If we look at the example below, on the first stave the key signature has flats. Look at the order of the flats; Bb, Eb, Ab and Db. The second last flat is the scale name, so it is Ab major. The second stave has two flats Bb and Eb, so this example is Bb major.
When working out sharps, we look at the last sharp, raise it a semitone and that gives the scale. The order of the sharps in the example below; F#, C#, G#, D#. The last sharp is D# and up a semitone is to E, so the scale is E major.
The only exceptions are F major, which has a Bb, so we have to remember this one. We also must remember that C major has no sharps or flats.
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