Are students even required to take a math class at Duke? Many colleges require 1 or 2 quantitative classes as part of distribution requirements but usually there are options that aren’t pure math and are designed for those students not so mathematically inclined. Some students never take a math class ever again after high school.
It’s not unusual to be lopsided on test scores. Sounds like the OP has done well grade-wise in high school math classes.
An 18 on math means you do not meet the college readiness standard. That is going to make the schools on your list that are not test optional almost impossible. Test optional schools are the way to go.
As @suzy100 so kindly posted back on post #12, the OP has an opportunity to take the ACT again (or the SAT) in late Oct/ early Nov and submit those scores. Some heavy studying on the math section between now and then and even some tutoring would be key.
Good thing I’m not majoring in anything STEM related 
Duke (Trinity) does have a requirement for math. However this can be completed by taking a Comp Sci class or even Stats.
http://trinity.duke.edu/undergraduate/academic-policies/curriculum#areas
Listen, 18 on math is not the end of the world. Just need to convince them that you have strengths in other areas.
The legacy pull is pretty strong at Duke. Statistically your chances are approx 50% higher than compared to non legacy students. Dean Guttentag revealed publicly that the acceptance rate for legacy kids is approx 33%.
I suggest to apply ED and at the same time work on raising your ACT score. Even if you get deferred, a higher score in the RD round may be enough to tip you over the edge. If you can get your math score into the mid 20s your composite will be 30+.
But if you wait until RD there are literally only about 800 spots left. And 35,000+ people applying for those. Being legacy doesn’t help much in RD.
I agree with all the advice here. Go for it, but have real safety options that are predictable. My son applied ED to Pratt with a 32 composite and he was sweating it big time, as anyone should who’s applying to these almost-impossible-to-get-into-schools. He was accepted but he had a friend with a 35 composite who was not. This shows that it’s not all about scores (as you probably already know), but imho, without a hook you better be at least at the lower level of the average score for admission and a 28 is below it. My concern is that your great essay and extra curriculars may not be considered or considered so secondary to your score that you’re selected out.
If your school is a feeder school, and you are legacy, and you have a decent GPA, and you can contribute to sports, with a low ACT, you still stand a chance, but may be deferred and accepted in the regular decision round. Everyone has a vulnerable spot on their app. I’d still retake it in case somehow you end up on a wait list and they invite you to update them and shore up any weaknesses.
OP isn’t being recruited for sports so no bump there. Shows leadership but that is all.
@neonpinklime wrote:
I don’t think this will happen. Let me explain why. Duke has publicly stated that there is no ACT/SAT cut-off. So there is no lower limit.
But there is a widely known category known as “auto-admit” or “auto-deny”. If you want details please read Rachel Toor’s book on the topic. Rachel was a former Duke admissions director. The Auto-deny limits change from year to year. My guess is that the auto-deny sum is around 45 for Trinity.
Based on the OPs info, here is my guess for scoring on the 6 factors
HS Curriculum: 5 x 2 = 10
Achievement: 5 x 2 = 10
Recs: 4-5 x 2 = 8-10
Essays: 5 x 2 = 10
ECs: 3.5 x 2 = 7
Test scores: 1.5 x 2 = 3
Total: 48 - 50
So the OP will most likely be above the auto-deny threshold. The auto-admit cutoff is usually around 55. This means OP’s application is headed for committee. Its a total wildcard on whether committee will overlook the low ACT score. My guess is that they will understand about some students not being good in Math. As long as the OP can offset the application with other areas of excellence, I think he/she stands a chance.