Hi,

The syllabus for Mathematical Olympiad (regional, national and international) is pre-degree college mathematics. The areas covered are:

Arithmetic of integers

Geometry

Quadratic equations and expressions

Trigonometry

Co-ordinate geometry

System of linear equations

Permutations and combination

Factorization of polynomial

Inequalities

Elementary combinatorics

Finite series and complex numbers

Elementary graph theory

To make the process of preparation for PRMO easy, these are books you can refer to-

Problem Primer for the Olympiads C R Pranesachar, B J Venkatachala and C S Yogananda (Prism Books Pvt. Ltd., Bangalore).

Challenge and Thrill of Pre-College Mathematics V Krishnamurthy, C R Pranesachar, K N Ranganathan and B J Venkatachala (New Age International Publishers, New Delhi).

An Excursion in Mathematics Editors: M R Modak, S A Katre and V V Acharya and V M Sholapurkar (Bhaskaracharya Pratishthana, Pune).

Problem Solving Strategies Arthur Engel (Springer-Verlag, Germany). Edited by K. Bencsath, P. R. Halmos.

Functional Equations B J Venkatachala (Prism Books Pvt. Ltd., Bangalore).

Inequalities an approach through problems (texts & readings in mathematics), B J Venkatachala (Hindustan Book Agency).

Mathematical Circles Fomin and others (University Press, Hyderabad).