The classic description is in Frances Hodgson Burnett "A Little Princess" where a very young girl comes from India to boarding school in London. Lessons include French, music, and art as well as apparently composition and arithmetic. http://www.gutenberg.org/ebooks/146

For the US, you can look at some of the contemporary period series' books for girls. Annie Fellows Johnston wrote "The Little Colonel" series: http://www.littlecolonel.com/books : "The Little Colonel at Boarding-School" , "The Little Colonel Maid of Honor" and "Mary Ware, the Little Colonel's Chum" all tell stories of school & studies, at approximately secondary school level. There was a significant emphasis on writing, private theatrics and artistic expression. High academic rigor and integrity is stressed. Some domestic science skills are taught as well; etiquette and "honor" seems to be important but learned by modelling on teachers, not by curriculum.

In Canada, L.M.Montgomery's "Anne of Green Gables" goes on in later books to the local secondary school and then to the regional college. ("Anne of Avonlea" and "Anne of the Island"). http://www.goodreads.com/author/list/5350.L_M_Montgomery. Anne was getting a teacher's training, so her education was in English, mathematics, and Latin. Her schools were co-educational which was still a bit shocking.

And it's off topic but must be mentioned: Rudyard Kipling's "Stalky and Company" is set in a boys' private school c 1880, and is both funny and illluminating.

These are all available in the public domain and are quick reads if you're looking for period cultural immersion.