This work uses data from SAEB?National System for Evaluation of Basic Education?to describe the cognitive achievement of 4th, 8th and 11th grade Brazilian basic education students. The achievement is measured on a scale that is the same for all grade levels. The test items are chosen to cover a synthesis of the curriculum frameworks of all Brazilian states. The achievement level of the great majority of the students does not meet the officially recommended levels. Also, there are large differences of achievement among students of different regions of the country, of different races, and of different socioeconomic status. The data, therefore, show the existence of large problems of quality and equity in Brazilian basic education. The students, their teachers, and the school principal provide, through their answers to contextual questionnaires, information on potential explanatory factors for the achievement levels. Using these data, it is possible, using adequate statistical methodology, to correlate the student achievement with the student and school factors. Several factors, under the control of school and public policies, are reported as having potential for improving the quality of education. The very few factors that affect the equity of the system act in the direction of increasing the inequalities among students of different races and of different socioeconomic backgrounds. The article concludes showing that the quality problem should be faced together with the equity problem, and for that, this latter dimension should be given a more prominent role in school improvement projects.