World Mathematics Tournament
Official Syllabus
Classes 5 – 10 · Six Strands of Mathematical Thinking
Number & Arithmetic
- Large numbers to 10,00,000: place value, comparison, rounding
- Factors, multiples, primes, divisibility rules
- LCM and HCF (basic methods)
- Four operations with BODMAS; smart/mental calculation
- Fractions and decimals: operations and conversions
- Introduction to percentage and ratio
- Number patterns and unit-digit observations
Algebra & Patterns
- Rule-based number and figure patterns
- Balancing simple equations (finding the unknown)
Geometry & Measurement
- 2D and 3D shapes; counting sides, faces, edges, vertices
- Angles: measurement, classification, addition
- Perimeter, area (incl. composite figures), intro to volume
- Symmetry (line); measurement and unit conversions
- Time, elapsed time, and introduction to speed
Data, Statistics & Probability
- Reading bar/line graphs, tables, and pictographs
- Average (mean) as equal sharing
- Likelihood of events: certain, likely, unlikely, impossible
Combinatorics & Counting
- Arranging and ordering objects
- Forming numbers under given conditions
- Simple distribution problems
- Systematic counting of shapes (triangles, squares)
- Simple combinations (choosing without order)
Reasoning & Problem-Solving Techniques
- Gaussian addition (summing 1 to n quickly)
- Chicken-and-rabbit problems (assumption method)
- Excess-and-deficiency problems
- Working backwards from the answer
- Cryptarithms using addition and subtraction
- Magic squares and number puzzles
- Pigeonhole principle (introductory)
- Age, calendar and date logic problems
Students are expected to be familiar with all topics from the previous classes as well.
Number & Arithmetic
- Whole numbers and integers: ordering and operations
- Prime factorisation; LCM and HCF (advanced)
- Divisibility rules and unit-digit of powers
- Fractions and decimals: all four operations
- Ratio, proportion, and the unitary method
- Percentage applications; intro to profit & loss
Algebra & Patterns
- Variables and algebraic expressions
- Linear equations in one variable (basic)
- Number and figure pattern rules
Geometry & Measurement
- Lines, angles, and angle relationships
- Triangles, quadrilaterals, circles: properties
- Perimeter, area, ratio of areas, intro to mensuration
- Symmetry, reflection; measurement conversions
- Speed, distance, time (basic)
Data, Statistics & Probability
- Bar/line graphs, pie charts, and mean
- Simple probability as a fraction of outcomes
Combinatorics & Counting
- Basic routing (paths on a grid)
- Advanced distribution problems
- Counting specific numbers under conditions
- Permutations and combinations (introduction)
Reasoning & Problem-Solving Techniques
- Advanced Gaussian sums and series of squares
- Pigeonhole principle (basic applications)
- Periodic and remainder problems
- Assumption-and-replacement method
- Cryptarithms and magic squares
- Cube-colouring (painted cube) problems
- Two-set Venn diagram reasoning
- Working backwards and guess-and-check heuristics
Students are expected to be familiar with all topics from the previous classes as well.
Number & Arithmetic
- Integers and rational numbers: operations
- Exponents and powers (laws); squares and cubes
- LCM, HCF and remainder problems via factorisation
- Ratio, proportion, unitary method (multi-step)
- Percentage, profit/loss/discount, simple interest
- Surds and square roots (introduction)
Algebra & Patterns
- Algebraic expressions and simplification
- Linear equations in one variable (multi-step)
- Algebraic identities (introduction)
- Arithmetic and geometric sequences (intro)
Geometry & Measurement
- Lines, angles, triangles, and angle sum
- Congruence of triangles (basic); Pythagoras (intro)
- Quadrilaterals and circles (circumference)
- Area and mensuration of 2D shapes
- Coordinate system (introduction)
Data, Statistics & Probability
- Graphs and charts; mean, median, mode
- Probability as a fraction of equally-likely outcomes
Combinatorics & Counting
- Addition and multiplication principles of counting
- Permutations and combinations (with formulas)
- Handshake and pairing problems
- Inclusion–exclusion (two and three sets)
Reasoning & Problem-Solving Techniques
- Pigeonhole principle (advanced)
- Telescoping and method-of-differences sums
- Invariants (introduction)
- Indefinite (Diophantine) equations: counting solutions
- Routing and shortest-path problems
- Journey problems (relative speed, meeting, overtaking)
- Mixture and alligation problems (introduction)
- Defining and using new operations
- Periodic remainder reasoning
- Working backwards and casework
Students are expected to be familiar with all topics from the previous classes as well.
