I know of districts using some degree of social promotion, but I’ve never heard of one promoting on performance but using standardized tests alone instead of class grades or clearing a certain bar for both grades and standardized test as the performance criteria.
Was that the case in the 1960s/1970s because that was when the author was in elementary through high school? I graduated high school in 1995 and what you are describing was not the case at my school nor any other school that I knew of at that time.
You can fail math all year long, but achieve the bare minimum in the subject during your annual standardized test and pass to the next grade.
Course credits/grades do not ~~affect~~ limit? progression in many/most? US school districts before high school.