Information about Topics to study for RMO
Mathematical Olympiad Examinations have no specific syllabus. However,the students are assumed to have knowledge of pre-calculus Mathematics. In Mathematics Olympiad examination, there are no theory questions. Generally,in RMO examination there are 6-7 problems to be solved in three hours. Here is a brief outline of the topics to be studied. It is expected that the student is well versed in all the topics that he/she has studied up to the 10th Standard, as well as in the topics from the 11th Standard. syllabus such as: Trigonometry, Geometry, Surds, Complex numbers, Quadratic Equations, Permutations and Combinations, Binomial theorem, A.P., G.P.,H.P. and Principle of Mathematical Induction.
1. Number Theory: Divisibility of integers, Euclid's algorithm to nd the GCD of two integers. Expressing the GCD of two integers as a linear combination of the two. There are in nitely many prime numbers. The fundamental theorem of arithmetic. Arbitrarily large gaps in the sequence of primes. Representation of positive integers in any base. Congruences. Chinese Remainder Theorem. Euler's function,(n): Fermat's little theorem. Greatest integer function, Arithmetic functions, Pythagorean triplets.
2. Algebra: Factorisation theorem. Remainder theorem. A polynomial of degree n has at most n roots. Relations between roots and coefficients of polynomials of degree n: Symmetric functions of roots. De Moivre's theorem and its applications. A.M.-G.M. inequality, Root mean square inequality, Cauchy-Schwarz Inequality, Tchebychev's Inequality.
3. Geometry: Euler line. Nine-point circle. Ptolemy's theorem. Ceva's theorem. Menelaus' theorem, Constructions and Geometric inequalities.
4. Combinatorics: Pigeonhole principle, Permutations and Combinations, Inclusion exclusion principle, Basic combinatorial numbers and combinatorial identities.