The manual is intended to prepare students for the exam in mathematics of the basic and specialized levels. It presents the main sections of mathematics: algebra, geometry, elements of probability theory and mathematical statistics. It will be useful for high school students, teachers and those who are going to take the exam after a break in training. The material of the manual is grouped into 29 paragraphs, covering all elements of the content in mathematics, checked on the exam. The book contains: brief theoretical information with examples of tasks;