It really depends on your hukou given China’s residency system. Each province has a small quota, though some get much more than others, it isn’t has hard as a Beijinger to get into Qinghua as a person from Henan. Many richer Chinese choose abroad for better educational opportunities, even those that are obviously going to get into Qinghua or PKU (e.g. Beijing’s top gaokao scorer a few years back went to HKU).

On average, Chinese from the big cities have better math background than all Americans, not on average for the entire country. Compulsory education in china stops at 9th grade, and small city/rural schools are incredibly underfunded compared to PISA-record beating shanghai.