Indeed. I guess it doesn’t surprise me that some high school, somewhere, offers them, but I’d expect it to be very rare. (FWIW, one year I had a high school kid in the Calculus III and Diff Eq classes at the college I taught at; but that was the exception rather than the rule.)
When I was in high school (1980s), there were a handful of us who were ahead in math and took Calculus our junior year. For our senior year, they put together a class that included a quarter each of differential equations, abstract algebra, statistics, and number theory. We didn’t go deep into any of these, but it was a nice taste of higher math; and between that and the unusually theoretical approach the high school Calc teacher took, it set me up pretty well to major in math in college.
Back in the 90s I served on a state-wide math textbook adoption committee and we approved a text for Discrete Math. I took studied that subject as a junior in college.
As for individual achievements, I know a person who is now an applied math PhD working in private industry that by the time he entered college had already taken so many college level math courses that he was a Calc. I teaching assistant as a freshman. His mother was a college professor in psychology and even in high school had taken so many IQ tests given by his mother’s grad students that he guided them in the proper administration of the test. Nice guy. I enjoyed working with him.
My high school had Trigonometry, AP Calculus, AP Statistics, and AP Physics. Successful completion of the AP (Advanced Placement) courses resulted in transferable college credits.
You didn’t have to take the test?
My school (California, '92-96) didn’t even have basic calculus offered officially. However, they arranged for the local community college to teach Calc I and II at the high school. The credits were recorded to the CC, not the HS. And we had to pay CC tuition.
I just checked my high school’s curriculum; they’ve got a full spread of AP classes at the college level, but it looks like you’d need to take a couple years of prep classes first, so mostly it’d be just juniors & seniors taking them.
I didn’t go to a public high school, but the highest class officially offered by my private school was the first year of Calc. There were plenty of people in my Calc I class that were not seniors, so the school ran an advanced math class half of which was studying for the second Calc AP exam, and the other half was a higher-level look at set theory than you get in normal math classes, going into countable and uncountable infinities. We discussed the issues arising from Godel’s Incompleteness Theorem and other philosophical stuff. We also took a look at some fractal stuff I think. That wasn’t my senior year either, nor was it for one other student (it wasn’t even her junior year - although she did graduate in 3 years, so maybe it was in a sense. I probably could have graduated in 3 years, but I didn’t plan on it and so instead had lots of free time in my schedule - she had actually planned things out to graduate in 3 years) so they didn’t run a class for the two of us. I studied multi-variable Calc on my own, and only had questions near the beginning of the semester, which made the teacher really irate in December when I said I wanted to take an exam on it, because he thought I had completely blown it off. Well, I had, I just studied all of it in 2 weeks before the end of the semester. I still maintained my 4.0 GPA with that class, but I decided to take Calc 3 again in college because I felt I hadn’t really learned it on my own, and I’d presumably have to take a placement test to bypass it, while my 5 on Calc BC gave me entry to Calc 3 without further placement.
Yes, sorry. I was including the final test as “successful completion”. But you’re right that it was certainly possible to get straight As in the class and fail the AP test or simply not take it at all, in which case no college credit would be awarded.
At my high school the top math classes are Calc AB and Calc BC, depending on which AP exam you were aiming for. Both are taught by the single best teacher on campus, bar none.
At the high school I graduated from, back in the Late Iron Age, plain Calculus was the highest math class offered. That’s the class that convinced me to be a Liberal Arts major.
Out of curiosity, can you clarify what you mean by this? Because I can think of two diametrically opposed ways of interpreting it.
Do you mean that it was Calculus that turned you on to the Liberal Arts? Mathematics is squarely within the liberal arts, in both the classical and modern sense of the term. Pure math, at least, fits comfortably beside other liberal arts subjects such as philosophy and intellectual history. And this can easily include Calculus, depending on how it’s taught.
Or do you mean that your Calculus class turned you off to, or made you believe you weren’t any good at, the STEM side of things? Mathematics is often grouped with Science, Engineering, and Technology; and Calculus in particular is often seen as the gateway to such technical subjects. STEM, which includes Math, is popularly seen as the quantitative, practical one of the “two cultures,” the antithesis of the “softer” arts and humanities.