All in 11 ,12 ncert
Find a good teacher of maths in your area for your sister and ask her to start solving prmo questions. She will learn new things by solving questions. In case of doubts ask her to search the question on internet. Hardly there would be a single question which doesn't has solution on internet. If you are not able to find you can post it here. I am there to help you.
From practicing new questions she would know new topics which she can ask a teacher or search about it.
After solving prmo paper i would suggest her to solve AIME papers.
Challenge and Thrill of Pre-College Mathematics
Indian National Mathematics Olympiad by rajeev manocha
also if you read both of these try MAA Problems by Evan Chen