Hello! I am looking to apply to Duke University. I have taken 11 AP classes, but no AP math classes. Would this put me at a disadvantage? I am most likely applying for a science related major. Thanks! 
Will you have taken Calculus by senior year?
No, I have only taken pre-calculus.
Duke does not appear to assume that students will start in a math course more advanced than calculus 1, even for majors like math and engineering majors. So going in having completed precalculus and being ready for calculus 1 is fine (of course, getting admitted is the hard part).
https://math.duke.edu/math-major
http://ece.duke.edu/undergrad/degrees/planning#sampleProgram
However, if you do complete precalculus in 11th grade and calculus is offered to you in 12th grade, it is a good idea to take calculus in 12th grade.
Would taking honors Calculus instead of AP Calculus make a significant difference? Thank you for your feedback!
Yes. It definitely would. I strongly advise taking AP Calculus regardless of what you plan to major in. I’m a future political science applicant but I will take AP calculus BC next year. Rigor is very important. Just my humble opinion.
Thank you! I appreciate it.