How to Prepare for Indian National Mathematical Olympiad (INMO)

About INMO

Indian National Mathematical Olympiad (INMO) is Stage-3 of the Mathematical Olympiad Programme. It will be held on the third Sunday of January (January 19, 2020). Only those students who are selected in RMO 2019 and those who have received an INMO certificate of merit in 2019 are eligible to appear for the INMO 2020.

INMO Syllabus

The syllabus covers pre-degree college mathematics including arithmetic of integers, geometry, quadratic equations and expressions, trigonometry, co-ordinate geometry, system of linear equations, factorization of polynomial, inequalities, elementary combinatorics, probability theory and number theory, finite series and complex numbers and elementary graph theory. The syllabus does not include calculus and statistics. The major areas from which problems are given are algebra, combinatorics, geometry and number theory. The difficulty level increases from PRMO to RMO to INMO to IMO.

Preparation Tips for INMO

• Build Mathematical Aptitude

To be able to score high in INMO, it is essential to build your mathematical aptitude. For that you need to work on developing your analytical thinking, enhancing your problem solving skills and improving your logical thinking ability. In addition, you need to develop a deep understanding of all the concepts.

• Refer to Mathematical Olympiad Books

Other than your textbooks, you should read and practice from the books mentioned below in the topic-wise tips with important books, when preparing for INMO. These books are immensely helpful for Olympiad aspirants and contain advanced level questions and problems. Preparing from such advanced level books will certainly give you an edge and acquaint you with questions of Higher Order Thinking Skills.

• Solve Previous Years’ Papers

Solving previous years’ question papers is instrumental to success in the exam. It familiarizes you with the question paper pattern and what kinds of questions are asked and their difficulty level. By solving previous years’ papers, you can identify your strengths and weaknesses and work on them. Additionally, while solving previous years’ papers, you should apply proper laws and work on your methods as it can introduce you to effective strategies and techniques. Moreover, solving previous years’ papers or mock tests in a time bound environment can improve your speed and accuracy.

Test Pattern

A detailed year-wise analysis of INMO papers since 2010 has suggested that primarily six questions on various topics are given to be solved in four hours time. The main topics covered are:

1. Geometry and Trigonometry
2. Number Theory
3. Combinatorics
4. Polynomials
5. Functions

Topic-wise Tips with Important Books

Geometry and Trigonometry:

Apart from deep understanding of similar triangles and cyclic quadrilaterals, a workmanlike approach about the basic trigonometry is a must. To this end, Plane Trigonometry by SL Loney is ideal. For geometry, The Challenge and Thrill of Pre-College Mathematics and Mathematical Circles (Russian experience) could be very helpful.

Number Theory:

Basic divisibility in integers, properties of prime numbers, basic properties and results on congruences especially linear congruences and squares and cubes are topics upon which one should concentrate. The list of books that one should follow is Elementary Number Theory by David M Burton, Mathematical Olympiad Challenges by Titu Andreescu and Răzvan Gelca.

Combinatorics:

Apart from a good book for IIT JEE, The Challenge and Thrill of Pre-College Mathematics as well as Combinatorics by S. Muralidharan (AIMER) can be quite handy.

Polynomials:

Again The Challenge and Thrill of Pre-College Mathematics and Problem Solving Strategies by Arthur Engel are good reads on this topic.

Functions:

For Functions, Functional Equations: A Problem Solving Approach by B.J. Venkatachala is the most dependable source.