My high school AP calc course started out somehow getting behind in the first week. After that, the teacher kept assigning homework for material we wouldn't even cover until the day it was already due to be turned in. It was pretty brutal for someone like me who was accustomed to coasting through all of my other courses.

I took a bit more math in college. It wasn't easier; the professor simply kept pace with the material. If you needed help, you had to go to a TA or the professor out of class hours (an option that wasn't really available for a high school setting).

I can easily imagine that many students who were exposed to college level math for the first time in one of those courses would flounder and drop out (though I didn't witness much of it myself).

But what incentivises the students to take a class that so many won't pass? I don't really understand the American university system but surely the sensible choice would be to take a course you're most likely to pass?

I guess its possible to learn stuff from a course you fail, but you should be able to find a course that you're likely to pass and learn something from?

It's mandatory for the degree, that's the motivation. It's typically required for all students who didn't score high enough on entrance exams or take enough math courses in high school. They also likely don't talk to their advisor and say, "I want to take something else, like prob/stat or calculus, to substitute for this requirement." STEM majors will find it easier to substitute another course than non-STEM majors (because they likely have the background to skip it from HS course work). Engineering universities and the like usually send their first year students straight to calculus, though.

It's a "weed out" class. When a huge number of people want to be STEM, but there is no way they're going to last, it's better to have a tough class that sets that expectation early, so they have time to pursue a more achievable major. In my case, huge State university, Freshman year Physics was the weed-out class. It was not advanced or (to me) particularly difficult, but there was a LOT of content, we moved very fast, and the workload was punishing. If I recall correctly, our first class was over 1000 people in a huge auditorium forum. By the time we took final exams, we were down to around 100 people.

So the 75%+ who don't pass this course don't graduate or what? They have to change degree?

I've never heard of so many failing a college algebra course, at my second university it was around 25% failing and mostly because they'd relaxed the entry requirements in order to increase enrollment.

However, for non-STEM and non-Business majors college algebra is rarely a prerequisite for any other courses so you can still continue your major without it, you do need to pass a math course before graduating though. They also have other math courses that can be used that aren't college algebra and may be easier.

At my university, CS was called math-CS, it required intenses calculus courses with a similar failure rate.

Of those who failed : ¼ retook the course, ¼ pivoted to the bussines-CS program (given by the CS department) , ¼ pivoted to bussines-IT (given by the business and management school) and as far as I know, the rest disappeared from the university.