The paper reveals the ways and means of improving the quality of training graduates in the field of "Oil and Gas Business" through a competence-based approach implementation to the content of vocational education modernization. The article provides a rationale for the expediency of using the task approach in the formation of professional competencies among students of a technical university and reviews the experience in implementing this approach. The authors emphasize the importance of the "mathematics" discipline as a basis for vocational training, special attention is paid to defining the types of competencies and general of bachelors' professional abilities formation, with an emphasis on reflecting the problems encountered in organizing educational material in accordance with the requirements of the 3rd generation state educational standard. This article analyzes the basic concepts of "task" and proposes the authors' understanding of the term "task". The authors presented the experience of developing practice-oriented tasks for students of a technical university. The experience this technology implementation in the study of "Mathematics" in the oil technical university in accordance with the requirements of third-generation standards is described. Special attention is paid to the technology of professional competencies of students of a technical university formation. This article describes the stages of the learning process organization when implementing the technology of the task-based approach to learning. Specific examples of organizing the methods of the professional competencies formation are considered. The authors reveal the essence of the mathematical task as the main means of forming the competence of technical university students, show the relevance of using task approach in the learning process and suggest a specific method of key competencies forming through technological problems solving. 1. Introduction