NMTC Syllabus : Class-wise and Level-wise Topics

The NMTC syllabus is not a list of chapters from a school textbook. AMTI publishes it as a cumulative, level-wise list of topics, and the questions are set in the style of mathematical olympiads. A Class 9 student preparing for the Junior (Bhaskara) contest is expected to know the Primary and Sub-Junior topics as well, plus the new ones added at the Junior level.

This page sets out the AMTI topic list for each level, shows where each topic usually starts, and gives a study order you can follow. The topic list comes from AMTI's 2025-26 circular. Topic lists can be revised, so check the circular your school receives each year.

Table of Contents

• NMTC Syllabus at a Glance

• Key Points About the Syllabus

• Primary Level Syllabus (Classes 5 and 6)

• Sub-Junior Level Syllabus (Classes 7 and 8)

• Junior Level Syllabus (Classes 9 and 10)

• Inter Level Syllabus (Classes 11 and 12)

• Senior Level Syllabus (Degree Students)

• How These Topics Show Up in Questions

• Overlap Between Levels and Stages

• How to Cover the Syllabus

• Common Mistakes When Using the Syllabus

• Books Recommended by AMTI

• Official Sources

NMTC Syllabus at a Glance

Key Points About the Syllabus

• It is cumulative: Each level includes everything from the level below it. Skipping the lower topics leaves gaps that questions will find.

• The final follows the olympiad syllabus: AMTI states that the Stage 2 paper covers the syllabus of the pre-regional, regional and national mathematical olympiads and the international olympiad. Stage 1 is described as mostly higher-order, Olympiad-style questions.

• School topics are the starting point: A school textbook covers the basics of many of these areas, but NMTC asks you to use them in unfamiliar combinations.

• English medium only: The contest is conducted in English at all levels, so learn the English mathematical vocabulary for your level.

• Weightage is not published: AMTI does not give topic-wise weightage. The topic lists below are a checklist, not a mark distribution.

Primary Level Syllabus (Classes 5 and 6)

This is the base list. Every later level builds on it, so students in higher classes should treat it as revision material.

At this level, the questions are usually short puzzles that reward patient thinking. Calendar problems, divisibility tricks and ratio puzzles are common starting points, because they can be set cleverly even with simple ideas.

Sub-Junior Level Syllabus (Classes 7 and 8)

Sub-Junior includes the whole Primary list and adds the topics below.

The step up from Primary is mainly in algebra. Students who can factorise confidently and handle identities fluently find the rest much easier, so spend the first weeks here.

Junior Level Syllabus (Classes 9 and 10)

Junior includes all Sub-Junior topics and adds a significant amount of new material. This is where the contest starts to look like a real olympiad.

Algebra and Inequalities

• Equations and polynomials: Higher-degree equations and the remainder theorem.

• Logarithms and sequences: Logarithms, sequences and series, and number bases.

• Proof techniques: Mathematical induction and inequalities.

Geometry

Circle theorems form the core: chords, arcs, cyclic quadrilaterals, tangents, the alternate segment theorem and intersecting chords. Apollonius' theorem and Stewart's theorem are also listed. These need care because the standard school books treat circles only lightly.

Number Theory and Counting

• Number theory: Modular arithmetic and the greatest and least integer functions.

• Counting: Counting principles, permutations and combinations, inclusion and exclusion, and the pigeonhole principle.

Inter Level Syllabus (Classes 11 and 12)

Inter covers all Junior topics and adds the following.

Many Class 11 and 12 students already study trigonometry, coordinate geometry and complex numbers in school, so these topics may feel familiar. The new work is in number theory and functional equations, which are not part of regular school courses.

Senior Level Syllabus (Degree Students)

The Senior (Aryabhata) contest is for degree students and has a final test only. AMTI says it is based on a typical B.Sc. Mathematics syllabus. It is outside the scope of school preparation, so school students can ignore this level.

