Московский университет — школе

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.

The present fundamental tutorial is aimed at getting the applicants ready for the entrance examination in mathematics required for entering a number of MSU faculties. The book can also be of use to high school pupils and mathematics teachers.

The manual contains a systematic presentation of all sections of the course "Russian language" with an overview of the material presented in the most common school teaching materials, as well as diagrams and samples of analysis of all language units and comments on these analyses. The task of the manual is to generalize and systematize students' knowledge of language and speech. The manual is compiled in accordance with the theoretical guidelines adopted in pre-university training at the Faculty of Philology of Lomonosov Moscow State University, and is intended for school students who study Russian in depth (at the profile level), and teachers.

The book contains theoretical materials regarding all parts of chemistry course, as well as 1500 examination tasks, questions and exercises accompanied by their detailed analysis and answers. The tasks vary in difficulty level - from basic to most advanced.

The book is intended for high school students, chemistry teachers, and pretenders.

The textbook is intended for repetition and systematization of student knowledge in preparation for exams and olympiads in mathematics. Aimed at applicants to those higher educational institutions where it is required to demonstrate a high level of knowledge in mathematics - both in theory and in practice of solving problems. Part 1 of the book includes the following sections: “The Theory of Real Numbers”, “Numerical Equalities and Inequalities. Abbreviated multiplication formulas. Known algebraic inequalities", "Algebraic equations and inequalities". The book contains all the necessary definitions, formulations and proofs of properties and theorems. Particular attention in the manual is paid to the analysis of various techniques and methods for solving problems (Part 1 includes more than 450 problems with solutions from variants of examination tasks at Lomonosov Moscow State University, MEPhI, MIPT, Bauman MSTU, MTUSI, HSE, Plekhanov Russian Economic Academy, Financial Academy and other universities), as well as about 625 problems for independent solution (with answers and solutions). Much attention is paid to problems with non-standard approaches to solution. The book includes a lot of additional and reference material that expands the student’s mathematical horizons.

The manual is recommended for high school students, students of preparatory departments and courses for preparing for Olympiads (at the level of Lomonosov Moscow State University) and the Unified State Exam (in the most difficult its parts), as well as teachers teaching elementary mathematics courses.

Published by decision of the Editorial and Publishing Council of Lomonosov Moscow State University. You can also purchase in our online store Part 2. Systems of equations and inequalities. Text problems. Sequences. Progression. Elements of set theory