Abstract
The article provides a summary of selected mathematical problems, discusses chapters covering selected problems, and demonstrates ways to solve selected problems using concrete examples. It is known that the selected mathematical problems are generalized by mathematical Olympiad problems by university students and schoolchildren, which have been conducted for many years. In addition, by solving selected mathematical problems, high school students begin to get acquainted with the elements of higher mathematics that take place at the university. During the research work, selective mathematical problems were carried out, the analysis of the studied literature, pedagogical analysis of selected tasks, observation, pedagogical experiment. In the course of the study, control works were carried out for students of grades 10-11 of the school from the tasks discussed in the article. As a result, we noticed that, in general, students have difficulties in solving selected tasks.Elective courses discussed this issue and considered ways to solve it. This article and the results of the study will be useful to teachers of secondary schools, young scientists, readers who will be engaged in science in the field of mathematics in the future.
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