Mathematics. 8-9 grades. Olympiad problems

The proposed manual covers the main methods and techniques for solving olympiad problems of various levels of difficulty for students in 8th and 9th grades. The manual contains 650 problems divided into 65 sets for each grade. Each set includes 5 problems on different topics. The problems presented in the book are dedicated to such classical topics as divisibility and remainders, invariants, Diophantine equations, Dirichlet's principle, trigonometric equations, linear and nonlinear systems with parameters, and so on. Answers and hints are provided for all problems, and solutions are provided for the most difficult ones, with some problems being solved in different ways. The majority of the problems are original. The final part of the book includes interesting creative problems related to numerical patterns. These problems are of great interest not only to students but also to teachers. The manual is intended for students in 8th and 9th grades preparing for olympiads of various levels, mathematics teachers, university students, and tutors.