roughly at what age do Americans students take precalculus and calculus 1 ?

16 and 17 or 17 and 18

15

That question is impossible to answer. Because the level of mathematics has been "evolving". I'm 25. My teacher in high school took it when she was in high school, senior year. So I assume she was 16-17. She was an advanced placement student. I took it in college at the age of 19 as a prerequisite for Calculus. I failed that course because of I didn't attend ( I was young and stupid). However, I then took an assessment exam that would allow me to skip it because I didn't want to take it again and I passed that with an 85%. Based on what I've seen in college, many people take it in college. Since many are taking it in college, that means that they NEED it as it relates to their career. On the other hand, if you take it in high school, most likely you're taking it as an advanced placement student. To me that says a lot.

Consider this:

1) Who is going to take precalculus in high school if they don't need it?

The only people I can see doing this are the students who are really passionate about the subject, particularly because not many people like math.

2) Who is going to take precalculus in college if it's not required of them?

College students are lazy. The last thing they want is difficult class they don't understand. Unless it's required, college students won't take it.

3) Unless you need to take calculus I by freshman year in college and know what you want to do for the rest of your life by junior year high school (because you'd have to take precal 12th grade), most students don't plan for it. It's amazing to see how many college students switch their majors. Probably like 50% of them do.

15-17