Dear Mary,
I would like to apologize to you for my absence from the gathering in your home yesterday. I had hoped to join you and have a wonderful time together, but I didn't show up.
Last semester, I failed the final exam of American Literature, so I have been preparing very hard for the make-up exam in the past few days, and stayed up very late the day before yesterday. As a result , my mind went blank, and I forget the invitation you had sent.
I feel extremely sorry about it and hope you can accept my sincere apology, If it is convenient for you , shall we meet and have dinner together on Saturday evening?
I'm looking forward to your reply.
Sincerely yours,
Li Ming