Why won't my sister leave me alone? I just want a bit of time to myself and she won't respect that. She just keeps persisting to the point where I just feel like screaming! She just refuses to get out my room and talking to her gently won't help. And yet sometimes when I want to spend time with her she doesn't exactly welcome me. And please don't say I start it off because I don't. What can I do to convince her that I just don't want her company at the moment and not have her persisting and begging me to let her stay with me?

She does it because that's what younger siblings do. Puppies do it with older dogs; most of the animal kingdom (to which we belong) does it. It's part of learning, and often is a mixture of idolizing and challenging. She'll grow out of it, but meanwhile it sounds like you have a pretty good attitude with being patient, being firm, trying various ways short of throwing her out of your room. Ask her, does she want an older sister who gets held back for flunking and is the laughing stock of the whole school all because she won't let you study? Work on some clever responses. Bribe her too - offer to walk in to town for an ice cream on Saturday if she leaves you alone for 3 days.

It's all apart pf being an older sibling. It gets better,
I adore my younger sister now. She is my best friend