Currently, much attention is paid to the development of mathematical abilities, skills of analytical and systemic thinking, the basics of schoolchildren and students. Ensuring the continuity of educational programs of secondary and higher education is the "core" of successful education of schoolchildren for the formation of research competence, instilling search and justification skills, a fundamental attitude to mathematics. The practical significance of the work is that by transforming the tasks of higher mathematics, it is possible to bring school mathematics and mathematics in higher educational institutions closer, thereby forming students' research search skills, the desire for knowledge beyond the framework of the program. The analysis of the obtained results is reasonable and shows that it will make objective changes in the pedagogical activity of mathematics teachers in search of ways to improve in applied research.