We use unique data to estimate the determinants of cognitive ability among 14-17-year olds in Senegal. Unlike standard school-based samples, tests were administered to current students as well as to children no longer--or never--enrolled. Years of schooling strongly affects cognitive skills, but conditional on years of school, parental education and household wealth, as well as local public school quality, have surprisingly modest effects on test performance. Instead, family background primarily affects skills indirectly through its impacts on years of schooling. Therefore closing the schooling gaps between poor and wealthy children will also close most of the gap in cognitive skills between these groups. (Contains 4 tables and 19 footnotes.)