This paper examines the determinants of students' performance on the entrance test at Universidade Federal de Pernambuco, Brazil. Particular attention is paid to the importance of family background variables, such as parents' education and family income, on students' performance and how they relate to the probability of attending public schools and private tutoring classes. Results suggest that parents' education and study environment are key determinants of students' achievements. Also, they are positively related to the probability of attending private schools and private tutoring classes, which are both estimated to have a positive effect on test scores. Finally, the quantile regression estimation shows that the effect of parents' education and family income varies across the conditional score distribution. These results highlight the need for developing policies that seek to improve the equality of opportunities in access to higher education. They are of special importance for a developing country like Brazil, in which not only the level of inequality is among the highest in the world but also the level of social intergenerational mobility is among the lowest compared to international standards. (Contains 4 tables, 2 figures and 17 notes.)