Getting prepared for RMO
Regional Mathematics Olympiad
The Regional Mathematics Olympiad (RMO) is the second stage in the selection for the selection of the Indian team to the IMO, the first being the pre-RMO. It is one of the tougher olympiads conducted across India, wherein only about 300 students are selected to sit for the Indian National Mathematics Olympiad(INMO).
The main thing that makes RMO tough, at least for the common students, is twofolds -- firstly, the syllebus is quite a bit different than the normal class X or XI curriculum that is followed in schools, especially in areas like combinatorics and number theory, the latter being a topic that is scarcely touched upon. Secondly, in topics that are known to us, like geometry, the level of questions, even if they don't require advanced theorems and results, they need a level of creativity that cannot be mastered overnight.
From hereon I will say what I did to clear it last year.. when I was studying in class IX.
Firstly, I focused heavily on geometry, and I would advise others to do so too, as in every year's question paper, there are two geometry problems as compared to the 1 inequality, algebra, combinatorics and number theory.
The way I practiced geometry is through studying CTPCM(Challenge and Thrill of Pre-College Mathematics), a book commonly available online as well as in the Indian market as well. The geometry problems given in the book are of good quality, though all the chapters and exercises start with simple problems. The main thing to focus on in geometry problems is the proper constructions that need to be made in order to solve a problem. This again is very different from school maths where we need to identify the correct theorem to use in a given figure.
Here however, the construction is the main thing. My strategy is to join all sets of vertices together, as it often helps, especially when there are circles involved. Oh, and the most important part of geometry : identify all possible cyclic quadrilaterals that you can. Most, if not all, problems require you to prove the cyclicity of some set of points, and if you manage to get that, half of the problem is done.
Anyways, for geometry, I followed that book rigorously. As for other topics, I never practicesed anything on combinatorics before INMO, so there would be no point in my discussing that now.
For number thoery, I used David Burton's Elementary Number Theory. However, number thoery, contrary to its name.. dosn't have that much of theory to it, at least in the RMO level. It can be best prepared by solving the previous year's papers from different regions.
Last but not the least is algebra. Now, this can be segregated into a couple of parts. Firstly, there are funcitonal equations, which I did not practice for RMO as it is not required at all. Secondly, there are inequalities. Besides geometry this is the topic that I studied the most. For this, I mostly used Excursion in Mathematics.I did all the sums that were given there, and I distinctly remember that I would be sometimes stuck on one problem for quite a while before getting it. In inequalities, it is interesting to note that the most you will ever need, even in the national level is the Cauchy-shwartz inequality, though knowing others is often an advantage.
The third part of algebra is polynomials.
This was always the hardest part for me. This too I practiced from Excursion. I also followed the Higher Algebra book by Hall and Knight which was also helpful in the sense that it has quite a number of theorems that can come in handy at times. Polynomials in itself is a vast subject when it comes to olympiad preparation.. but since this blog is how I prepared, and that too related to RMO only, this is all I did.
.... The actual fun starts at INMO ;) .
The main thing that makes RMO tough, at least for the common students, is twofolds -- firstly, the syllebus is quite a bit different than the normal class X or XI curriculum that is followed in schools, especially in areas like combinatorics and number theory, the latter being a topic that is scarcely touched upon. Secondly, in topics that are known to us, like geometry, the level of questions, even if they don't require advanced theorems and results, they need a level of creativity that cannot be mastered overnight.
From hereon I will say what I did to clear it last year.. when I was studying in class IX.
Firstly, I focused heavily on geometry, and I would advise others to do so too, as in every year's question paper, there are two geometry problems as compared to the 1 inequality, algebra, combinatorics and number theory.
The way I practiced geometry is through studying CTPCM(Challenge and Thrill of Pre-College Mathematics), a book commonly available online as well as in the Indian market as well. The geometry problems given in the book are of good quality, though all the chapters and exercises start with simple problems. The main thing to focus on in geometry problems is the proper constructions that need to be made in order to solve a problem. This again is very different from school maths where we need to identify the correct theorem to use in a given figure.
Here however, the construction is the main thing. My strategy is to join all sets of vertices together, as it often helps, especially when there are circles involved. Oh, and the most important part of geometry : identify all possible cyclic quadrilaterals that you can. Most, if not all, problems require you to prove the cyclicity of some set of points, and if you manage to get that, half of the problem is done.
Anyways, for geometry, I followed that book rigorously. As for other topics, I never practicesed anything on combinatorics before INMO, so there would be no point in my discussing that now.
For number thoery, I used David Burton's Elementary Number Theory. However, number thoery, contrary to its name.. dosn't have that much of theory to it, at least in the RMO level. It can be best prepared by solving the previous year's papers from different regions.
Last but not the least is algebra. Now, this can be segregated into a couple of parts. Firstly, there are funcitonal equations, which I did not practice for RMO as it is not required at all. Secondly, there are inequalities. Besides geometry this is the topic that I studied the most. For this, I mostly used Excursion in Mathematics.I did all the sums that were given there, and I distinctly remember that I would be sometimes stuck on one problem for quite a while before getting it. In inequalities, it is interesting to note that the most you will ever need, even in the national level is the Cauchy-shwartz inequality, though knowing others is often an advantage.
The third part of algebra is polynomials.
This was always the hardest part for me. This too I practiced from Excursion. I also followed the Higher Algebra book by Hall and Knight which was also helpful in the sense that it has quite a number of theorems that can come in handy at times. Polynomials in itself is a vast subject when it comes to olympiad preparation.. but since this blog is how I prepared, and that too related to RMO only, this is all I did.
.... The actual fun starts at INMO ;) .
Well, my reaction to this bullshit is aptly summed up by Udit Sanghi's reply to your "Preparing for IOITC" post.
ReplyDeleteAn insightful post on RMO Exam and Syllabus. Please share more details on IMO Olympiad Exam too. Such post really helps in understanding the pattern of Maths Olympiad exam and do the preparation with more clarity. Thanks for the useful post.
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