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).