Name the key

A signature with no notes after it still says something: which key the music is in. Two keys, in fact — every signature is shared by a major key and its relative minor.

Sharps: the last sharp is the 7th of the major key, so the key is one semitone up from it. Three sharps end on G♯: A major.

Flats: the second-to-last flat names the major key outright. B♭, E♭, A♭ — the middle one says E♭ major. One flat has no second-to-last; that one is F major, learned on its own.

The relative minor starts on the 6th of the major: A major and F♯ minor share three sharps.

last ♯ + semitone = major · second-to-last ♭ = major · minor = its 6th

Three sharps, F♯ C♯ G♯: A major, and F♯ minor with it.

Practise this in the trainer — it opens with this lesson the first time the concept comes up.