Your sentence is neither correct, nor an example of second conditional. Second conditional is for unreal situations. The situation with your daughter is real.
Your example has an unknown past condition (whether she studied), a past result (the finished test), and a future reveal (when the results are published). This is a very complex set of things to put into one sentence. If you're not yet comfortable with second conditional, then this might not be the right example sentence to learn from.
But here goes!
Depending on how much detail of the situation you want to include in the sentence, choose from among these:
- "If she studied hard for the exam, she will have passed."
This sentence captures all the detail, including that she may have studied in the past, that the exam is finished, and that the results will be published in the future. It means, "When the results come out, if she studied for the exam, we will learn that she has passed."
- "If she studied hard for the exam, she will pass."
This sentence captures that she may have studied in the past, and that we're going to get the results in the future.
- "*If she studied hard for the exam, she passed."
This sentence captures that she may have studied in the past, and that the exam is finished.
(Note: None of these conditional sentences are part of the standard 1st/2nd/3rd conditional etc. For more info on this, see this answer to a similar question)