)".
"It turns out he needs to take the exam. He's supposed to take the examination next week"
He is required/ expected to.
"It turns out he needs to take the exam. He's going to take the examination next week"
Same first sentence. Means that he is going to take it or, roughly, 'he said he'll take it' type of attitude and tone..
"He has been studying for weeks, and he is going to take the exams next week"
^Shows that he is prepared. 'Because he studied, he is going to take the exams'
"He didn't study at all, and he is suppose to take the exams next week."
^Shows that he is not prepared, but is suppose to take exams. 'He is suppose to take the exams next week, but he didn't study."
Hope that helped. Your post kinda confused me, but English is my best subject so..