One possible version:
Dear Mrs.Clemens,
I’m writing to make an apology to you .Much as I like your English class , I was absent from your test .Last weekend , I was happily skating when suddenly I fell by accident and had my left arm broken.
I’d like to ask you to give me a chance to take a make-up test .Please let me know when it is convenient for you after you make the arrangement .In addition , I’d also like to know your homework for me , such as the reading list for books and the essay to write .Finally , I’d appreciate it if you could tell me the requirements for homework.
I’m sorry to have to put you to so much trouble .Wish you all the best !
Looking forward to your early reply .
Your.
Li Hua