Generalization and Systematization of Knowledge in Preparation for Solving the Most Com-plex Problems of the USE in Mathematics at the Profile Level

This article substantiates the relevance and significance of studying the elective course "Problem Solving with Parameters" for generalizing and systematizing theoretical material on key topics of the school mathematics course, as well as for developing creative thinking and gaining experience in solving non-standard problems of increased complexity contained in the texts of the profile level of the USE mathematics. The formation of the course content and its testing were carried out for three years in the classroom with mathematically gifted eleventh-graders and one semester with first-year students of the Faculty of Economics as part of the scientific circle. As a result of the work carried out, the authors managed to identify the main methods for solving problems with parameters and analyze the most common mistakes made by students.