In French, to express passing an exam, you cannot use the expression "passer un exam".
Learn about the difference between "passer un exam" and "to pass an exam" in French
Look at these sentences:
Elle passe le bac, mais elle n'est pas sûre de l'avoir.She's taking her A-levels, but she's not certain to pass them.
Et l'exam que tu as passé le mois dernier ? - Hélas, je ne l'ai pas eu / je ne l'ai pas réussi !What about the exam you took last month? - Unfortunately, I didn't pass. (it)
J'ai passé le concours d'entrée, j'espère que je l'obtiendrai !I took the entrance examination , I hope I'll get it!
Passer un examen in French never means to pass an exam: it actually means to take an exam, with no implication of its outcome.
Note that you will never use prendre to say to take an exam !
To say that you passed an exam, you would use réussir (à) un exam/ obtenir un exam / avoir un exam.
See also Avoir un exam = To pass an exam (French Expressions with avoir)
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