The OP did not say BC. I am not aware of any US college or university that specifies BC or higher math (as opposed to the few US colleges or universities that specify “calculus” as required or recommended for some or all applicants).
But it looks like the OP’s student is in an accelerated algebra 2 course which allows going directly to calculus if the student does well enough in it. So if the student does well enough in the current math course, the student will be able to take calculus while in high school. I.e. it does not look like there will be a problem here, unless the space in the calculus course is rationed unreasonably (i.e. less space available than the number of students whose achievement in accelerated algebra 2 indicates readiness for calculus) or is based on something other than student performance in the accelerated algebra 2 course.
Even if the student does not enroll in calculus in high school, the number of US colleges and universities that would be excluded is small.
As long as OP’s kid is following an acceptable math pathway at their HS, I expect they will be fine for college admissions. It is still preferable/advantageous for students looking to apply to selective/highly selective schools to have had calc in HS…and seems like OP’s kid can do that provided they do well in algebra 2.
Even though many colleges don’t state they require calc in HS, the vast majority of those accepted to many rejective schools have had calc in HS. In effect, it’s become a de facto requirement at some schools.
As as example, 85% of students admitted to Wesleyan for Fall 2023 had calc in HS…and this is a liberal arts school without an engineering major. I am not picking on Wesleyan, but they are one of the few schools that is transparent about this and share their data. I strongly suspect the 15% of admitted students who didn’t have calc in HS satisfied at least one institutional priority. I also don’t think Wesleyan is an outlier among highly rejective schools in terms of proportion of admitted or enrolled students who had calc in HS. Class Profile, Admission & Aid - Wesleyan University
Some schools are trying to back off their calc requirement/strong preference, because, well, it’s an access issue. Cal Tech and UIUC are example of schools that have instituted other ways to demonstrate math proficiency that don’t necessarily include taking calc in HS.
I also don’t know any school that has on their website that they require Calc BC, but a Lehigh AO in an admissions session (circa 2019) said they strongly prefer engineering applicants to have had Calc BC. I expect there are other schools that behave the same.
As far as college admissions is concerned, OP’s kid is fine because that’s how their sequence is. The issue really comes up after one has made the decision to attend a certain university. Each math department has its own placement criteria for their Calculus 1, and if they use a precalc-heavy placement test (i.e. lots of trig), the student may get placed into college precalculus. So OP’s kid needs to be prepared for that. I would strongly encourage OP’s kid to prep for the AP calc test . If they score high enough, they at least have the option to skip the calculus sequence. (Math professor here who has seen zero progress in the way calculus is taught at most places since the early 80’s when I attended college.)
Agree with post above and just wanted to add our personal experience. Kiddo did not take calculus or pre-Calc in hs and had no problem with college admission. Issue was that once they got to college and decided to declare a major which required calculus, the college did not offer a pre-Calc course. Calc professor strongly advised kid against taking his Calc class without having taken pre-Calc or Calc in hs, but kid had no choice and powered thru it - it was not a good experience since kid was only one in class in that situation.
As far as I know Pre-Calculus is essentially a review of Algebra 2 plus Trigonometry. At least when I was in HS, many years ago, the later semester in Pre-Cal was essentially intro to calculus where students learned to do derivatives.
HS curriculum is so varied now, it is difficult to make this generalized statement. My son takes whatever math his HS offers, but has also been taking CC Math classes since the 10th grade on currently. At least in our local CC, Calculus pre-req is either Algebra+Trignometry taken in separate semesters OR Pre-Cal taken as one 6 unit class. Which means to me Pre-Cal is basically two classes combined into one at a faster pace in the CC. Students who completed A+T are not eligible to enroll in Pre-Cal. My son enrolled in Cal after completing Algebra + Trig in separate classes.
As for the question about taking Calculus in HS to be a better engineering applicant: I’ll frame my answer this way: CalTech asks its applicant to certify Calculus readiness by either showing it’s in progress at HS or CC or the applicant completed a Kahn Academy course (in case student claims Cal is not offered and they struggle to take the class). MIT says its applicants have completed the most rigorous curriculum offered. UT Austin wants a certification for math readiness that by Dec 8, applicants have already completed Cal in HS or College with a grade of B or better (or you can submit SAT/ACT scores instead).
On the other hand, you have places like Calpoly Pomona that will grant math credits for engineering even if you have taken easy CC math classes designed for life science majors (this is an anomoly BTW, I have not seen this level of laxity in other schools).
Most students take Cal 1 as Freshman. Majority of these students have already taken Cal in HS and happily repeat the class hoping for an easy A. But that easy A is never really that easy.