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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