INMO: syllabus, mock tests and practice
Indian National Mathematical Olympiad — Stage 4 of India's Mathematical Olympiad programme, conducted by HBCSE. Top scorers are selected for the International Mathematical Olympiad Training Camp (IMOTC) and ultimately represent India at the International Mathematical Olympiad (IMO). Subjective proof-based paper. For students in Class VIII–XII.
- Classes
- Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
- Syllabus years
- 2026-27
- Mock tests
- 24
- Downloads
- 33
About the INMO exam
How the exam works
INMO is a proof-based mathematics Olympiad stage. The current schedule specifies six questions and four and a half hours. Write complete reasoning and proofs; qualification is governed by HBCSE's current selection rules.
Who can apply
The 2026 IOQM portal lists Classes 8–12 and birth dates 1 August 2007–31 July 2014, subject to its complete eligibility rules. RMO and INMO require qualification or a specifically permitted exemption under the current selection policy. These are 2026-cycle rules; do not assume the same birth-date window for the next IOQM edition.
When it happens
Next INMO: 17 January 2027, 12:00–16:30 IST, as listed in HBCSE's 2026–27 mathematics schedule. RMO is on 15 November 2026, 13:00–16:00; its registration starts 2 November according to MTA(I). INMO participation depends on the current selection rules; it is not an open direct-entry exam. Checked 1 November 2026.
How to register
IOQM accepts centre-based and individual online registration during its published window. The 2026 fee was ₹300, or ₹180 for KV/JNV pupils. Eligible candidates must separately register for RMO/INMO as instructed; the MTA(I) FAQ says no further exam payment is involved. Keep your enrolment number, date of birth, photo and school/identity documents ready. Verify the current notice before starting a new-cycle application.
Official website, syllabus and past papers
The mathematics syllabus centres on algebra, geometry, number theory and combinatorics, with non-routine problem solving. Use the official syllabus and stage-specific source papers.
INMO syllabus
INMO syllabus, All classes · 2026-27
Number Theory
- Divisibility, Primes and Factorisation: Prove results about divisibility, primes, prime factorisation and divisor functions with complete, rigorous arguments.
- GCD, LCM and Euclidean Algorithm: Use the Euclidean algorithm, Bezout's identity and gcd and lcm properties in proofs.
- Congruences, Fermat and Euler: Use congruences, residue systems, Fermat's little theorem, Euler's theorem and the Chinese remainder theorem.
- Diophantine Equations: Solve and prove results on integer equations using factoring, parity, modular restrictions, bounding and descent.
- Orders, Primitive Roots and Valuations: Study the order of an element modulo n and p-adic valuations, and apply them to hard divisibility problems.
Algebra
- Polynomials and Roots: Study polynomial identities, factor theorem, Vieta's relations and the behaviour of roots.
- Inequalities: Prove inequalities using AM-GM, Cauchy-Schwarz, rearrangement and clever substitutions.
- Functions and Functional Equations: Solve functional equations over integers and reals and prove properties of functions.
- Sequences, Series and Recurrences: Analyse sequences, finite series and linear recurrences.
- Complex Numbers: Use the algebra and geometry of complex numbers, including roots of unity, in proofs.
- Mathematical Induction: Prove statements for all natural numbers by induction and strong induction.
Geometry
- Triangles, Similarity and Area: Prove results using congruence, similarity, angle bisector and area relations.
- Circles, Power of a Point and Cyclic Quadrilaterals: Use angle chasing, tangents, radical axis and power of a point to prove results on circles.
- Triangle Centres and Lines: Study the centroid, incentre, circumcentre, orthocentre, nine-point circle and Euler line, with Ceva's and Menelaus' theorems.
- Trigonometry, Coordinates and Vectors: Use trigonometric identities, coordinate methods and vectors to prove geometry results.
Combinatorics
- Counting and Inclusion-Exclusion: Count arrangements, selections and sets with the addition and multiplication rules and inclusion-exclusion, and justify each count.
- Pigeonhole Principle: Use the pigeonhole principle and its generalisations in existence proofs.
- Recursion and Generating Ideas: Set up and solve recurrences and use bijections and double counting.
- Graph Theory: Study graphs, trees, connectivity, matchings, colouring and Euler paths, and prove results about them.
- Invariants, Colouring and Extremal Principle: Use invariants, colouring and extremal arguments to prove existence and impossibility.
- Probability: Compute probabilities using counting, conditional probability and expected value.
Rounds and levels
- 2026-27: Practice for INMO 2026-27 (exam date: 17 January 2027).
- Previous-year papers: Past INMO question papers.
More exams on SkillStar
INMO: questions parents ask
- Which classes can prepare for INMO on SkillStar?
- INMO practice on SkillStar is arranged for Grade 8, Grade 9, Grade 10, Grade 11 and Grade 12. Each child sees what's right for their own class.
- What is in the INMO syllabus for 2026-27?
- 21 topics in Number Theory, Algebra, Geometry and Combinatorics, laid out subject by subject on this page. On SkillStar your child can tick off each topic as they learn it.
- Are there INMO mock tests on SkillStar?
- Yes, 24 mock tests. Each one is marked the moment your child finishes, with a question-by-question review, and can be taken again as often as they like.
- Can I download INMO papers?
- Yes. The INMO Downloads tab on SkillStar has 33 files for this exam.
- How does my child start INMO practice?
- Sign up free as a parent, add your child with their class, and pick INMO from the exam list. Every new family gets welcome credits, lots of content costs nothing, and anything paid shows its price in credits before you decide.
- Is SkillStar the official INMO website?
- No. SkillStar is an independent practice platform and is not affiliated with, or endorsed by, the organisers of these exams. Exam names belong to their respective owners. Check dates, fees and registration with the INMO organisers.
SkillStar is an independent practice platform and is not affiliated with, or endorsed by, the organisers of these exams. Exam names belong to their respective owners.