Even when angry, Hermione doesn’t use any violent or painful spells, and she indeed doesn’t pass Defence. Even with a troll coming after her, she doesn’t try to kill it.

She does.

Cool blue fires clung to the floor in small masses, surrounding a blazing pool that seemed to burn with a deadlier, hotter blue.

In one narrow circle the marble tiles were scorched and shattered by some explosive spell that only the most prodigious of first-year witches could have cast, with the last of her strength.