If you are looking for specific established programs or materials, these are the gold standards:
: Mastering techniques required for the All-Russian Olympiad of Schoolchildren and other "Level I" university-hosted competitions. matematicheskii kruzhok dlia 9 klassa programma
A typical 9th-grade program balances advanced algebra, geometry, and discrete mathematics: : Polynomials and Vieta's formulas for higher degrees. Modular arithmetic and Diophantine equations. Complex inequalities (Cauchy-Schwarz, AM-GM). Geometry : If you are looking for specific established programs
: Often publishes their "Small Mekhmat" circle programs. Complex inequalities (Cauchy-Schwarz, AM-GM)
Advanced properties of circles (power of a point, radical axis). Geometric transformations (homothety, inversion). Vector methods and barycentric coordinates. : Graph theory (Eulerian paths, planar graphs). The Pigeonhole Principle (advanced applications). Invariants and semi-invariants in game theory. Instructional Methods
: Offers structured distance learning courses for 9th graders focusing on "Additional Chapters of Geometry/Algebra."
: Learning to approach problems that do not have a pre-defined "formulaic" solution. Key Curriculum Topics