How These Topics Show Up in Questions

The following four examples are original problems that show the style at each level. They are meant to illustrate how a plain topic becomes a problem, not to predict questions.

Primary: LCM in a Real Setting

Three bells ring at intervals of 12, 15 and 20 minutes. They ring together at 9:00 a.m. When will they next ring together? The LCM of 12, 15 and 20 is 60, so the answer is 10:00 a.m.

Sub-Junior: Identities Instead of Equations

The sum of two numbers is 20 and the sum of their squares is 250. Find their product. Instead of solving for each number, use (a + b) squared = a squared + b squared + 2ab. That gives 400 = 250 + 2ab, so the product is 75.

Junior: Pigeonhole Principle

Show that among any five integers, two have a difference divisible by 4. A number leaves one of four remainders when divided by 4. Five numbers and four possible remainders mean two numbers share a remainder, so their difference is a multiple of 4.

Inter: Wilson's Theorem

Find the remainder when 10! + 1 is divided by 11. Wilson's theorem says that for a prime p, (p - 1)! leaves remainder p - 1 on division by p. So 10! leaves remainder 10, and 10! + 1 is divisible by 11. The remainder is 0.

In all four, the idea is short once you see it. The difficulty is in seeing it, which is why solving many varied problems matters more than reading theory.

Overlap Between Levels and Stages

Because the syllabus is cumulative and Stage 2 follows the olympiad syllabus, much of your effort is shared across both stages.

How to Cover the Syllabus

Since the contest comes only once a year, work backwards from the Stage 1 date. A rough plan for a student starting a few months ahead looks like this.

1. Weeks 1 to 4, foundation: Complete the topics of the level below yours, especially factorisation, identities and divisibility.

2. Weeks 5 to 8, your own level: Cover the topics added at your level, one area a week, solving at least 10 problems per topic.

3. Weeks 9 to 10, mixed practice: Move to mixed sets so that you must recognise the topic from the problem itself.

4. Final weeks, timed sets: Attempt full papers in 2 hours for Stage 1 practice, then handwritten solutions of 3 hours for Stage 2 practice, and revise your error log.

Common Mistakes When Using the Syllabus

• Studying only the current class: Because the list is cumulative, a Class 10 student who has not revisited Sub-Junior algebra will lose time on questions that look new but are not.

• Reading theory without problems: Knowing a theorem is different from seeing where to apply it. For every topic, solve problems of varied difficulty.

• Ignoring the written format: Students who practise only answer-type questions struggle in Stage 2, where marks depend on clear reasoning.

• Treating one source as the full syllabus: Third-party pages sometimes mix up level names or add topics from other olympiads. Use the AMTI circular as the reference.

• Leaving counting and number theory for last: These two areas have the most new ideas for school students, so start them early and revisit them often.

Books Recommended by AMTI

AMTI's circular lists reading for the contest. Some are meant for higher levels, so pick by your class, and pair the problems with timed practice on Testkart so that reading turns into speed.

• Problem solving in general: Problem Solving Strategies by Arthur Engel, Mathematical Circles (Russian Experience) by Dmitri Fomin and others, and Adventures in Problem Solving by Shailesh Shirali.

• Algebra and trigonometry: Elementary Algebra for Schools and Elementary Trigonometry by H. S. Hall and S. R. Knight.

• Geometry: Elements of Geometry (Parts I to VI) by S. Barnard and J. M. Child.

• Counting: Combinatorics for Mathematical Olympiads by Dr. S. Muralidharan.

• Other titles: Olympiad Maths by M. K. Singhal and A. R. Singhal, Challenge and Thrill of Pre-College Mathematics, and AMTI's own publications.

Official Sources

The topic list above is taken from AMTI's circular, and the book list is on the AMTI website. Always compare it with the circular your school receives for the current year.

• Official website: https://www.amtionline.com/

• AMTI book list: https://www.amtionline.com/booklist.html