GROUP BY
doesn't do what you want - particularly not like that. Have a look here:
SQL GROUP By and the "Column 'name' is invalid in the select list because..." error[
^] which explains what it does do!
You need to think about your data and what you want to retrieve:
"Passed test"
and
"Latest date"
So do that:
SELECT TOP 1 Name, TestStatus, ExamDate FROM Exam
WHERE TestStatus = 1
ORDER BY ExamDate DESC
TOP 1
says "return only the first value", the
WHERE
restricts it to passed tests, and the
ORDER BY
controls the order in which rows are returned.