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Will taking Multivariable Calculus look better to colleges compared to AP Calculus BC as an Engineering Major?

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I am currently a Junior taking AP Calculus AB and I qualify for taking Multivariable Calculus next year as a senior. However, the teacher who is teaching the class at my school is really harsh and is basically the devil incarnate and I do not want to deal with him and ruin my senior year. However, on the other hand, I am also worried that if I do not take the higher math course, colleges will not see that I challenged myself in high school and as an engineering major they will not see me suitable for admission. Do you think I should take Multivariable Calculus next year or should I just take AP Calculus BC next year for the GPA boost and for a light senior year? Thanks!!

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The vast majority of high school students applying to colleges, even into engineering and hard science majors, don't even have the opportunity to take Multivariable Calc in high school (nor would they consider taking BC Calc a "light" option). So no, taking BC instead definitely shouldn't set you back, as long as the rest of your schedule is appropriately rigorous for the types of schools you're applying for. BC Calc is the most difficult math course that most high school even have available to their students, so even though colleges will typically compare you to other applicants from your school, having BC instead of Multi shouldn't set you back much at all.

(Also, I'm surprised you'd even be able to take Multi after just AB—there are things you'd normally learn in BC that should be pretty crucial for doing Multi successfully.)

Hey thanks so much for your answer! I just have a few comments about your answer though so I would appreciate it if you could clarify some of my other doubts too. Basically I go to a very very very competitive high school where literally half of my grade takes Multivariable Calculus and I feel like I would be the odd one out to colleges if I didn’t take it. While you’re right about the fact that most kids don’t take it I feel like colleges will only compare me with the kids in my school.
I don’t know if I’m right about any of this so please feel free to correct me and clarify whether any of my comments were incorrect.
Also regarding my qualifications for Multivariable Calculus I have the grade for the class in AP Calculus AB but I need to take the BC Exam and get a 4 on it to Get into the class. Thanks!!
From my experience, one course doesn't usually make much of a real difference between applicants from the same school; it's more a pattern of taking easier courses vs. harder ones that colleges look for. I can't say for sure, but even considering your high school, I don't think it would have a huge impact on you. The only relevance would be as a tiebreaker of sorts with someone with your exact same profile and achievements, so if you're worried about that, then it could be a good idea to take it