Heaven's Lost Property (2009)

S2E6 Reach a Decision! The Up and Down of Heaven and Hell

Astraea transfers into Tomoki's school and makes several failed attempts to eliminate him. Later, she joins Tomoki, Nymph, Mikako, and Sohara in a quiz contest meant to prove he isn't the "idiot" his classmates call him. The plan backfires spectacularly, and Tomoki ends up branded an idiot across the entire city instead of just at school. As Astraea grows closer to the group and starts to feel accepted, her inner conflict deepens. Meanwhile, Daedalus learns that Chaos, a new second-generation Angeloid, has been dispatched to Earth.