This paper is devoted to changes in the way in which mathematical assessment is conducted in Russia and Ukraine, the two largest states formed after the collapse of the Soviet Union. Previously, in the USSR, there existed two parallel systems of examinations, as follows: "exit exams," which were taken by schoolchildren graduating from high schools, and which were conducted using the same texts across the entire territory of each Soviet republic; and "entrance exams," which each college conducted independently (with the approval of the Ministry). In the new states, a gradual transition occurred to conducting so-called uniform exams, in which exit and entrance exams were combined. This change reflected society's quest for a fair and effective system, which could avoid corruption, unfairness toward different categories of students, and the like. In this paper, examinations are analyzed as an expression of society's influence on the teaching of mathematics. Consequently, the paper analyzes, on the one hand, the stages in the appearance and formation of examination procedures, the problems offered on exams, and the influence of exams on the teaching of mathematics; and on the other hand, the attitude toward exams in society, discussion of them in the press, and other general issues. A necessary space in the paper is allocated to background information, with a discussion of how exams were conducted in the USSR and of the general changes that have taken place in both countries.