Well, the conventional sequence in high schools in the US is for one year (32-34 weeks, or thereabouts) of coursework as follows:
1 yr Algebra I
1 yr Geometry
1 yr Algebra II
1 yr Precalculus
1 yr Calculus
"College Algebra" is also sometimes rolled into that Precalculus course, and this is often the first time that students see some of the trigonometry that they'll need for advanced calculus topics. For the first portion of calculus, bright students shouldn't NEED anything more than Algebra II.
I have no idea how the scope and sequence compares with AoPS.
When I was in high school it was...
Algebra I
Geometry
Algebra II
Trig Semester/ Analytical Geometry Semester
Calculus
I started Algebra in 9th grade and ran out of years after Trig/Analytical Geometry and then only needed College Algebra and Statistics in college to get my degree in Psychology.
My PG brother took Algebra and Geometry in the 9th grade (as in 2 different classes of math and the geometry was a gifted section of it) and was able to take AP calculus in 12th grade.
