The main purpose of the textbook is to prepare applicants for a written entrance exam in mathematics at the humanities faculties of universities. The authors selected the necessary tasks and proposed methods for solving them. The manual ends with a reference book of formulas and terms. The manual summarizes the experience of teaching mathematics at preparatory courses and at the Lyceum at the Faculty of Public Administration of Moscow State University. M.V. Lomonosov. For applicants, high school students, teachers.