Someone I work with asked me whether 'I did studying' is a correct sentence. Initially I told the person that is was incorrect. Then I tought about it and realized that it is common to say 'I did some studying'. For example, if someone says ' What did you do last night?' - 'I did a some studying, I did a bit of reading etc..'

Are both 'I did studying' and 'I did some studying' correct? If only the second one is correct, why is that?

Thank you.
1. I did some studying.
2. I did the studying I was supposed to do.
3. I did my studying.
4. I did studying.
5. I did homework

In [1], "studying" is being modified by the determiner "some" to indicate a quantity greater than zero. It's being used as a gerund (noun).

Similarly, in [2] and [3] "studying" is being treated as a noun.

But "studying" isn't a true noun. When it is the object of the verb "do", it needs determiners such as "some", "the" and "my" to identify it as a noun. Otherwise, its function becomes that of a verb. In [4], it is being used -- incorrectly -- as a verb.

"Homework", on the other hand, is a true noun, and therefore [5] is correct.

The correct past-tense form of this sentence is:

I studied last night.

If you wish to emphasize that you studied as opposed to doing something else, you can use the intensive form, which is the addition of "do" in an affirmative sentence:

I did study last night.
"i did study"
 taiwandave's reply was promoted to an answer.