My school system had a similar progression, though trig was on its own and you either took basic calc (essentially just limits and differentials) or AP calc, or

My school system had a similar progression, though trig was on its own and you either took basic calc (essentially just limits and differentials) or AP calc, or a statistics-lite course that was basically "business math" for kids who weren't on a college track but might try for an associates degree or maybe community college. Though, arithmetic and algebra 1 were just called "math" (all pre-common-core, of course). This was at a somewhat rural school in the Midwest, for what it is worth.