You asked:
"at what age do the required Math courses begin to utilise sequential math and then algebraic concepts?"What required math courses do you speak off?
If you are asking about the Alpha Omega curriculum that I linked to, there are no required math courses. Nothing is required. A parent could teach it in Kindergarten, 12 grade or never. There are no required curriculum for home schooled children. If you are speaking of the public school system I also have no idea. But I will say that the printed requirements for each grade level where I live is total BS. In other words, if you look at the required curriculum that say a 4th grader is supposed to have learned to be promoted, It bares almost no resemblance to what is actually taught in class. If they actually taught a 3rd of it I would be impressed.