From J-Novel Club:
Exams can be life-changing. Failing one just ended Allen’s promising career at the royal court before it began. Now, to make ends meet, the lowborn sorcerer must help one of the kingdom’s highest-born young ladies pass hers. Duke Howard’s daughter Tina has a brilliant mind, but the prestigious Royal Academy demands magic. Try as she might, she can’t cast a single spell, and her impairment has baffled the kingdom’s finest minds for years. With the all-important entrance exams just three months away, Allen and his unorthodox brand of spellcasting seem like her last hope to realize her dream of learning sorcery in the capital. So why does her father, the duke, want the young tutor to dash her dreams instead?