Study Materials
Brief Outline of the Topics to Study
Number Theory
Divisibility of integers, Euclid algorithm to find GCD of two integers. There are infinitely many prime numbers. The fundamental theory of arithmetic. Arbitrarily large gaps in the sequence of primes. Representation of positive integers in any base. Congruences. Chinese Remainder Theorem. Euler’s functions. Fermat’s little theorem. Greatest integer function. Arithmetic integers. Pythagorean triplets.
Algebra
Factorisation theorem. Remainder theorem. A polynomial of degree n has at most n roots. Relation between roots and coefficients of polynomials of degree n. Symetric function of roots. De moivers theorem and application. AM – GM inequality, Root mean inequality, Cauchy-Schwarz inequality, Tchebycheff’s inequality.
Geometry
Euler line. Nine point circle. Ptolemy’s theorem. Ceva’s theorem. Menelaus theorem. Construction and geometric inequality.
Combinatorics
Permutations and Combinations. Principle of Inclusion and Exclusion. Basic combinatorial numbers and Identities. Pigeonhole principle.
Question papers and Solutions of RMO, INMO and PRMO are listed below.
To view the papers click on links.
PRMO
RMO
INMO
IMO
For past papers of International Mathematical Olympiad click the link below...
https://www.imo-official.org/problems.aspx
Following are the link for Regional and national Level Papers
https://olympiads.hbcse.tifr.res.in/wp-content/uploads/2021/03/INMO21FINAL.pdf
http://olympiads.hbcse.tifr.res.in/wp-content/uploads/2021/03/IOQM-question-paper.pdf
http://olympiads.hbcse.tifr.res.in/wp-content/uploads/2021/03/IOQM2021Anskey.pdf
https://olympiads.hbcse.tifr.res.in/wp-content/uploads/2020/04/inmo-20-QP-4_0.pdf
https://olympiads.hbcse.tifr.res.in/wp-content/uploads/2020/02/sol-inmo-20.pdf
https://olympiads.hbcse.tifr.res.in/wp-content/uploads/2019/10/rmoengfirst2019.pdf
https://olympiads.hbcse.tifr.res.in/wp-content/uploads/2019/10/rmosolutions2019.pdf
https://olympiads.hbcse.tifr.res.in/wp-content/uploads/2019/08/PRMO-2019-Question-Paper.pdf
https://olympiads.hbcse.tifr.res.in/wp-content/uploads/2019/08/PRMO-2019-ans-key-19.pdf
Sample OMR sheet showing marked answers
RMO 2016
INMO 2016
3.Solution
PRMO 2015
RMO 2015
RMO Paper 2015 (Mumbai region)
RMO 2014
RMO 2013
RMO 2012