UKMT & BMO
Masterclass.

IMC & SMC Focus

• Algebraic Fluency: Rapid manipulation of polynomials, indices, and surds.
• Geometry Tactics: Advanced circle theorems, similar triangles, and area ratios.
• Logic Puzzles: Mastering the quirky, highly creative word problems signature to UKMT.

BMO1 & BMO2 Core

• Congruences & Theorems: Euler's Totient, Fermat's Little Theorem, and Modulo arithmetic.
• Diophantine Equations: Solving linear and non-linear polynomial equations over integers.
• Divisibility Logic: Euclidean algorithm, prime properties, and constructing rigorous proofs.

BMO1 & BMO2 Core

• Polynomials: Symmetric polynomials, Vieta’s formulas, and root bounding.
• Inequalities: AM-GM-HM, Cauchy-Schwarz, and rearranging techniques.
• Functional Equations: Substitution techniques and identifying standard functions (BMO2).

BMO Exclusive

• Advanced Configurations: Cyclic quadrilaterals, radical axes, power of a point, and homothety.
• Advanced Counting: Bijections, Principle of Inclusion-Exclusion (PIE), and generating functions.
• Principles: Pigeonhole Principle (strong form), Extremal Principle, and Invariants.