Grades 3–12
Mathematics Olympiad
Mathematics is everywhere — in the rhythm of music, the design of nature, the flow of traffic. The Copernicus Mathematics Olympiad turns that sense of wonder into problem-solving power, inviting students to experience the elegance of logic, the beauty of symmetry, and the thrill of unlocking solutions once thought impossible.
Syllabus
Five categories across grade bands.
Category 1 — Grades 3 & 4
Number operations
- Addition, subtraction, multiplication, division up to 10,000
- Place value and number properties
- Rounding to nearest 10, 100, 1,000
Fractions
- Four operations with fractions
- Equivalent fractions
- Simplifying, comparing, ordering
Divisibility & prime numbers
- Divisibility rules
- Prime vs composite
- Factors, multiples, prime factorisation
Measurement
- Length, area, volume, mass, time
- Unit conversions
- Real-world problems
Geometry
- Classifying triangles, quadrilaterals, circles
- Sides, angles, symmetry
- Parallel and perpendicular lines
- Area and perimeter
Logic & data
- Logical reasoning puzzles
- Bar graphs, Venn diagrams
- Reading data from tables and charts
Word problems & patterns
- Multi-step word problems
- Arithmetic and geometric sequences
- Time and calendar
Category 2 — Grades 5 & 6
Numbers & arithmetic
- Whole numbers, decimals, fractions, mixed numbers
- GCD and LCM
- Percentages
Algebra & equations
- One-step linear equations
- Variables in equations
- Simple interest
Geometry
- Properties of polygons
- Angles (acute, right, obtuse, complementary, supplementary)
- Perimeter, area, volume
- Lines of symmetry
Measurement & statistics
- Unit conversions
- Mean, median, mode, range
Ratios & proportions
- Solving ratio problems
- Proportions in real life
Problem solving
- Translating word problems
- Pattern recognition and logical reasoning
All topics of Category 1
- Cumulative from Grades 3–4
Category 3 — Grades 7 & 8
Numbers & algebra
- Advanced fractions
- Squares and square roots
- Rational and irrational numbers
- Algebraic expressions
- Equalities and inequalities
Equations & functions
- Systems of linear equations
- Linear functions, slope and intercept
Ratios, proportions & combinatorics
- Rates and proportions
- Counting principles
- Introduction to permutations, combinations, probability
Geometry
- Regular polygons
- Area and circumference of a circle
- Composite figures
- Pythagorean theorem
- Congruence and similarity
Measurement & coordinate geometry
- Volume and surface area (prisms, cylinders)
- Cartesian plane, distance and midpoint
- Equations of lines
Reasoning & problem solving
- Word problems
- Patterns and sequences
All topics of Category 2
- Cumulative from Grades 5–6
Category 4 — Grades 9 & 10
Number theory & algebra
- Real numbers, absolute values
- Exponents and exponential expressions
- Polynomials
- Quadratic functions
Logarithms & exponentials
- Properties of logarithms
- Exponential growth and decay
Geometry
- Coordinate geometry, conic sections
- Properties of circles
- Volume and surface area (pyramids, cones, spheres)
- Law of sines and cosines
Statistics & probability
- Mean, median, mode and outliers
- Simple, complementary and independent probability
Functions & graphs
- Reading and interpreting graphs
- Domain, range, inverse, transformations
Problem solving
- Sequences and series
- Linear and quadratic inequalities
All topics of Category 3
- Cumulative from Grades 7–8
Category 5 — Grades 11 & 12
Advanced algebra
- Polynomial equations and inequalities
- Remainder and factor theorems
- Non-linear equations, Vieta's formulas
Inequalities & analysis
- Absolute value and systems of inequalities
- Arithmetic and geometric series, sigma notation
Logarithms & exponentials
- Advanced logarithm laws
- Growth and decay applications
Binomial theorem
- Expansion and specific terms
- Applications in combinatorics
Combinatorics & probability
- Permutations, combinations
- Pigeonhole, inclusion-exclusion
- Conditional probability, Bayes' theorem
Geometry & trigonometry
- Conic sections
- Trigonometric identities and equations
Additional topics
- Function types and transformations
- Introductory calculus — limits and differentiation
All topics of Category 4
- Cumulative from Grades 9–10
Format · Marking · Dates · Fees
The essentials.
Exam format
- Duration: 75 minutes
- Questions: 20 total
- Preliminary: 20 multiple-choice questions
- Global: 15 multiple-choice + 5 open-ended questions
- Qualifying: 40% in the Preliminary Round qualifies for the Global Round
- Languages: English, Spanish, Russian, French
Marking scheme
Preliminary
- 5 easy questions — 4 marks each (−1 for incorrect)
- 10 average questions — 5 marks each (−2 for incorrect)
- 5 hard questions — 6 marks each (−3 for incorrect)
- Total: 100 marks
Global
- 5 easy questions — 3 marks each (−1 for incorrect)
- 5 medium questions — 4 marks each (−2 for incorrect)
- 5 hard questions — 6 marks each (−3 for incorrect)
- 5 open-ended — 7 marks each (no negative marking)
- Total: 100 marks
Dates
- Round 1 (Preliminary): Saturday, 10 January 2026
- Round 2 (Preliminary): Saturday, 21 February 2026
Fees
- Preliminary: $20 USD
- Some countries may charge up to $30 to cover local awards, certificate printing and medal shipping.
- Global: Varies by venue — confirmed after Preliminary Round results.
- $200 USD non-refundable processing fee per Global Round registrant.
- Absolute Winners (youngest top scorers) of each category receive a fee waiver for the Global Round.
Recognition
Medals & certificates.
G
91–100%
Gold
Gold Medal + 10% discount on Global Round registration.
S
75–90%
Silver
Silver Medal + 5% discount on Global Round registration.
B
50–74%
Bronze
Bronze Medal for strong international performance.