Based on data provided by the National Assessment of Educational Progress, this study examines mathematics achievement in relation to various background variables, contrasts achievement levels of black and white (females and males) youth, and evaluates group achievement differences in the light of group differences in background variables. Students chosen for the study consisted of 4000 white and 600 black youths, aged 13 and 17. Background variables examined included region of residence, parental occupation level, reading materials in the home, level of parental education, and school grade in which the student is enrolled. Also considered among the 17 year olds were the effects of mathematics courses taken in high school and of grade point average. This report analyzes the systematic relationship found between mathematics achievement differences between blacks and whites and many of these variables, and discusses the findings' implications for predicting achievement. (GC)