The publication is addressed to high school students to prepare for the exam in mathematics. The manual contains useful information for solving problems of a profile level, basic concepts, definitions, formulas, as well as detailed solutions to more than 500 problems. With the help of this manual, the student will be able to learn how to solve problems of different difficulty levels. The publication will assist students not only in preparing for the exam, but also for additional entrance examinations in mathematics, and can also be used by teachers in organizing the educational process.