SYSTEMATIZATION AND GENERALIZATION OF KNOWLEDGE ON THE TOPIC «VECTORS» IN PREPARATION FOR THE UNIFIED STATE EXAM TO SOLVE PROBLEMS IN ALGEBRA AND GEOMETRY

The concept of a vector is one of the fundamental concepts of the school geometry course and the basis for studying subsequent sections of mathematics and other natural sciences. Many years of experience of the authors of the article showed a low level of systemic knowledge on the topic of «Vectors» among applicants and first-year university students, as well as the inability to solve not only applied, but also typical problems on this topic. The article analyzes the reasons for this situation and suggests one of the ways to solve the problem. The work analyzes the content of an open bank of tasks of the Unified State Exam in mathematics (profile level, topic «Vectors»), substantiates the rationality of solving a number of geometric problems of the Unified State Exam using the vector-coordinate method, classifies the types of problems in stereometry that are rationally solved using the vector-coordinate method, which, in the opinion of the authors, ensures not only the consolidation of theoretical knowledge and operational skills on the topic of «Vectors», but also contributes to the formation of meta-subject competencies that allow the transfer of algebraic apparatus to solving geometric problems. The article compares the traditional method of solving a stereometric problem and the vector-coordinate method, indicating the advantages of the latter and some of its disadvantages. It also shows examples of using the vector-coordinate method in solving problems of planimetry and algebra. The conducted research allows us to conclude that in the overwhelming majority of problems in stereometry of the open bank of the Unified State Exam, the use of the vector-coordinate method is the most rational.

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