Firebolt by Adrienne Woods

When sixteen-year-old Elena Watkins discovered Paegeia, she also found out that dragons and magic are real. Not only does she have to learn how to do spells and wield weapons, she must tame a dragon of her own if she wants to graduate from the Dragonia Academy. She feels lost and unsure about everything. But when the King of Lions sword goes missing, she steps up and becomes one of nine pupils hoping to find it, and hopes to prove that she has what it takes to become a dragon rider and perhaps that she does belong in the world of Paegeia.