FWIW, your understanding is incorrect. While true that in US schools, all students are expected to complete a full 13 years of schooling (Kindergarten + 12 grades), students receive individualized courses of study. By high school, there may be 3-4 levels of instruction for Math ranging from remedial to college-bound, to college-level coursework. Additionally, non-college-bound students at most schools have the option of taking classes that prepare them for more traditional blue collar work (like automotive repair, etc) and often students have the option to go to a different school more aligned with their talents/skill level.

The primary difference between US and European education is in the US taking particular courses of study is the decision of the student/parents and not of the state.