All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
It is not permissible for you, dear brother, to combine the Jumu‘ah (Friday) prayer along with the ‘Asr prayer, even according to the view of the scholars who say that it is permissible to combine prayers for the resident [non-traveler] for a need, such as the Hanbali School, as they do not permit combining the Jumu‘ah and the ‘Asr prayers.
The optional time of the ‘Asr extends until the time when the sun has a yellow gleam, and also until sunset when necessary.
So try to finish the exam before the expiry of the time of the ‘Asr prayer, and pray it before sunset.
Allah knows best.