Shiing-Shen Global Olympiad: Mathematics Syllabus

This syllabus defines the full scope of mathematical concepts assessed in the Shiing-Shen Global Olympiad. Candidates are expected to demonstrate conceptual mastery, analytical depth, and problem-solving rigor.

1

Foundations of Algebra

  • Quadratic equations, discriminants, and nature of roots
  • Systems of linear and non-linear equations
  • Arithmetic and geometric progressions (AP & GP)
  • Laws of indices and logarithmic identities
  • Binomial theorem for positive integer exponents
2

Trigonometry & Circular Functions

  • Right-angled trigonometry and circular measure (radians)
  • Sine rule, cosine rule, and area of triangles
  • Compound, double, and half-angle formulas
  • Trigonometric identities and equations
  • Inverse trigonometric functions and domains
3

Coordinate Geometry of the Plane

  • Straight lines: gradients, intercepts, intersections
  • Parallel and perpendicular line conditions
  • Circles: equations, tangents, secants
  • Locus problems and midpoint theorems
  • Introduction to conic sections
4

Differential Calculus

  • Limits, continuity, and first principles
  • Product, quotient, and chain rules
  • Maxima, minima, and inflection points
  • Rates of change and kinematics
  • Implicit differentiation and related rates
5

Integral Calculus

  • Indefinite integrals and basic rules
  • Definite integrals and fundamental theorem
  • Integration by substitution and parts
  • Area under curves
  • Volumes of revolution
6

Vectors & 3D Geometry

  • Vector operations and scalar multiplication
  • Magnitude, unit vectors, direction cosines
  • Dot and cross products
  • Equations of lines and planes
  • Distances in three-dimensional space
7

Probability & Discrete Mathematics

  • Sets, Venn diagrams, and operations
  • Mutually exclusive and independent events
  • Conditional probability and Bayes’ theorem
  • Discrete random variables
  • Expectation and variance
8

Statistics & Data Analysis

  • Measures of central tendency
  • Measures of dispersion
  • Normal distribution and Z-scores
  • Correlation and regression
  • Sampling and statistical significance
9

Olympiad Number Theory

  • Modular arithmetic and CRT
  • Fermat’s and Euler’s theorems
  • Diophantine and Pell’s equations
  • Quadratic residues
  • Orders, primitive roots, and LTE
10

Advanced Synthetic Geometry

  • Power of a point and radical axis
  • Ceva’s and Menelaus’s theorems
  • Cyclic quadrilaterals and Simson line
  • Geometric inversion and homothety
  • Projective geometry fundamentals
11

Competitive Combinatorics

  • Inclusion-exclusion and double counting
  • Stars and bars, circular permutations
  • Recurrence relations and generating functions
  • Graph theory principles
  • Ramsey theory and extremal problems
12

Algebra & Functional Equations

  • Vieta’s formulas and symmetric polynomials
  • Roots of unity and irreducibility
  • Cauchy functional equation
  • Classical inequalities
  • Rearrangement and Schur’s inequalities
13

Game Theory & Strategic Thinking

  • Nim and Sprague–Grundy theorem
  • Invariants and monovariants
  • Pigeonhole principle (strong form)
  • Winning strategies in zero-sum games
  • Tiling, parity, and construction problems

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