A trigger could still perform this task, and may well be more appropriate depending on what methodology you use with regards to placement of business logic

This should cover it

CREATE TRIGGER exam_note ON dbo.exam
FOR insert
AS

UPDATE exam
SET e_note =
(SELECT CASE WHEN e_score <= 50 THEN 'Half'
ELSE 'Full' END
FROM inserted i
WHERE i.keyval = exam.keyval)