About calculus: https://www.gaokzx.com/c/201901/33164.html
Using the elite students from private schools who you know as a counter argument is really not that strong. Only 14% of the high school students are in private schools.
The top results (for me) all say that it's not literally correct that only 50% of middle school students make it to high school, but most (suspiciously) only mention numbers for Beijing. https://zhuanlan.zhihu.com/p/368135272 has a table covering every province, showing that the rate goes from 53.11% in Henan to 70.49% in Heilongjiang.
It's interesting that there's no calculus on the gaokao. It's an elective in high school (same as the US). I wouldn't have guessed that. However, some very basic linear algebra does seem to be in the compulsory high school math curriculum(1). More than I learned in high school in the US, anyways.
Also, generally the private schools are considered worse options. The elite students with the highest middle school test scores mostly go to public high schools. Maybe students at the private high schools are more likely to go overseas, and so they are more likely to take the calculus electives. But even among the private school students, only a small percentage will go overseas.
For the vocational school thing, I had no idea it was so extensive. Very interesting. I knew about sports high schools, where most of the graduates go on to teacher colleges and become PE teachers. What other kinds of vocational high schools are there? How does it work for smaller cities - how many special types of vocational school can they really support?
(1) https://baike.baidu.com/item/%E9%AB%98%E4%B8%AD%E6%95%B0%E5%...
My wife took the art/liberal arts track in high school and most definitely didn’t learn calculus (she still got into one of the best arts academies, though). So at least on that track, you won’t learn calculus (you generally take the same classes together, unlike the USA). I’m not sure about the STEM track, but my bet is first tier Shanghai and Beijing would be way different from a tier 88 like Chenzhou. I also can’t imagine kids at a school like renmin zhongxue not learning calculus, and that’s just a middle school.
Teacher schools (normal universities) require high school. I’m not sure about tourist or sports schools. But the tourist college I visited (in Zhangjiajie) seemed more like a college than the vocational schools I’ve seen. I didn’t ask, though. I assume Beijing Sports university is a real university, but I’m not sure about the other more provincial ones.
OTOH, friends of same age who were in Shanghai did get exposed to linear algebra.
I'm not sure where the original commenter is at in China where 50% are not going to high school. "Ailun" is also right about the private school thing. It's big in China. Finally, the idea that Chinese students are not learning calculus is patent nonsense.
And I’ve never heard that high schools don’t teach calculus. The Chinese people I know who went to the US in later high school years and for college all found that the calculus classes were repetitive for them.