See Harmonized Scales for a lesson/tutorial about this test.
This proficiency test should be played with half notes at 60 BPM.
Start with the key of «C Major» so that you will only be playing natural notes.
Start with the CMaj triad lowest on the neck on DGB (the 1st inversion with the C on the first fret of the B string).
Raise the 5th in the chord to the next scale degree (G moves to A). You are now playing an Am triad.
Continue raising the fifth of each triad and progress through all the chords in the key in sixths: CMaj → Am → FMaj → Dm → Bdim → GMaj → Em → CMaj.
Once you reach the next inversion of CMaj, descend by playing chords in thirds, dropping the root note each time: CMaj → Em → GMaj → Bdim → Dm → FMaj → Am → CMaj.
Repeat the exercise beginning with the 2nd inversion CMaj with the C at the 5th fret of the G string.
Finally, repeat the exercise beginning with the root inversion CMaj with the C on the 10th fret of the D string.
When first learning the exercises, it helps trememdously to say the chord names out loud and visualize the root note movement as you play.
It is not necessary to repeat the exercise in all keys (but it can’t hurt!).
You can play the entire exercise starting on all three inversions of CMaj with half notes at 60 BPM without mistakes.
Repeat in other keys or at faster tempos.
Find chord progressions in songs you like and accompany them.