Dear Mr. Smith,
I am indeed very sorry that I missed the eamination on International Business English Writing you gave last Friday. I feel awful about it and want you to know what happened that day. I suddenly fell sick early that morning and my parents had to send me to the hospital. Please find enclosed a copy of the medical bill.
I sincerely hope you can understand my situation and accept my apology. I would appreciate your allowing me to take a make-up examination. I will come to your office during your office hour on Monday to discuss this possibility with you. Once again, I apologize for any inconvenience caused.
yours,