Firstly, adopt the means of ensuring that you do well by working hard, and thereafter place your trust in Allaah Ta'aala without relying on your own intelligence or efforts. This is the perfect recipe for good results inshaAllaah.
There are no specific Duas mentioned in the Ahaadeeth for passing an examination. However there are certain Duas that our elders have suggested.
Before studying you may pray:
Allahumma infa'nee bimaa 'allamtanee wa'allimnee maa yanfa'unee. O Allah! Make useful for me what You taught me and teach me knowledge that will be useful to me.
Innaka 'alaa maa tashaa-u Qadeer wa anta hasbun-Allahu wa ni'mal wakeel. (O Allah!) You do whatever You wish, and You are my Availer and Protector and the best of aid.
After you have finished studying pray:
Allahumma innee astawdi'uka maa qara'tu wa maa hafizhtu. Faruddahu 'alayya 'inda haajatee ilayhi. Innaka 'alaa maa tashaa-u Qadeer wa anta hasbiya wa ni'mal wakeel. O Allah! I entrust You with what I have read and I have studied. (O Allah!) Bring it back to me when I am in need of it. (O Allah!) You do whatever You wish, and You are my Availer and Protector and the best of aid.
Please do take the time to refer to the links below for more duas.