| Summary: | The assessment of knowledge and skills acquired by the student at each academic stage is crucial for every educational process. This paper proposes and tests an approach based on a structured assessment test for mathematical competencies in higher education and methods for statistical evaluation of the test. A case study is presented for the assessment of knowledge and skills for solving linear algebra and analytic geometry problems by first-year university students. The test includes three main parts—a multiple-choice test with four selectable answers, a solution of two problems with and without the use of specialized mathematical software, and a survey with four questions for each problem. The processing of data is performed mainly by the classification and regression tree (CART) method. Comparative analysis, cross-tables, and reliability statistics were also used. Regression tree models are built to assess the achievements of students and classification tree models for competency assessment on a three-categorical scale. The influence of 31 variables and groups of them on the assessment of achievements and grading of competencies is determined. Regression models show over 94% fit with data and classification ones—up to 92% correct classifications. The models can be used to predict students’ grades and assess their mathematical competency.
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