Secondary Competition Math

This Programme will prepare students for various secondary Math Olympiad competitions (e.g., SMO Junior, SMO Senior, SMO Open).

SMO Junior

The SMO Junior 1st Round is, to an extent, a harder version of the SMOPS/RIPMWC. However, knowledge of the Sec 1-2 math syllabus is also required, which includes, but is not limited to algebraic expansion & factorization, simultaneous equations, quadratic equations, indices & surds, inequalities, and similar & congruent triangles. In particular, creative algebraic manipulation are often required to handle the Geometry, Counting and Number Theory problems which appear similar to Primary 6 Olympiad problems.
The SMO Junior 2nd Round requires the knowledge of how to formulate & write rigorous proofs, including the common proof frameworks (e.g., contradiction, cases, induction). Additionally, some ideas (e.g., AM-GM, Pigeonhole Principle, Similar Triangles) need to be applied in a slightly different manner than the computational 1st Round problems.

SMO Senior

The SMO Senior 1st Round focuses heavily on the algebraic topics introduced up to O level syllabus: e.g., trigonometry, logarithms, polynomials, quadratics, surds and the Binomial Theorem. Problems will generally be more algebraically intensive than in the SMO Junior. Additionally, knowledge of circle geometry, modulo arithmetic and the inclusion-exclusion principle are required for the non-algebraic problems.
The SMO Senior 2nd Round is significantly more difficult than the Junior 2nd Round. Problems are generally evenly distributed among Algebra, Combinatorics, Geometry and Number Theory. Potential topics tested include advanced inequalities (e.g., Cauchy-Schwarz), functional equations, properties of triangle centres, graph theory, Euler/Fermat’s Theorems and recurrence relations.

SMO Open

The SMO Open 1st Round is essentially the culmination of all preceding short-answer contests. As such, many problems will be harder versions of questions encountered in the SMO Junior & Senior. The remaining problems mostly come from A-level syllabus topics such as calculus, vectors, complex numbers and sequences & series. Additionally, some additional tools (e.g., generating functions, Pell’s Equations, Lagrange Interpolation, Ceva/Menelaus’ Theorems) may be required.
The SMO Open 2nd Round functions as the selection for the SIMO National Training Team. As such, problems from all Olympiad topics may be tested, with the average problem difficulty comparable to easy-mid IMO problems.

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