I have my Certificate of Merit test in a few weeks and I have to be able to play 13 arpeggios from memory. I have no problem with memorizing scales or anything else but I cannot seem to memorize arpeggios. It's not as if I don't know what the notes are supposed to be its just that they never come out right when I play them. I kind of play by ear so that might be some of it. I don't know. Does anyone one have any suggestions? Thanks

My suggestion is that you should try singing them mentally, as if they were melodies (as they are). So the first step is learning to sing all those "melodies" by heart, without errors.

Your fingers should then automatically follow the melody, more than the mechanics of them.

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This was a recommendation I received from a professional horn player. And it works for me!

Slow down, play them with the notes/music in front of you, with your metronome ON. Play one quarter note per second, or tempo of quarter note = 60 (largo).
Using the metronome is important to your brain's understanding, don't simply go a particular speed, tapping your foot. Turn the metronome ON!
Make sure each note comes through with good tone, and with proper pitch. (turn on your tuner, also, and pause occasionally at the top or bottom of the arpeggio to tune that note).
Go through all the arpeggios at this speed, as long as you can always hit the correct note.
As you can keep pretty tone and pitch, speed up a little bit until you are messing up the notes, then go back to the next SLOWER metronome setting and go through them all at that setting. Make sure you go through all the arpeggios at least two or three times at this comfortable speed before you try to speed up again.
You will find a point when your fingers and brain have learned the arpeggios, after a week or so of this careful practice.

Once you have learned the arpeggios, and can play them in sixteenth notes at quarter note= 60 or =80, note that particular speed. During your test, go SLOWER than that. Your brain is otherwise occupied with being nervous (if you have a normal test or performance anxiety) and can't go as fast as it can during practice.

Try making up rhymes in your head. I play the trumpet and for the concert F scale which is really G I go:
13, 2, 13, 0, 13, 2, 13 and add a tune for it for the fingerings. I had trouble with these too until I tried this. Hope it helps!

Wooot!!! That was the easiest thing for me the arpeggios. Try to play it really really slowly!!! It's in my fingers. Some people they don't have it. I would suggest you to play first the scale. Let's say D major. From the tonic note to the third octave. (Tonic to tonic). After that play its relative harmonic minor!!! Which is B minor. Play the apreggio in D+ and play the arpeggio in B-. If you make a mistake it's ok just go ahead. Don't overplay it. I really really really really recommend to buy techique a book!!!! It is really good!!!! M. A. Reichert - Seven Daily Exercises Op.5. Play it slowly. Stop on the upper note take a breath and start it again on the upper note and go down. It is in major and melodic minor too. Excellent exercises for warm up and for fingering!!! Play it slowly! And you're going to feel it in your fingers!!! )) And also the speed will come by itself!

I know it's not about the speed, but in this book everything you need is included! and it is only 9 dollars! carl fisher edition.