Do most students aiming for selective colleges take the SAT and/or ACT in junior or senior year?

From what I remember, the SAT (reasoning) math only covered algebra and geometry, so high school juniors in late spring who were at normal grade level would have covered the needed math in school. I have not read of any more advanced math being added to that section.

The kid did not retry the SAT or ACT (whichever was initially better) in fall of senior year after realizing in the summer that s/he was just below the threshold? That is the idea of taking the tests earlier than senior year – to see where one stands and have a chance to retry if one is slightly short of the goal.