Introduction

NMTC stands for National Mathematics Talent contest. This is a math olympiad type exam conducted by the Association of Mathematics Teachers of India ( AMTI). It is a very prestigious exam that goes all the way up to 1968. Several brilliant mathematicians from India have taken this math olympiad and have walked this path. All math enthusiasts nationally are expected to participate in the NMTC. The aim of the NMTC Math Olympiad is quite simply to identify and nurture students who have good mathematical intuition. The NMTC math olympiad has non-routine questions as a way to determine students who have a natural flair.

NTMC - Exam Stages

The math olympiad is conducted in 2 stages. The first stagel is Preliminary stage. 10% of students are selected for the next level which is the final test. The Preliminary level usually has objective questions with negative marks while the final test has subjective questions that require elaborate proofs. The top 3 rank holders from the final test get honorary certificates, mentions and a cash prize.

NMTC - Exam Levels

NMTC Math Olympiad conducted by AMTI is held for students starting from Class 5. There are different names for different contests as follows:

It is interesting to note that the NMTC math olympiad is combining classes. For example, 5th & 6th are going to get the same paper. So is 7th & 8th. This seems to stem from the fact that AMTI believes that math olympiads need not strictly follow school syllabus as it is more math intuition based rather than knowing any particular formula or template.

Syllabus for the NMTC Math Olympiad

The NMTC math olympiad broadly has the following chapters:

1. Arithmetic
2. Algebra
3. Geometry
4. Mensuration
5. Number Theory
6. Combinatorics

The split up of topics under each chapter is below for different levels as per AMTI:

Primary:
ARITHMETIC: Fractions, percentages, profit and loss, tests of divisibility, LCM, HCF, Ratio and proportion, Calendar
MENSURATION: Triangles, Quadrilaterals, Circles.
ALGEBRA: Algebra as literal Arithmetic, Addition, subtraction, multiplication and division of simple Arithmetic expressions.
GEOMETRY: Straight lines, parallel lines, Angle properties of triangles, quadrilaterals and polygons.

Sub Junior:
All the topics for primary and,
ARITHMETIC: Square roots and cube roots, Allegation, average , time and work, time and distance, Races, Games of skill, Travelling around a circle.
MENSURATION: Three Dimensional: cubes, cuboids, sphere, cone, cylinder, pyramids.
ALGEBRA: Algebraic equations of degree 1 and degree 2. Algebraic identities, factorization of algebraic expressions, laws of indices, basics of surds.
GEOMETRY: Triangle inequalities, parallelograms, trapezoids, Pythagoras theorem.
NUMBER THEORY: Prime and composite numbers, divisibility.

Junior:
All the topics for Primary, Sub junior and the following:
ALGEBRA: Quadratic and Higher degree Algebraic equations, Remainder theorem, Logarithms, Sequences and series, Scales of notations, Mathematical Induction, Basic inequalities
GEOMETRY: Circle theorems, Chords, Arcs, Angles in segments, Cyclic Quadrilaterals, Tangents, Alternate Segment theorem, intersecting chord theorem, Apollonius theorem, and Stewart’s theorem
NUMBER THEORY: Modular arithmetic, Greatest Integer function, least integer functions.
COMBINATORICS: Fundamental principle of counting, Basics of permutations and combinations, Principle of inclusion and exclusion, Pigeon hole principle

Exam Procedure:
The NMTC exam will be conducted only offline this year. It could be either in your institution or an AMTI authorized centre ( Present in the list when applying). The time duration for the preliminary test is 2 hours and the final test is 3 hours. Please note that the medium of NMTC exam would only be englis for this year.

NMTC - Exam Dates

Last Date of Application: Nov 15th,2021

Stage 1: Preliminary test: 4th December, 2021: 2pm to 4pm

Stage 2: Final Test: 22nd January, 2022, 2pm to 5pm

NMTC- How to apply

There are 2 ways to apply for the NMTC Math olympiad:

1. Through your school/Institution
2. Individually/Open Quota

For applying through your school, please ask your school correspondent to visit the AMTI website. There are clear instructions on the sheet to be downloaded, the fees and the information to be provided by the school on behalf of all the students. As per our understanding, the school will be entrusted with the task of conducting the exam as well.

