In recent years, artificial intelligence technologies have been developing rapidly, opening up new opportunities for teaching mathematical disciplines within the higher education system. In this regard, the study aimed to develop a methodological model for teaching higher mathematics based on artificial intelligence, as well as to propose diagnostic and analytical tools for evaluating its effectiveness. In the course of the work, the specific functions performed by the virtual problem set and the intelligent chatbot were identified, the sequence of technology application and its internal structure were established, criteria for measuring learning achievements were formulated, a questionnaire for assessing student satisfaction was developed, a procedure for data collection and statistical processing was established, and the proposed analytical apparatus was tested on model data. The methodological model consists of four closely interrelated blocks — target, content-technological, organizational-activity, and evaluation-result — and three levels of intelligent support were developed: orienting, guiding, and explanatory. Two groups of indicators — learning achievements and student satisfaction — were proposed to evaluate the results, and validation performed on model data confirmed the operability of the proposed analytical protocol. The scientific novelty of the study lies in combining the virtual problem set and the chatbot within a unified learning cycle featuring adjustable levels of AI support and a two-component evaluation system. The practical significance is determined by the possibility of applying the developed model and tools in higher education institutions of the Republic of Kazakhstan.