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Twenty sixth formers at Sir Joseph Williamson's Mathematical School in Rochester have been told to stay home and self-isolate after a Year 13 student tested positive for Covid.
Principal Eliot Hodges said those being asked to stay away until November 17 may have come into contact with the infected student but he stressed to the rest of the school that they should attend as normal.
He said the school was following the advice of Public Health England.
The school had "reviewed all the activities of the infected individual over the period of time they were potentially contagious, which was only one day" and concluded that the vast majority of students had not been in close contact with him.
However Mr Hodges said parents should be watchful for any Covid symptoms and self-isolate if they noticed any.
He also appealed to all parents, carers and family members to avoid discussing the issue on social media, adding: "This can often create misinformation and increase anxiety unnecessarily."
The grammar school has nearly 1,200 pupils.