This article presents the original model of the computer adaptive testing and grade formation, based on scientifically recognized theories. The base of the model is a personalized algorithm for selection of questions depending on the accuracy of the answer to the previous question. The test is divided into three basic levels of difficulty, and the student automatically goes from one level to another according to the current level of the knowledge that he shows. Such examination creates an image to the student that the test was set up just for his level of knowledge. On the basis of responses, by applying Bayes' theorem and the Maximum a posteriori approach, the evaluation grade is formed. In fact, based on empirical probability values, which correlate with obtaining of a certain final grade and the accuracy of answers to each question individually, model creates a score that corresponds to the current level of student's knowledge. After each test answer, the empirical probability value is updated. That further contributes to the statistical stability of the evaluation model. Testing stops when the student answers the minimum number of questions, determined by a teacher, or, when evaluations show a clear convergence towards a single value. The research method and some results of the testing of the hypotheses as well as authors' conclusions about CAT as a tool for evaluation of students are presented at the end of the article.