🔢 Mathematics
Topics
The full Mathematics syllabus, level by level.
The syllabus below shows what can be examined in Mathematics at each level of the Dreamline STEAM Olympiad. Levels follow school grades, so every student competes within their own age group, and topics are cumulative — a later level assumes everything before it. Read it together with the past papers when you plan revision.
Syllabus by level
What may be examined at each level. Topics are cumulative — later levels assume earlier ones.
- 1.Number Sense & Arithmetic
- 2.Patterns & Sequences
- 3.Logic & Mathematical Reasoning
- 4.Visual Arithmetic & Number Puzzles
- 5.Measurement, Comparison & Balance
- 6.Geometry & Spatial Reasoning
- 7.Visual Geometry, Symmetry & Shape Counting
- 8.Grids, Paths & 3D Thinking
- 9.Counting Possibilities
- 10.Time, Calendar, Money & Real-Life Mathematics
- 11.Cuts, Gaps & Arrangements
- 12.Coloring & Spatial Logic
- 13.Magic Squares, Mini-Sudoku & Number Grids
- 14.Olympiad Challenge Problems
- 1.Advanced Number Sense & Arithmetic
- 2.Factors, Multiples & Divisibility
- 3.Patterns, Sequences & Number Cycles
- 4.Smart Calculation & Strategies
- 5.Cryptarithms & Number Codes
- 6.Geometry & Measurement
- 7.Composite & Overlapping Figures
- 8.3D Geometry & Cube Reasoning
- 9.Symmetry & Transformations
- 10.Grids, Paths & Spatial Reasoning
- 11.Non-Routine Word Problems
- 12.Working Backward & Reverse Operations
- 13.Time, Calendar & Intervals
- 14.Age, Ranking & Position
- 15.Counting & Combinatorics
- 16.Guaranteed Outcomes
- 17.Sets, Venn Diagrams & Counting Groups
- 18.Logic, Classification & Deduction
- 19.Data Handling & Interpretation
- 20.Olympiad Challenge Problems
- 1.Number Sense, Arithmetic & Strategies
- 2.Factors, Multiples & Divisibility
- 3.Patterns, Sequences & Number Cycles
- 4.Fractions, Decimals & Percentages
- 5.Algebraic Thinking & Equations
- 6.Ratios, Proportions & Scale
- 7.Rate, Distance & Time
- 8.Work, Rate & Productivity
- 9.Angles, Lines & Polygons
- 10.Perimeter, Area & Dissection
- 11.Triangle Geometry & Pythagorean Reasoning
- 12.Circle Geometry
- 13.3D Geometry & Spatial Reasoning
- 14.Symmetry & Transformations
- 15.Coordinates, Grids & Spatial Problems
- 16.Combinatorics & Systematic Counting
- 17.Probability & Data
- 18.Pigeonhole Principle, Parity & Invariants
- 19.Logic, Games & Graphs
- 20.Olympiad Challenge / Multi-Topic
- 1.Number Sense & Advanced Arithmetic
- 2.Exponents, Powers & Roots
- 3.Algebraic Expressions & Linear Equations
- 4.Introductory Factorization & Algebraic Identities
- 5.Ratios, Proportions & Percentages
- 6.Sequences, Patterns & Introductory Recurrences
- 7.Inequalities, Bounds & Optimization
- 8.Factors, Multiples & Divisibility
- 9.Remainders & Introductory Modular Arithmetic
- 10.Diophantine Equations & Integer Reasoning
- 11.Divisors & Arithmetic Functions
- 12.Angles, Triangles & Quadrilaterals
- 13.Similarity, Pythagorean Theorem & Right Triangles
- 14.Area, Perimeter & Geometric Dissection
- 15.Circle Geometry
- 16.Coordinate Geometry & Transformations
- 17.3D Geometry & Spatial Reasoning
- 18.Counting & Combinatorics
- 19.Probability, Expected Value & Data
- 20.Logic, Graphs, Parity & Invariants
- 1.Advanced Number Sense & Mathematical Techniques
- 2.Exponents, Radicals & Algebraic Manipulation
- 3.Algebraic Identities & Advanced Factorization
- 4.Polynomials, Roots & Vieta's Formulas
- 5.Equations, Systems & Quadratics
- 6.Inequalities & Algebraic Bounds
- 7.Sequences, Recurrences & Series
- 8.Functional Equations
- 9.Divisibility, GCD & Diophantine Equations
- 10.Modular Arithmetic & Congruences
- 11.Euler's Totient Function & Advanced Number Theory
- 12.Arithmetic Functions & Divisor Problems
- 13.Triangle Geometry & Triangle Centers
- 14.Circle Geometry & Power of a Point
- 15.Trigonometry & Advanced Geometric Methods
- 16.Transformations, Homothety & Inversion
- 17.Coordinate & Analytic Geometry
- 18.Combinatorics & Counting
- 19.Graph Theory, Invariants & Extremal Methods
- 20.Probability, Expected Value & Mixed Olympiad Problems
- 1.Advanced Algebraic Identities & Polynomial Methods
- 2.Polynomial Theory & Irreducibility
- 3.Advanced Inequalities
- 4.Functional Equations
- 5.Modular Arithmetic
- 6.Advanced Congruences
- 7.LTE (Lifting the Exponent)
- 8.Diophantine Equations, Pell Equations & Vieta Jumping
- 9.Quadratic Residues & Quadratic Reciprocity
- 10.Arithmetic Functions
- 11.Advanced Triangle Geometry
- 12.Advanced Circle Geometry
- 13.Inversion, Homothety & Transformations
- 14.Barycentric Geometry & Complex Coordinate Geometry
- 15.Advanced Counting, Bijections & Inclusion-Exclusion
- 16.Recurrences & Generating Functions
- 17.Extremal & Probabilistic Combinatorics
- 18.Graph Theory, Matching & Planarity
- 19.Games, Invariants & Combinatorial Geometry
- 20.Logic questions.