The problem of selection of entrants to study at the University (HEI) is still relevant and should be based on the results of marketing research as the demand for certain specialties and labor market supply for certain positions and requirements for them.

Although a lot has been done over the last 10–15 years to enable capable individuals to enter the HEI budget form of education. The national competition, which was introduced during the distribution of budget places between entrants and the HEI, solved many problems that existed in the past. This approach is a really big step forward in improving the quality of training, because it, this quality directly depends, in particular, on which applicants will become students.

The introduction of the current system of enrollment in the HEI and the distribution of the state order between the HEIs allowed:

• eliminate suspicions of biased entrance exams;
• restore children’s faith in justice;
• adjust them to the development of their lives by their own work and not to find ways to get inflated grades;
• form in parents the desire to provide children with quality education, rather than overestimation;
• significantly reduce the impact of administrative intervention in the process of assessing students’ knowledge.

However, the introduction of a new system of enrollment in the HEI and the system of distribution of public procurement between them did not provide the expected increase in the quality of education. This is evidenced by the results of the assessment of the level of secondary education in Ukraine by international institutions, as presented in the previous section. In addition, a comparison of the average scores of external independent evaluation certificates in mathematics and Ukrainian language and literature in 2008–2009 and 2018–2019 shows a decrease in test results by 7–8 % (Table 3.8). Thus, if we reject the possibility of complicating tests in these subjects over the past ten years, we have a decline in the quality of secondary education!