So far, I'm suspecting that Roy is going to try and ace the exam. Persia being a candidate is there to secure a position for Roy and as someone that'll concede once Roy overtakes him in terms of score. But maybe it's something else? It seems too simple...
The message that they're sending to everyone right now is that the Aveiram faction considers that the most important thing is to have the most competent candidate and that this supercedes Roy's lineage as an Aveiram.
If Roy can then obtain the best academic score, he will very effectively grab everyone's attention. First because of his achievement of getting the top score, second because Centrum will step down as a candidate while Roy takes over and third because his scores will be compared to the opposing faction candidate's scores (and as far as I'm aware Van may be popular and very impressive as a knight, but he's academically average).
Roy wants everyone to know that Aveiram's candidate is the most competent, while Spelbia's candidate has popularity with commoners. This should indeed attract the neutral noble's votes. After all, nobility has a tendency to have pride in their status and likely consider that they are best suited to lead because they are better. In essence, it will be more palatable for them to vote for a noble who is highly competent because that sends a message that nobility is competent and that their status is well deserved.
Well, this is all a start in order to ensure that his candidacy is done in the most impactful manner. He may take additional actions to increase his popularity in the next 6 months. Also, this all hinges on him getting the top score though it does seem like in certain subjects he'll perform very well.