I recently applied for a job and found out I got the job this week. I have to undergo a background check and send my transcripts. I included a course that I had taken but failed the exam on my resume. This course is not a requirement for the job but I’m concerned now he will see I didn't pass and because I included it on my resume when I should not have they will rescind my offer. I don’t know if my best bet is to be honest or hope they don’t notice. I will add that I have passed the course I need for this job. Do I bring it up and say it was a mistake?
Read very, very carefully what you wrote in your CV. You said you took the course. Did you learn something useful in the course, or was it a waste of time? And what exactly did you write in your CV? Did you give an indication that you took and passed the exam?
If you did not mention anything about taking the exam, and it would be reasonable for someone to take the course with the intent of gaining knowledge, then you could say something like "I re-read my CV, and I think what I wrote about this course could be misleading. I took the course out of general interest, because I believe what it teaches will be useful in my career, but I never had any intention to pass the exam". Expect questioning.
Does failing the exam mean you failed the course? If it does, then obviously this will come up on your transcript, and they will find out anyway. The best you can do for yourself right now is to come clean. It is probably the only chance you have of not losing the job you just acquired.