I am studying to write the advanced harmony exam for RCM. This was never really my forte, too many things to remember. I understand how to modulate and what to use. However when it comes to writing a composition and having to modulate I get bogged down. A part of the exam is that they give you an opening fragment and you have to continue it using a modulation. My question is how do you know what key to modulate to if not indicated? Do you chose the new key first or a pivot chord? Does my question make sense?

Thanks in advance.

Most modulations are up one 1/2 step - like -

in F -

F (I chord)
Db7 (V of the new key - Gb - common tone of the 2 chords - F)
Gb

You can modulate to other keys, too, but it gets more jumpy -

F
Bbm7 (ii of new key, Ab - one m3rd up from F)
Eb7 (V7 of Ab)
Ab

I think the jazz song GIANT STEPS uses the Circle of 5ths to do modulations. You might want to study chord progressions to give you ideas. Also, chart out key changes in the bass line first, then see if there are any common tones in the melody. The more of these you have, the smoother the transition...

The most common modulation is to the dominant. Have a look at several sonatinas and you'll see how it's managed by quite a few composers.

The 1/2 step modulation bnich mentioned is commonly used in popular/contemporary church music. It's basically a common-tone modulation: the tonic becomes the third of the bVI, which then becomes V in the new key. You can do the same with other notes. For example, if you take the fifth of a chord and treat it the same way:

F (I chord)
Ab7 (the C in the F chord becomes the 3rd of this chord, which is V7 in Db Major)
Db