Abstract. The academic performance of the study group is tracked at each stage of the monitoring of the educational process in the university. Changes in the learning process related to academic performance require constant monitoring, adjustment, and management. In every situation or human life, for example, if we talk about health, it is better to do preventive action than to treat the consequence of disease. In the learning process, by analogy, it is easier to prevent the worsening performance of a study group than it is to look for the fault after a failure. To achieve this, it is necessary to forecast academic performance in advance, to carry out preventive work in study groups. The aim of the article is to find ways to predict the performance of the study group, knowing the result of the previous exam or the control of the study group. In the course of preparing the article, along with general methods of analysis and synthesis, comparison and generalization of mathematics, basic concepts of probability theory, applications of the derivative, and methods of solving the differential equation were used. As a result of the study, a time-dependent function of academic achievement is constructed. This function has been analyzed with respect to the parameters. The behavior of this function when each parameter included in this function is modified individually has been established. The use of the learning achievement function is demonstrated, and ways of using it to predict the result of the next exam are shown. Using this model, you can evaluate the preparation of the study group, their organization, the work of the teacher in the subject and the curator of the group.

Keywords: function, derivative, progress, progress of learning, sample function, learning group.