I decided to do a monologue from Shakespeare's King John. It is Constance's "I am not mad..." speech. Here it is for your reference:
Constance, King John
"I am not mad: this hair I tear is mine;
... My name is Constance; I was Geffrey's wife;
Young Arthur is my son, and he is lost:
I am not mad: I would to heaven I were!
For then, 'tis like I should forget myself:
O, if I could, what grief should I forget!
Preach some philosophy to make me mad,
And thou shalt be canonized, cardinal;
For being not mad but sensible of grief,
My reasonable part produces reason
How I may be deliver'd of these woes,
And teaches me to kill or hang myself:
If I were mad, I should forget my son,
Or madly think a babe of clouts were he:
I am not mad; too well, too well I feel
The different plague of each calamity."
I think I could have done better job, because I didn't quite feel in-the-moment while doing the monologue, but the teacher said I did a good job, so I was pleased. He even said I could use it for an audition!
Monologues are tough. In previous classes where we had to rehearse scenes, at least you were talking to another person so it was less intimidating than staring out at the class.
Anyway, next week we're doing another piece. Hard to believe, but I'm actually going to select another Shakespeare monologue! This time, it'll be from a comedy. Rosalind, from As You Like It. I won't have time to memorize it, but the class is really about Voice and Speech and not about auditions, so I think it'll be fine.
Here are some Shakespeare resources I found helpful as was I researching background on the monologue.
The Complete Works of William Shakespeare http://shakespeare.mit.edu/
No Fear Shakespeare (Shakespeare's text side-by-side to Modern English)
http://nfs.sparknotes.com/