Dark Companion by Marta Acosta

 When foster teen Jane Williams is invited to attend elite Birch Grove Academy for Girls and escape her violent urban neighborhood, she thinks the offer is too good to be true. She's even offered her own living quarters, the groundskeeper's cottage in the center of the birch grove.

Something's not quite right about the school -- or is it Jane? She thinks she sees things in the birch grove at night. She's also beginning to suspect that the elegant headmistress and her sons are hiding secrets. Lucky is the gorgeous, golden son who is especially attentive to Jane, and Jack is the sardonic puzzling brother.

The school with its talented teachers and bright students is a dream for a science and math geek like Jane. She also loves her new friends, including hilarious poetry-spouting rich girl, Mary Violet. But the longer Jane stays at Birch Grove, the more questions she has about the disappearance of another scholarship girl and a missing faculty member.

Jane discovers one secret about Birch Grove, which only leads to more mysteries. What is she willing to sacrifice in order to stay at this school...and be bound to Birch Grove forever?