I just took the SAT and there was one question I wasn't sure. What's difference between verb-ed and did+verb?
For example, I did become = I became ? Past Tense?
I've just Googled did + verb and got this hit on the Merriam Webster Learners Dictionary which points out that, in the case of the did + verb construction, only the auxiliary verb (to do) is in the past tense while the main verb (to become in your example) appears in the present tense. This in contrast to the past tense of to become which is became. I suspect that this is what the SAT question was looking for, although there might be more to it which you have not given us.
I've answered your question because you are a new contributor but there are a couple of aspects to your question which, strictly, make it off topic for English Language and Usage. Firstly it is, really, more suited to the Stack Exchange English Language Learners forum because it's fairly basic. Secondly you could, and perhaps should to keep your question on-topic, have done some research before posting. You might well find that the moderators close or migrate this question. If you have a more on-topic question in the future it would be good to see you again.