Best Books and Resources for NMTC Preparation

Primary & Sub-Junior (Class 5–7)

• *Mathematical Circles* — Dmitri Fomin, Sergey Genkin, Ilia Itenberg. A discussion-style collection of logic and pattern problems that builds reasoning without requiring content beyond the school syllabus — a strong fit for this level.
• *An Excursion in Mathematics* — published by Bhaskaracharya Pratishthana. A well-loved Indian text that eases students into competition-style thinking through accessible, well-sequenced problems.
• *Challenging Mathematical Problems with Elementary Solutions, Vol. 1* — A.M. Yaglom and I.M. Yaglom. Denser than the two above, but a good next step once a Class 7 student is comfortable with basic pattern problems.
• Past NMTC Primary and Sub-Junior papers, worked through slowly and discussed rather than timed initially — AMTI sells compiled booklets of past papers directly through its own channels, and many coaching institutes maintain organized archives by level as well.

Junior (Class 8–9)

• *Challenge and Thrill of Pre-College Mathematics* — V. Krishnamurthy, C.R. Pranesachar, K.N. Ranganathan, B.J. Venkatachala. An Indian-context classic closely aligned with the level NMTC Junior and IOQM both test.
• *Elementary Number Theory* — David M. Burton. A clear, thorough treatment of divisibility, modular arithmetic and prime factorization — exactly the number theory foundation Junior level starts to demand.
• *The Art of Problem Solving, Volume 1* — Sandor Lehoczky and Richard Rusczyk. Covers algebra, geometry and counting as a well-structured introduction to competition mathematics.
• Past NMTC Junior papers, alongside IOQM-level material once a student is close to Class 8-9, since the two exams overlap heavily in both content and difficulty.

Inter & Senior (Class 10–12)

• *Problem-Solving Strategies* — Arthur Engel. Widely regarded as one of the most comprehensive olympiad problem-solving references, covering algebra, number theory, geometry and combinatorics with genuine depth.
• *Functional Equations: A Problem Solving Approach* — B.J. Venkatachala. A focused Indian-context text on exactly the functional-equation problems that show up at Inter and Senior level.
• *Inequalities: An Approach Through Problems* — B.J. Venkatachala. Covers AM-GM, Cauchy-Schwarz and related inequality techniques methodically, with problems pitched at NMTC Senior and INMO level.
• *Geometry Revisited* — H.S.M. Coxeter and S.L. Greitzer. A classic for synthetic geometry proof-writing, moving beyond formula-based approaches to genuine construction and argument.
• Past NMTC Inter and Senior papers, alongside past INMO papers for comparable proof-writing practice — both are available through AMTI and HBCSE respectively.
• A mentor who can review written solutions — at this level, feedback on proof quality matters as much as the reference material itself.

A Note on Using Past Papers Well

Past papers are most valuable when reviewed for the reasoning, not just checked against an answer key — since NMTC Part B rewards the argument, working through official or well-explained solutions to past papers teaches the expected level of rigor far more effectively than just checking whether the final answer matches.

How to Actually Use These Books Well

• Work slowly through fewer books, not quickly through many. A student who genuinely finishes and reviews mistakes in one book learns more than one who skims three.
• Match the book to the level, not the ambition. A Class 7 student handed Engel's Problem-Solving Strategies too early usually comes away discouraged rather than challenged.
• Write Part B answers in full, even when practicing from a book. NMTC rewards the written argument, so practice should build that habit from day one, not just problem-solving speed.

Summary Table