Abstract: Family background factor can be a very important part of a person’s life. One of the main interests of this paper is to investigate whether the family background factors alter performance on mathematical achievement of the stronger students the same way that weaker students are affected. Using large sample of 2000, 2001 and 2002 mathematics participation in Alberta, Canada, such questions have been investigated by means of quantile regression approach. The findings suggest that there may be differential family-background-factor effects at different points in the conditional distribution of mathematical achievements.