Mathematics in the Unified State Exam and Olympiads: the Application of Identities and Inequalities

The manual is devoted to the basic for the formation of mathematical thinking theme — the same equations and inequalities. The book formulates and proves the most important algebraic, trigonometric, logarithmic, hyperbolic, etc. numerical and functional identity equations and inequalities used in solving a wide range of mathematical problems, showing relationships between them. The manual contains 300 tasks of different types with solutions from the introductory assignments and samples of the Unified State Exam in which various identities and inequalities are used to perform transformations and construct necessary assessments. The book may become study support for Math lessons in high school and expand the outlook of the students. It may also be useful for homework assignments.

Recommended for high school students of physical, mathematical and regular schools to prepare for the higher level USE on Mathematics, olympiads and Lomonosov Moscow State University entrance exams.