PRMO: syllabus, mock tests and practice
Pre-Regional Mathematical Olympiad archive: original past papers, answer keys and playable numerical-answer tests.
- Syllabus years
- 2026-27
- Mock tests
- 9
- Downloads
- 15
About the PRMO exam
How the exam works
PRMO past papers provide numerical-answer practice. For the current national mathematics selection route, use IOQM → RMO → INMO and the subsequent selection/training stages. PRMO archive dates do not describe a current application cycle.
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
This category is an archive of past PRMO papers. There is no separately announced next PRMO in the current route checked: the first stage is IOQM. IOQM 2026 was held on 6 September; its next edition's date is not verified. Current qualifiers proceed to RMO on 15 November 2026 and INMO on 17 January 2027. MTA(I) says RMO registration opens 2 November. 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.
PRMO syllabus
PRMO syllabus, All classes · 2026-27
Number Theory
- Integers, Divisibility and Primes: Study divisibility rules, factors and multiples, primes 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.
- Remainders and Modular Arithmetic: Work with remainders and congruences, including last digits and cycles of powers.
- 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 relations between roots and coefficients.
- Quadratic Equations and Expressions: Solve quadratics and study the discriminant, nature of roots and maximum and minimum values.
- Systems of Equations: Solve systems of linear and simple non-linear equations by substitution, elimination and symmetry.
- Inequalities: Use basic inequalities such as AM-GM to find greatest and least values.
- Sequences and Series: Work with arithmetic and geometric progressions and finite series, using sums and telescoping.
Geometry
- Triangles: Congruence, Similarity and Area: Use congruence and similarity, the Pythagoras theorem and area relations in triangles.
- Circles and Cyclic Quadrilaterals: Use angles in a circle, chords, tangents and cyclic quadrilaterals to find lengths and angles.
- Trigonometry and Coordinate Geometry: Use trigonometric ratios, identities, distance and section formulae and lines and circles on the coordinate plane.
- Mensuration and Areas: Compute perimeters, areas and volumes of plane figures and solids, including composite figures.
Combinatorics
- Counting, 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.
- Probability: Compute probabilities of events using counting, at an introductory level.
School Mathematics Foundations
- Arithmetic, Ratio and Percentages: Revise Class 8-10 arithmetic: fractions, ratios, percentages, averages and speed-time-work.
- Algebra and Geometry Basics: Revise Class 8-10 algebra and geometry: exponents, surds, linear equations, angles, triangles, circles, areas and volumes.
Rounds and levels
- Previous Year Papers: Original PRMO papers from the supplied archive, including Mumbai regional editions.
- Official Sample Papers: Official PRMO sample questions.
More exams on SkillStar
PRMO: questions parents ask
- What is in the PRMO syllabus for 2026-27?
- 19 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 PRMO mock tests on SkillStar?
- Yes, 9 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 PRMO papers?
- Yes. The PRMO Downloads tab on SkillStar has 15 files for this exam.
- How does my child start PRMO practice?
- Sign up free as a parent, add your child with their class, and pick PRMO 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 PRMO 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 PRMO 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.