Number & Arithmetic
- Rational numbers; exponents and standard form
- Squares/square roots and cubes/cube roots
- Direct and inverse variation; advanced ratio
- Percentage, profit/loss, simple & compound interest
- Speed-distance-time (relative speed); time-and-work
Algebra & Patterns
- Algebraic expressions, identities, factorisation
- Linear equations: one and two variables
- Introduction to quadratics and inequalities
- Polynomials and the factor theorem (intro)
Geometry & Measurement
- Lines, angles, polygons, and angle sums
- Triangles: exterior angle, congruence, inequality
- Pythagoras (advanced); similar triangles (intro)
- Mensuration: 2D area and 3D surface area/volume
- Transformations and coordinate geometry (intro)
Data, Statistics & Probability
- Charts (advanced interpretation); mean, median, mode
- Theoretical probability of events
Combinatorics & Counting
- Permutations and combinations (applications)
- Inclusion–exclusion principle
- Counting paths, rectangles and squares in a grid
- Distribution and arrangement problems
Reasoning & Problem-Solving Techniques
- Modular arithmetic and periodic remainders (intro)
- Base (non-decimal) number arithmetic
- Parity arguments and invariants
- Casework and systematic enumeration
- Defining new operations and functions
- Extreme principle (introduction)
- Mixture, concentration and replacement problems
- Journey problems (relative speed, encounters, round trips)
- Mathematical induction (introduction)
- Advanced cryptarithms and number puzzles
Students are expected to be familiar with all topics from the previous classes as well.
Number & Arithmetic
- Real, rational and irrational numbers; surds
- Laws of exponents and rationalisation
Algebra & Patterns
- Polynomials: operations, identities, factorisation
- Linear equations in two variables (graphical & algebraic)
- Quadratic expressions; inequalities
- Arithmetic and geometric progressions
Geometry & Measurement
- Coordinate geometry: distance and Cartesian plane
- Euclidean geometry: axioms, lines, angles, transversals
- Triangles and quadrilaterals: congruence and theorems
- Circles: properties and basic theorems
- Angle-chasing and the area-ratio technique
- Heron’s formula; surface area and volume of solids
Data, Statistics & Probability
- Statistics: mean, median, mode; histograms, polygons
- Experimental and theoretical probability
Combinatorics & Counting
- Permutations and combinations (advanced)
- Probability computed through counting
- Inclusion–exclusion and set theory
- Geometric probability (introduction)
Reasoning & Problem-Solving Techniques
- Modular arithmetic (congruences)
- Mathematical induction
- Pigeonhole principle (advanced, worst-case)
- Invariants and monovariants
- Functional patterns and recursion
- Set-theory and inclusion–exclusion reasoning
- Journey and mixture problems (advanced)
- Optimisation by the extreme principle
- Proof strategies: contradiction and construction
Students are expected to be familiar with all topics from the previous classes as well.
Number & Arithmetic
- Real numbers: Euclid’s algorithm, FTA, HCF–LCM
Algebra & Patterns
- Polynomials: zeros, factor and remainder theorems
- Pair of linear equations in two variables
- Quadratic equations: roots, discriminant
- Arithmetic progressions: nth term, sum of n terms
- Inequalities and introduction to functions
Geometry & Measurement
- Coordinate geometry: distance, section formulae, area
- Trigonometry: ratios, identities, standard values
- Heights and distances (applications)
- Circles: tangents and properties
- Similarity, proofs; surface area and volume of solids
- Triangle centres: circumcentre, incentre, centroid, orthocentre
- Advanced angle-chasing and geometric reasoning
Data, Statistics & Probability
- Statistics: mean, median, mode, ogives
- Classical probability; events and outcomes
Combinatorics & Counting
- Advanced permutations and combinations
- Probability through advanced counting
- Conditional probability (introduction)
- Binomial-style and casework counting
Reasoning & Problem-Solving Techniques
- Advanced modular arithmetic and number theory
- Advanced mathematical induction
- Invariants, parity and colouring arguments
- Optimisation and the extreme principle
- Advanced casework and systematic enumeration
- Functional equations and recursion (intro)
- Proof techniques: contradiction, construction, contrapositive
- Integration of multiple techniques in one problem