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The article conducts research on the construction of analytical methods of computer tests in higher mathematics. These computer tests contain test items of various types, including problems with "embedded answers" which include several related subitems. Also, on the basis this method quality analysis of the control work was conducted. The technic is based on the methods of Classical Test Theory (CTT) and Item Response Theory (IRT), which have proven their effectiveness in statistical analysis of tests. The focus of the work is on the use of Multidimensional Item Response Theory (MIRT) models, which allows to analyze simultaneously the whole vector of students' competencies and to scrutinize them more carefully. The study also uses one-dimensional IRT models, the results of which are compared with the use of MIRT. Among the one-dimensional models, the well-known Muraki and Birnbaum models were selected, and among the multidimensional models, the choices were the two-dimensional 2-PL and GPCM. The multidimensional models involved in the study are compensatory. The application of non-compensatory models was not considered. The comparison of compliance with the data of different models was carried out on the basis of special information criteria. One-dimensional models were discovered to be somewhat more effective. The R programming environment was chosen as the main toolkit, which provides a powerful set of software for the test statistical analysis. The mirt package is selected as the main software package. Tests results from a modular test in analytical geometry have been chosen as data for research. The test was written by 105 students from IT stream, specialty 121, at FIOT NTUU "Igor Sikorsky Kiev Polytechnic Institute". The test was placed on the MOODLE platform and was conducted remotely. The analysis of test results on the basis of selected models demonstrated the consistency between the results of both one-dimensional and multidimensional models. However, multidimensional models also allow to expound the analysis of various additional competences, in this case - knowledge of vector algebra and knowledge of lines, planes, and surfaces in space. The analysis showed that the test was, in general, composed correctly; also the analysis allowed to systematize the items by complexity; and for questions such as "embedded answers " to detail the complexity of the subitems. Evaluating the overall results of the application of one-dimensional and multidimensional models of IRT, it should be noted their effectiveness in the analysis of both tests in higher mathematics and in the control of knowledge in other disciplines.

The paper extends the results obtained by Paranjape, Park, Klesov and Kruglova. A method of finding the distribution of the maximum of a Chentsov field restriction on a polyline is suggested. To do this, it was proposed to simulate a random process that corresponds to the restriction. The suggested algorithm has high computational efficiency which is crucial due to a large number of points of division of the process trajectory. The selection of the distributions of extreme functionals from the field was performed by means of the statistical programming language R. The Weibull distribution was chosen as the most suitable distribution, which was confirmed by the Kolmogorov criterion, as well as by Q-Q and P-P diagrams.