In modern society, the role of supplementary education is increasing from year to year. Additional education is aimed at increasing the mobility of the individual in the world of professions and in social life. One of the forms of additional education is the pre-university training of high school students in various subject (and inter-subject) areas. It is important to understand how to better integrate the process of pre-university training into the system of continuous additional mathematical education for high school students and in what forms to implement it in order to achieve the most positive effect. These questions are the purpose of the study of this article. The research methods were theoretical analysis, generalization and systematization of scientific works of the authors investigating the issues of organizing additional mathematical education for high school students. Having summarized the available works on the problem under study, the author concluded that the main approaches to its study are personality-oriented and systemic approaches. They imply the actualization of such a form of additional mathematical education as specialized education at the senior level of secondary school. Within the framework of a systematic approach, the organization of pre-university mathematical training presupposes continuity and phasing, the creation of a single educational space.