In asking a question, which is preferred, “Did you know?” or “Do you know?”
Knowing can be roughly sub-divided as knowing how to and knowing that. If the question is about knowing how to, then the normal ‘rules’ apply when deciding on the appropriate tense.
Do you know how to make sushi? (present tense)
When you started school did you know how to tie your shoelaces? (past
When knowing means knowing that, then the past tense is used for knowledge that existed in the past:
Did you know that she was married when you asked her to dance?
You can use the present tense for present knowledge:
Do you know that the meeting has been cancelled?
However, it is also very common to use the past tense idiomatically to refer to present knowledge. So there is no problem asking:
Did you know that the meeting has been cancelled?
The past tense is often used when the questioner expects that the listener does not in fact know. For example, see these three questions from the first page of Google results for “Did you know that …”:
Did you know that he’s Bob Dylan’s son?
Did you know that the iPhone 2G is a collector’s item?
Did You Know That Earth Is Getting Lighter Every Day?