to sit for the exam, to sit the exam = to take part in the exam
http://books.google.com/books?lr=&hl=zh-TW&q=sit+the+exam( sit the exam)
http://www.merriam-webster.com/dictionary/sit
to sit a baby = to take care of a baby as a baby-sitter
18.
Informal. to serve as baby-sitter for: A neighbor can sit the children while you go out. ( definitions from dictionary.com