Is the sentence right or wrong?
Has Karen already prepared for the exam?
We use the present perfect, when the action has happened recently and it is important for the present moment.
Remember these words-indicators of the present perfect:
just — a short time beforealready — before we expected, (!) only in positive sentences yet — like "already", (!) only in negatives and questions
He has just called the police.
We have already had breakfast.
Have you started the exercise yet?
My friends haven't arrived yet.