The proposed manual describes the main types of tasks of increased and high difficulty levels used in the exam in mathematics. Particular attention is paid to the analysis of tasks that caused the greatest difficulties. For training and self-preparation for the exam, tasks are offered with a detailed answer of various levels of difficulty in all substantive blocks. The manual is addressed to high school students, teachers and parents. It will help students test their knowledge and skills in the subject, and teachers - to assess the degree of achievement of the requirements of educational standards by individual students and ensure their targeted preparation for the exam.