Serge Lang, a math professor at Yale, used to give his Calculus students a fairly simple algebra problem on the first day of classes, one which almost everyone could solve, but some of them solved it as quickly as they could write while others took a while, and Professor Lang claimed that all of the students who solved the problem as quickly as they could write would get an A in the Calculus course, and all the others wouldn’t. The speed with which they solved a simple algebra problem was as good a predictor of the final grade in Calculus as a whole semester of homework, tests, midterms, and a final.
I did not take a math class my senior year in high school. Then in 4 years for my undergraduate I only took one semester of college algebra. When I shift to computer science and take a Calculus course last semester, I have to solve solve two problems for every regular problem. First, the algebra behind the problem, and then the actual calculus problem. If the algebra was second nature, then I could focus my brain on the Calculus. But with rusty algebra skills, Calculus is just that much harder.