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An apology letter for failing the math exam.
Dear teacher XXX, hello:

This math exam, unfortunately, failed to complete the passing requirements, which lowered the average score of the class math exam. I feel very sad and embarrassed. Mathematics has always been one of my hard-working courses. I study with the mentality that hard work will pay off, but I always miss the exam. The failure of this exam proves that I still don't study hard enough and the method is still wrong. While apologizing to the teacher, I also promised to study math well, correct my previous wrong learning attitude and correct my wrong math methods. I also hope to learn from students who have good math scores and ask them for advice. I also hope that the teacher will not give up on me and give me more care and support. I believe that with the efforts of teachers, classmates and myself, I will definitely get good grades in the next exam.

Please believe me and accept my deep apologies. At this point, it is useless to say more. Please look at my efforts and my future achievements. Thank you again for your hard teaching. I hope the teacher will urge me to study more and be strict with me in order to improve my math scores. Thanks, teacher.

A classmate

Any day