1.表达自己对未能按时交论文一事的歉意
2.说明未能按时交论文的原因。
3.表示自己将尽快补交论文并保证以后按时交作业。
范文：
Dear Mr.Wang,
I am writing you this letter to apologize for my failing to hand in the paper on time.I am very sorry for the inconvenience brought by my delay.Please accept my sincere apology with gratitude.
The reason for my delay was the I was knocked down by a cold.Moreover,I had a fever and was too weak to write a single word.Therefore,it's not in my power to finish the paper on time.I hope you could understand me and excuse me for my delay.
I will do my utmost to finish my paper and hand it in as soon as possible.In my opinion,the importance of punctuality you cannot be emphasized too much,so I assure you that I will hand in my homework on time from now on.
Sincerely yours
Yu Ming
