An important result of the preparation of the future teacher of mathematics is the formed professional competences. The process of formation should be carried out systematically, starting from the first year. While studying at the university, the foundations of modern mathematical knowledge should be laid, the need for professional self-development and self-education should be formed. The purpose of the study: the development of tools that contribute to the formation and development of professional competencies of students, future teachers of mathematics, in the study of mathematical disciplines. The study analyzed the professional competencies of a mathematics teacher, the components of mathematical culture and established their relationship. The competencies that can be formed during the first year of study are defined. Identified the need to convert standard mathematical problems. Based on the research, a technology for creating special complex problems based on standard mathematical problems has been developed. Tasks consist of two parts: subject (mathematical) and professionally-oriented. Tasks can be used to form subject and professional competencies, diagnose their formation. The article presents the requirements for them, types and examples of tasks. The result of the assignments from the point of view of the formation of subject and professional competences is described.