Is the F for one test, the semester? Is the problem that you don’t understand the material or that you are slacking off (ex. not doing homework etc.)? I would do everything possible to improve the grade – see the teacher after school, get a tutor if you can, do extra problems, be sure you understand how to correct the mistakes you have made, utilized online resources (Khan academy is one).
If the F is your first semester grade it will hurt your applications to schools that get mid-year reports, especially when combined with your existing 82 GPA. A strong grade in AP calc could have gone a long way towards proving that you can handle college level work. I’d consider expanding your list of colleges. And keep in mind that an F as a year-end grade can be grounds for any acceptance being rescinded.