Tonight, after 3 months of preparation, I took the exam. Not only did I passed pass it, I aced it.
The previous reply mentioned 'inversion' in questions, but entirely omitted to mention exactly why it occurs in your example even though it is not a question. The answer is that it has nothing at all to do with the inversion that occurs in certain kinds of questions, but is entirely due to the presence of the word "only". I'll explain:
Subject-auxiliary inversion occurs in declarative clauses only when certain types of element are put in front position. Negatives are one very obvious type of element that trigger subject-auxiliary inversion when fronted:
Never had I seen such chaos. At no stage were they in danger.
"Only" is not negative, but it is semantically close to a negative, in that "Only John liked it", for example, entails "No one other than John liked it". The inversion is also found with some items that are not similar to negatives:
"John enjoyed it and so did Robert".
So that is why your sentence, even though it is not a question, exhibits subject-auxiliary inversion.
Perhaps, Mr.Matthews, if you remembered that others view replies to questions, you might have given a fuller understanding of the 'why' it's 'pass' not 'passed', in your first response. There are others who view responses to questions, including non-native speakers with varying levels of English. Your bald statement as to the correct tense lacked consideration for them.
It seems my efforts, at least, do goad you to expand, even though your motive is more a rather ugly competitive spirit.
My first response gave the required answer to the core question, i.e. that the plain verb-form "pass" is required as a result of the presence of the dummy auxiliary verb "did". The reason for its presence in the OP's particular example is a little complex (it has nothing to do with questions) and one that I could have explained but chose not to for fear of confusing the OP.
Nevertheless, had you managed to explain why subject-auxiliary inversion occurs in declarative clauses, I would have passed quietly over your answer without comment. But your answer was defective in that it focused entirely on inversion in interrogatives (questions), which is irrelevant here since the OP's sentence is a declarative one, not an interrogative one.
You made no mention of certain elements triggering inversion when fronted; more specifically, you gave no explanation at all as to why the word "only" can trigger inversion when it is fronted, yet its presence in the OP's example is precisely the reason that it exhibits inversion!
If you intend to explain subject-auxiliary inversion, at least do so adequately, with a fully supportive explanation of why it occurs in declarative clauses like the one cited by the OP.
However, we can only assume that your omission of crucial points in your answer is due to the fact that you are clueless about this aspect of English grammar.