Keyword: «use in mathematics»

The unified state examination in mathematics has been held in our country for more than fifteen years. Over the years it has undergone some transformations, connected both with the examination work and with the content aspects: the typification of tasks became more transparent; in recent years, the exam is held on two levels - basic and advanced. Despite the abundant amount of materials on the Internet, which give an opportunity to understand the structure and complexity level of the exam options, the issue of substantive and statistical processing of the past years exam results remains an urgent one for analysis by the teachers preparing the students for passing the USE and by the graduates themselves. In addition, the analysis of the results of students who passed the Unified State Examination in their own region is of a special interest for teachers. Thus, the purpose of the article is to analyze the results of 2017Unified State Exam in Mathematics in Kirov Region. Statistical data are given allowing to compare the results in the region with the average results for the Russian Federation, and also to monitor the dynamics of the results in the region. The authors, who have great experience in checking up exam papers, describe typical mistakes and problems of students, based on the content of the work and statistical data. The materials of the article may be interesting for mathematics teachers, school directors and their deputies, as well as for graduates of secondary general education institutions preparing themselves for the final certification in mathematics in the form of the Unified State Exam.

In the Russian Federation, various textbooks containing samples of standard examination options are published annually to prepare graduates of general educational institutions for the Unified State Exami-nation in mathematics (profile level). In our opinion, the most «approximate» to the real tasks offered at the USE in mathematics are the manuals published with the scientific and methodological support of the Federal Institute of Pedagogical Measurements (FIPI), edited by I.V. Yashchenko. In almost all standard versions of examination tasks offered in manuals edited by I.V. Yashchenko, among the tasks that require their detailed solution (i.e., tasks from part 2), there are tasks of an applied nature (in the versions of recent years, this is task number 15). Since graduates of general education schools do not have sufficient practical life experience (they have not yet been involved in obtaining loans from banks or running a serious business, etc.), the conditions of many applied tasks proposed in the above manuals cause many students difficulties when comprehending them, and even more so, when constructing an algorithm for solving them. In this regard, this article proposes simple methods for solving problems of an applied nature from the Unified State Examination in mathematics, based on the visualization of the formulations of the problems under consideration.

The article illustrates, using specific examples, various ways of constructing mathematical models and algorithms for solving problems of an applied nature from standard variants of the Unified State Exam in mathematics (profile level), presented in manuals edited by I.V. Yaschenko, popular among teachers and graduates of general education institutions. According to the authors of the article, familiarization of gradu-ates of secondary schools in the process of preparing for the Unified State Exam in mathematics with vari-ous ways of constructing mathematical models and algorithms for solving problems of an applied nature will contribute to a significant improvement in the quality of their training, and each of the graduates in their practical activities will have the opportunity to choose from various ways to solve this group of problems the most convenient and a way that is understandable to him.