" I blew the question about it" is a slang term for "I got the question wrong/I made a mistake"

The speaker lost an opportunity to get the answer correct. To loose an opportunity is to blow an opportunity. You can blow just about anything that could easily go write if you just more prepared. I blew my chance during the interview because.... (something you were unprepared for) I blew my chance with the girl I had a date with because.....(something you were unprepared for) I blew my opportunity to be in the newspaper when I said .... (something you should have not said)

"blew the question about it" in this sentence means that this person is sure that his answers were incorrect during the exam. "blew" in a sense means that you "made something wrong"

look at your own sentences : I really blew the question about it on the mid-term exam. I want to do better on the final exam. the second sentence has clue to help you understand what is the first. I mean when you say you want to do better in the next exam it means your previous was not good or even awful. so: - I really blew the question about it on the mid-term exam means: - I made mistakes answering the questions. or - I was doing bad on my previous exam. ;)