@likefireworks The shorter answer is that a 5 on BC should clear your mathematical sciences core requirement (for majors that don’t require a third quarter) and that you will have the option/be encouraged to try the 160s. I also took multi my senior year without a proof-based background, but am doing alright in 160s. In fact, few incoming first-years have ever taken multivariable calculus, and even fewer have been truly exposed to proofs (geometry stuff doesn’t count). With that, I would encourage you to at least give proof-based mathematics, which all the math majors and myself argue is “real” math, a chance. You’ll have to do some proofs in 150s anyway, but they will be far fewer in number. You can also drop from the 160s to the 150s, and there is a 2-week add/drop period where you could try out 160s and switch to the 150s if you decide that proofs aren’t your cup of tea.
The longer answer includes an explanation of the testing and placement process. There are two math placement exams; the first is over the summer, and maybe all you should review is some formulas if you’re like me and tend to forget them. The summer exam can place students into 153 at the highest, and placement is determined via a combination of your test score, your SAT scores, high school courses, and AP credits, so even if you screwed up some formula-related stuff on the placement test but have good calculus grades and scores, you’ll still get 153 (I know this from experience lol). It is a fairly final placement unless you intend to take the second, much more difficult placement exam during the beginning of O-Week (orientation), which is pretty much entirely calculus (including some basic multivariable) as well as some proofs. Students are strongly encouraged to take this exam if they have taken calculus before.
The second exam is an opportunity to say “I know more math than I remembered over the summer” in case you didn’t get the placement you wanted at first. This is the exam that determines whether you are “encouraged” to take 160s, to take 199 (which you’ll get if you know/remember ALL of your calculus but don’t know how to write proofs yet), or Honors Analysis (only the strongest first-years who already know how to write proofs are placed there). The results are based pretty much entirely on your test score alone. With this, if you still don’t get the placement you want, you can talk to John Boller, who’s a big and awesome guy in the math department, or whoever’s designated that year, really, and the person will sort of test you on the spot and decide if you indeed should be at a higher placement or should stay where you are. I don’t believe it is possible, or at least is extremely rare, for any exam to make your placement any lower.
The only difficulty, really, is placing higher. Taking 150s is no problem if you don’t want to take the 160s. And yes, you can jump straight to 153 if you have the required AP credit. You’ll see all the above information over the summer and again during orientation week.
My suggestion to you specifically, but again, only a suggestion, is to not let your lack of background in proofs deter you from taking the 160s. If you’re not going to take the 160s, do it either because 1) you’ve tried a bit and are genuinely not interested in it, 2) are certain you are not going to need it for your major or 3) don’t think you’ll have the time. As I mentioned before, nearly everyone who does the 160s has no proofs background since it’s rarely taught in American schools, so if you have the time to put into the course (the math department claims the average is about 10 hours a week for the normal Honors Calculus sequence), it’s worth a try. Even if you’re not a stem major, it could be fun/worth it: one of my friends who will definitely be majoring in some sort of humanities is taking it and doing well. It’s just like learning a new way of thinking, which is what learning any field outside your comfort zone is about, really, and I encourage you to try it. As someone who used to be terrified of and very unconfident about math, I think I have at least some authority to say this to you lol.