If your school/institution is unable to register for AMTI on your behalf, you can apply individually through the open quota. The steps are as below:

Download the Open Quota- Data Consolidation Sheet - amtionline.com under the head “NMTC”

Fill up the Open Quota - Data Consolidation Sheet and send the scanned copy along with the fees transfer details to AMTI through email pn support@amtionline.com along with the fees transfer details. Please fill the sheet only in English.

Amount to be transferred is INR 150/student

Bank account details to which NEFT to be done is below:

Bank : Axis Bank Account Type : Saving account Account Number : 920010074677919
IFSC code : UTIB0000006 Branch : Mylapore, Chennai-600004.

Once this is done, please inform AMTI by email support@amtionline.com. We strongly suggest you to visit this page to have clear instructions before you process the payment.

NMTC Exam pattern- Preliminary Stage exam

We will start with a caveat here. This exam pattern that is explained below is from our observations of the previous NMTC exams. By design, NMTC Math Olympiads are different and hence the pattern could be changed any year. However, having said that, it has remained consistent for the last few years and that is what we will be presenting.

The NMTC Math Olympiad exam duration would be for 2 hours and the total number of questions are expected to be around 30. These 30 questions are split into 2 sections: Part A & Part B.

Part A: In Part A, there are 20 problems with 4 choices to choose from. Each correct answer gives you 1 mark while wrong answer gives you -0.5 marks. There would be several questions from Number theory in this section and it is likely to take time to solve it.

Part B: This would be similar to FITA ( Fill In The Answer ) where no option choices are provided. There are 10 FITA questions each offering +1 for every correct answer and -0.25 for any wrong answer. Since there are no choices, these questions usually have a logic that once found out leads to the answer quickly.

As you can see above, the high negative marking penalizes any candidate from guessing the answer to the question. Hence, it is very important that students focus on accuracy to crack the test instead of relying too much on speed. As mentioned earlier, all the questions in both PArt A & Part B would be non-routine in nature.

NMTC Exam: Type of Questions/What does Non-Routine questions mean?

A common query that we hear from parents is asking what non-routine questions mean. Very simply non-routine questions are those which are designed to test the students’ applicability of a concept. Hence in a non-routine question, several layers of concept come together and usually there is more than one way to solve the question. However, the interesting aspect is that conceptual knowledge is almost always the same as what is taught in school.

Here is a video that does a good job of explaining what non-routine questions are along with a very good chess board question that you must try!

Example Question: Consider a normal chessboard with 64 squares. We have to fill the chess board with numbers from 1 to 100. There is only 1 rule on the chessboard. The number on any square in the chessboard must be the average of the numbers on the squares around it. In how many different ways can we fill the chessboard?

Once you try solving it on your own, you can look at the video below. Please navigate to minute 1:40 to start seeing the question and the solution follows from there.

Notice that it appears difficult at first but once you get the idea, there is an AHA moment! That is the definition of a good non-routine question.

Below are a couple of more examples of non-routine questions along with their solutions:

Qn1: In how many ways can 2 squares be chosen from a 8 cross 8 chessboard such that the squares are not on the same row or same column.

Qn 2: When we write down numbers from 1 to 100, how many times does the digit 3 get repeated?

NMTC - Preparation Strategy

It is important to remember that NMTC math olympiads are non-routine math questions. Hence there is no specific template or formulas that will help in the exam. Having said that, the best way to prepare for this is by doing a bunch of non-routine problems. There are several suggested books in the AMTI website that one can refer to for kickstarting the preparation.

We at PiVerb have been training several students through live online classes for Math Olympiads for over 6 months now. You can visit our website www.piverb.com or see our youtube page here to see questions and solutions to sample NMTC Math Olympiad problems.