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Junior high · OlympiadAdventure modeCategory 21 · 20 modules

Mathematical Olympiad: Junior

Mathematical Olympiad for junior high school: congruences, Diophantine equations, advanced factoring, Ceva and Menelaus, power of a point, and combinatorics.

Topics that often appear in the junior high OSN/KSN (Indonesian National Science Olympiad), national math competitions, and international competitions (AMC 8, MATHCOUNTS, IMSO, junior olympiads): number theory, algebra, geometry, combinatorics

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Number Theory Island

Number Theory

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  1. 1Divisibility and congruences (modular arithmetic)You are here
  2. 2The Euclidean algorithm and linear Diophantine equations
  3. 3The fundamental theorem of arithmetic and arithmetic functions
  4. 4Fermat's little theorem and Wilson's theorem
  5. 5Nonlinear Diophantine equations

Algebra Island

Algebra

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  1. 6Advanced factoring and algebraic identities
  2. 7Nonlinear systems of equations
  3. 8Polynomials and the remainder theorem
  4. 9Vieta's formulas and roots of equations
  5. 10The AM–GM inequality and functional relations

Geometry Island

Geometry

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  1. 11Special lines of a triangle: Ceva and Menelaus
  2. 12Circles and cyclic quadrilaterals
  3. 13Power of a point
  4. 14Similarity and triangle areas in depth
  5. 15Analytic solid geometry

Combinatorics Island

Combinatorics

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  1. 16Permutations, combinations, and the binomial theorem
  2. 17The principle of inclusion–exclusion (PIE)
  3. 18Stars and bars (combinations with repetition)
  4. 19The pigeonhole principle in depth
  5. 20Expected value and recurrence relations