Dear Mr.Smith It was a pleasure having you teach us English Speech last term. I am writing to invite you to be a judge for the upcoming English speech contest. You have more experience in English speech than the other teachers. The enthusiasm and extra effort that you make to engage with your students really helps them to improve. Being a judge would require giving comments and advice to the participants. The competition will be held at the Center of Students' Activities, at 18:00, on December 21. I look forward to your participation and I am convinced that, with your support, the contest will be a success. Please reply at your earliest convenience. Yours sincerely, Li Ming

In the future, you'll have better luck getting corrections if you post paragraphs under NOTEBOOK instead of ANSWERS. But since you have relatively few mistakes, I will help you. Dear Mr.Smith (American English uses a comma after a salutation; British English doesn't) It's great to recall your teaching us English Speech. Today, I am writing to invite you to be a judge for the upcoming English speech contest. ('quite' isn't normally used in a sentence like this. Look for redundancy and wordiness. There's no need to say something is in the past when you are recalling it. 'I' is always capitalized.) Compared with other teachers, you have more experience in English speech. It is your effort that motivates students to learn English and help them do better at it. Accordingly, it is necessary for you to be the judge and give comments and advice to the participants. The competition will be held at the Center of Students' Activities at 18:00 on December 21. (It's more concise to say "motivates" rather than "arouses the enthusiasm of". "Advice" is noncountable.) I am looking forword to your attendance. I am convinced that, with your support, the contest will be successful. Please reply at your earliest convenience. (Avoid beginning sentences with "And" where possible. Avoid an unnecessary passive voice.) Yours sincerely, Li Ming