The main goal of teaching students to solve Olympiad and non-standard mathematical problems is to enhance their mathematical abilities and overall level of preparedness. This article examines the essence, classification, and theoretical and methodological foundations for the use of Olympiad and non-standard problems in the school mathematics curriculum. Based on an analysis of scientific and methodological literature, the conceptual differences between “standard problems,” “non-standard problems,” and “Olympiad problems” are identified, and their role in developing students’ logical, analytical, and creative thinking is substantiated. The views of domestic and international scholars are compared, and an author’s classification model of Olympiad problems according to content and solution methods is proposed. In addition, the main methods and heuristic techniques used in solving non-standard and Olympiad problems are systematized, and effective ways of integrating them into the instructional process are demonstrated. The research findings confirm that the systematic use of such problems promotes the development of students’ mathematical culture, cognitive activity, independent thinking, and research skills. The proposed methodological conclusions are intended for use in school mathematics teaching practice, elective courses, and Olympiad training programs.

Key words: school mathematics course, Olympiad problems, non-standard problems, problem-solving methods, heuristic techniques, mathematical thinking, mathematical culture, Olympiad training, teaching problem solving.