Arpeggios are not part of the ABRSM music theory syllabus, but they are included in every Trinity music theory grade.
If you take a practical (instrumental) exam , you will probably have to play arpeggios. This page explains how to play them.
Arpeggios are just broken chords which usually go up to the tonic (key note) and back down again.
If we use a chord of C major as an example, we’ll see that the notes we need are C, E and G.
To create the arpeggio, first we play these three notes, one after the other and starting on the lowest note:
Then we add another tonic note (or “key note”) at the top, to make the arpeggio sound finished:
And then we come back down again, playing the same notes but in the opposite direction:
Let’s think about rhythm next. Because there are three different notes in the chord, in exams we usually play them in groups of threes, and make the last note nice and long to finish on, like this:
Arpeggios can be played over any number of octaves, but in an instrumental exam you’ll need to know how many octaves you’re supposed to play. Check the exam syllabus.
Here’s a C major arpeggio over 2 octaves:
In later grades, you will probably be asked to play dominant 7th and/or diminished 7th arpeggios. These chords are made up of four notes, so we play usually them in groups of fours, not threes.
Dominant 7th arpeggios are built on the dominant note of the key you are in. For example, in C major, the dominant note is G. The chord of G major is G-B-D. To this, we add the note which is a seventh higher than G, which is F. So the dominant 7th arpeggio in C major looks like this:
Diminished 7th arpeggios are described simply by the note they start on. Diminished 7ths are built with minor third intervals. If we start on B, then the next note (a minor third higher) is D, then F, then Ab. Here’s a diminished 7th arpeggio starting on B:
Notice that if you start on D, then the arpeggio contains the notes D-F-Ab-Cb. Cb is another way of “spelling” B (it’s an enharmonic equivalent). So the notes of the arpeggio will actually sound the same. Starting on F, we get F-Ab-Cb-Ebb (Ebb=D). In fact, there are only three unique diminished 7th arpeggios.
In later grades you might also have to play arpeggios in different “inversions”. This means you don’t start on the tonic, but on one of the other notes of the chord. “First inversion” means you should play a C major arpeggio from E-E, instead of C-C, and “second inversion” means you should play it from G-G. The normal way, C-C is called “root position”. Chords with four notes in them, like diminished and dominant 7ths, have a root position and 3 inversions.
You can buy books which have all the required scales and arpeggios printed out (with fingerings if appropriate) for each instrument in the graded exams. They’re very useful for reference if you’re taking instrumental exams.