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Abstract: The article deals with the topical problem of development of mental activity of students in teaching fundamental disciplines. The article proposes the solution of this problem with the help of special system of tasks. The author describes the general scheme of designing learning tasks in the theory of algorithms aimed at development of the analytic-synthetic component of students’ thinking. The main purpose of the creation of the proposed scheme is to provide a means to construct a model of knowledge and work out a system of prompts to difficult questions. The level of development of the analytic-synthetic component of thinking is determined by the ratio of the number of questions asked by the students and the teacher in order to find the right solution. The paper gives examples of difficulty of evaluation of tasks in the theory of algorithms in terms of entropy and algorithmic approach. To analytic-synthetic tasks the author refers tasks, designed on the basis of the entropy approach and aimed at developing analytic-synthetic component of thinking.