How are you doing in your other classes? Will you have at least a 1.5 GPA (1.667 if you are in LSOE or CSON)? Then you should definitely follow the advice of your calc teacher and withdraw from the class. According to the "Academic Policies" posted on the BC website, you'll still be "in good standing" and won't be kicked out. But you will have to make up those deficiencies as soon as possible -- probably by attending summer school, since I would not advise overloads for a student in trouble (and your GPA will probably not be high to get permission for overloads anyway).
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To continue enrollment in a full-time program of study, a student must ordinarily maintain a cumulative average of at least 1.667 (1.5 in Management and 1.5 for the first three years in Arts and Sciences) as the minimum standard of scholarship and must not fall more than two courses behind the total number of courses a student of their status is expected to have completed (five courses each semester in the first three years and four each semester in senior year with the exception of Nursing where students take four courses in the first semester freshman year and four courses in the second semester senior year). Any student who is permitted by the deans to continue enrollment in a full-time undergraduate program is considered to be in good standing.
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You do NOT want an F on your record, as it will kill your GPA -- better to take the W:
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Students who withdraw from a course after the drop/add period will receive a grade of W. The grade of W is not included in the calculation of the grade point average.
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I hope that this is indeed just a “rocky start” and you do have your act together now and will be able to buckle down next semester. Do you know how you got so off-track? Please, please take advantage of the resources available to you through the Academic Advising Center and the especially the tutoring offered by the math dept. to help you get through calc.