The article discusses the theoretical foundations and pedagogical features of the organization of search and research activities of students when teaching the subject "Algebra and the beginning of analysis.  The concept of "search and research activity" in teaching mathematics has been clarified. The concept of " search and research task" is considered and tasks are complied. The pedagogical analysis of textbooks of natural and mathematical direction is carried out and the advantages of textbooks are shown. The research used the methods of pedagogical analysis, observation, questioning, pedagogical experiment, pedagogical analysis of the content of the subject "Algebra and the beginning of analysis", analysis of pedagogical and psychological literature. As a result of the study, research tasks were developed aimed at developing the search and research activities of students. In the course of the study, a survey was conducted. As a result of the analysis of the polls, it turned out that the student who work with additional literature, interested in independent research, creativity, were able to complete the tasks. The results of the research can be used by specialists-mathematicians who teach algebra and the beginnings of analysis in the school curriculum, they can use tasks as a tool for the development of search and research activities of students.