"yours faithfully" is very old fashioned, it's something you would expect to read from a 80yo aristocrat. "Sincerely yours" is what I would use, and expect to receive, in a (very) formal letter. You can knock it down to 90% formal by just saying "sincerely" (without the "yours"). In business/semi-formal settings, you could write "best regards"/"kind regards". (This is from experience. Obviously, exams sometimes go by their own rules. It is possible that the person who prepared the IELTS rulebook is indeed an 80yo aristocrat who expects to see his arcaic language in everyday use! Maybe someone who has recently passed IELTS might have different advice)