Mathematics: Olympiad Problems. Grades 8-9

The proposed manual examines the main methods and techniques for solving olympiad problems of varying complexity for students in grades 8-9. The manual contains 650 problems, divided into 65 sets for each grade. Each set includes 5 problems on various topics. The problems presented in the book are dedicated to such already classic themes as divisibility and remainders, invariants, Diophantine equations, the Dirichlet principle, trigonometric equations, linear and nonlinear systems with parameters, etc.
Answers and hints are provided for all problems, and solutions are given for the most difficult ones, with some problems solved in different ways.
Most of the problems are original. The concluding part of the book presents engaging creative problems related to numerical patterns. These problems evoke increased interest not only among school students but also among teachers. The manual is aimed at students in grades 8-9 preparing for various levels of olympiads, mathematics teachers, pedagogical university students, and tutors.