You are looking for the :hidden selector
Please note that the proper way of selecting an element by ID is simply:
$("#test1");
Doing it the way you are doing is making jQuery do unnecessary parsing and is much slower.
If you want to select #test1 only if it is hidden, you do this:
$("#test1:hidden");
If you wanted to select all <span> elements that are hidden under #p1, you do this:
$("span:hidden", "#p1");
As noted in the comments, the opposite of this selector is the :visible selector:
$("span:visible", "#p1");
Would then select any visible <span> elements in the element #p1.