IOQM: syllabus, mock tests and practice
Indian Olympiad Qualifier in Mathematics — Stage 1 of India's Mathematical Olympiad programme, conducted by MTA(I). Top scorers qualify for RMO (Stage 2) and eventually INMO and IMO. Each answer is a whole number from 00–99. 30 questions, 100 marks, 3 hours. No negative marking. For students in Class VIII–XII.
- Classes
- Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
- Syllabus years
- 2026-27
- Mock tests
- 8
- Downloads
- 15
About the IOQM exam
How the exam works
IOQM is the first stage of the national mathematics Olympiad programme. It is a three-hour numerical-answer examination with 30 questions, answers entered from 00 to 99, 100 marks and no negative marking. Qualifiers can proceed to RMO under the published 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
IOQM 2026 was held on 6 September 2026 and registration is closed. The next IOQM edition's date and registration window were not verified. Current qualifiers: RMO is on 15 November 2026, 13:00–16:00; MTA(I) now announces RMO registration starting 2 November. INMO follows on 17 January 2027, 12:00–16:30. 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.
IOQM syllabus
IOQM syllabus, All classes · 2026-27
Number Theory
- Integers, Divisibility and Primes: Study divisibility rules, factors and multiples, prime and composite numbers and prime factorisation. Practise counting divisors and finding digits to reach a whole-number answer.
- GCD, LCM and the Euclidean Algorithm: Find the greatest common divisor and least common multiple using prime factors and the Euclidean algorithm. Solve word problems built on them.
- Remainders and Modular Arithmetic: Work with remainders and congruences, including last digits and cycles of powers. Use Fermat's little theorem in simple cases.
- Integer Equations: Solve linear and simple non-linear equations in integers by factoring, bounding and checking cases.
- Number Bases and Digit Problems: Convert between bases and solve problems on digits, digit sums and number patterns.
Algebra
- Polynomials and Factorisation: Use algebraic identities, factorisation, the remainder theorem and the relations between roots and coefficients.
- Quadratic Equations and Expressions: Solve quadratics and study the discriminant, nature of roots and the sum and product of roots. Find maximum and minimum values.
- Systems of Equations: Solve systems of linear and simple non-linear equations by substitution, elimination and symmetry.
- Inequalities: Prove and use basic inequalities such as AM-GM to find greatest and least values.
- Sequences and Series: Work with arithmetic and geometric progressions and other finite series. Use sums, telescoping and recurrence.
- Complex Numbers: Learn the algebra of complex numbers, modulus, conjugate and roots of unity at an introductory level.
- Functions and Mathematical Induction: Study functions defined by rules and relations, and use the principle of mathematical induction.
Geometry
- Triangles: Congruence, Similarity and Area: Use congruence and similarity, the Pythagoras theorem, angle bisector and area relations in triangles.
- Circles and Cyclic Quadrilaterals: Use angles in a circle, chords, tangents and cyclic quadrilaterals to find lengths and angles.
- Triangle Centres and Special Lines: Study the centroid, incentre, circumcentre, orthocentre, medians, altitudes and their properties.
- Trigonometry for Geometry: Use trigonometric ratios, identities and the sine and cosine rules to solve geometric problems.
- Coordinate Geometry: Apply distance, section formula, lines and circles on the coordinate plane to geometric problems.
- Mensuration and Areas: Compute perimeters, areas and volumes of plane figures and solids, including composite figures.
Combinatorics
- Counting Principles, Permutations and Combinations: Use the addition and multiplication rules, arrangements, selections, and inclusion-exclusion.
- Pigeonhole Principle: Learn the pigeonhole principle and use it in simple existence and counting problems.
- Recursion and Recurrence Relations: Set up and solve recurrences for counting problems and sequences.
- Elementary Graph Theory: Learn vertices, edges, degrees, paths and connectedness, and solve simple graph-based problems.
- Probability: Compute probabilities of events using counting, including conditional probability and expected value at an introductory level.
School Mathematics Foundations
- Arithmetic, Ratio and Percentages: Revise the Class 8-10 arithmetic expected before Olympiad problem solving: fractions, ratios, percentages, averages and speed-time-work.
- Algebra Basics: Revise Class 8-10 algebra: exponents, surds, linear equations and basic identities.
- Basic Geometry and Mensuration: Revise Class 8-10 geometry: angles, triangles, quadrilaterals, circles, areas and volumes.
Rounds and levels
- 2026-27: Practice for IOQM 2026-27 (exam date: 6 September 2026).
- Previous-year papers: Past IOQM question papers.
More exams on SkillStar
IOQM: questions parents ask
- Which classes can prepare for IOQM on SkillStar?
- IOQM 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 IOQM syllabus for 2026-27?
- 26 topics in Number Theory, Algebra, Geometry, Combinatorics and School Mathematics Foundations, laid out subject by subject on this page. On SkillStar your child can tick off each topic as they learn it.
- Are there IOQM mock tests on SkillStar?
- Yes, 8 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 IOQM papers?
- Yes. The IOQM Downloads tab on SkillStar has 15 files for this exam.
- How does my child start IOQM practice?
- Sign up free as a parent, add your child with their class, and pick IOQM 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 IOQM 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 IOQM 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.