Can someone explain how to change the key signature when transposing from concert pitch to Bb/Eb/F and vise versa?

Firstly, with all these transpositions, the instruments sound lower then written, so a Bb instrument sounds a tone lower, an A instrument a minor 3rd lower, and an F instrument a perfect 5th lower.

Therefore, you have to write the parts they play from the appropriate interval higher so that they sound at the correct pitch.

So if you want a Bb instrument to sound a scale of C major, you have to write a scale of D major, i.e. write every note up one from original and add two sharps to - or take off two flats from - the key signature.

If you want an A instrument to sound a scale of C major, you have to write a scale of Eb major, i.e. write every note up two from original and add three flats to - or take off three sharps from - the key signature.

If you want an F instrument to sound a scale of C major, you have to write a scale of G major, i.e. write every note up 4 from original and add on sharp to - or take off one flat from - the key signature.

I hope that helps. It's not the easiest one to get your head round, but if every time you do it you remember that when the player of the instrument looks at a scale of C, you will hear the scale that the instrument is pitched in. Then you can work out how much higher you have to write their parts. Do the logic in reverse to do the process backwards.

I love to help on these questions, but I can't improve on BrianTrumpet's answer.

For grade 5 theory you are told the interval and direction of transposition but it's good if you can start to understand it for yourself too.

To decide the new key signature first identify the original. Then go up or down as directed to find the new tonic.
Don't worry about whether it's major or minor but take it as though it's major. If it IS minor the key signature will still be right and the accidentals will be what makes it minor rather than major.

Do you issue commemorative badges on such occasions, kenm?

Thanks, that really helps.

So you're given the instructions of which interval you need to transpose, but you do need know all your key signatures to transpose it correctly, that makes sense.

It would certainly help where you are asked to include the key signature but you are meant to know all your key signatures at grade 5 anyway and this question is just testing applied knowledge.

Have you been using a work book?
Past papers would help too once you feel you've got things in your head.