There is no supplication in the Sunnah called 'the exam dua', but there is something more useful: supplications for steadiness, for an expanded chest, for ease of speech and understanding — exactly what someone being examined needs.
First among them is the supplication of Musa when given the heaviest of tasks: 'My Lord, expand for me my chest, ease for me my task, and untie the knot from my tongue that they may understand my speech.' Four requests: composure, ease, fluency and comprehension.
Supplication does not replace study, nor study supplication. Tie the camel, and trust.
رَبِّ اشْرَحْ لِي صَدْرِي وَيَسِّرْ لِي أَمْرِي وَاحْلُلْ عُقْدَةً مِنْ لِسَانِي يَفْقَهُوا قَوْلِي
Rabbi ishrah li sadri, wa yassir li amri, wahlul 'uqdatan min lisani, yafqahu qawli.
My Lord, expand for me my chest, ease for me my task, and untie the knot from my tongue that they may understand my speech.
رب اشرح لي صدري ويسر لي أمري واحلل عقدة من لساني يفقهوا قولي
رَبِّ زِدْنِي عِلْمًا
Rabbi zidni 'ilma.
My Lord, increase me in knowledge.
رب زدني علما
اللَّهُمَّ لَا سَهْلَ إِلَّا مَا جَعَلْتَهُ سَهْلًا، وَأَنْتَ تَجْعَلُ الْحَزْنَ إِذَا شِئْتَ سَهْلًا
Allahumma la sahla illa ma ja'altahu sahla, wa anta taj'alul-hazna idha shi'ta sahla.
O Allah, nothing is easy except what You make easy, and You make what is hard, if You will, easy.
اللهم لا سهل إلا ما جعلته سهلا، وأنت تجعل الحزن إذا شئت سهلا
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The supplication of Musa: 'Rabbi ishrah li sadri, wa yassir li amri, wahlul 'uqdatan min lisani, yafqahu qawli' (Ta-Ha 25–28).
