Singapore Mathematical Olympiad (SMO) Syllabus and Preparation Tips
The Singapore Mathematical Olympiad (SMO) is a prestigious math competition held annually in Singapore to assess students’ mathematical abilities. The syllabus may vary slightly each year.(Singapore Mathematical Olympiad (SMO) Syllabus and Preparation Tips)
A tentative overview of the SMO syllabus across all categories:
For Junior Section (Secondary 1 and 2 / Grades 7 and 8) SMO Syllabus:
1. Arithmetic and Number Theory:
- Integers, fractions, and decimals
- Divisibility rules, prime numbers, and prime factorization
- Greatest common divisor (GCD) and least common multiple (LCM)
- Modular arithmetic and basic congruences
2. Algebra:
- Basic algebraic manipulations and simplifications
- Linear equations and inequalities
- Quadratic equations
- Polynomials and factoring
- Sequences and series
3. Geometry:
- Basic properties of triangles, quadrilaterals, and circles
- Congruence and similarity
- Pythagoras’ theorem
- Perimeter, area, and volume calculations
- Geometric transformations
4. Combinatorics and Probability:
- Basic counting principles (addition and multiplication rules)
- Permutations and combinations
- Basic probability concepts
For Senior Section (Secondary 3 and 4 / Grades 9 and 10) SMO Syllabus:
1. Advanced Number Theory:
- Divisibility and properties of integers
- Diophantine equations
- Advanced modular arithmetic
- Number sequences and series (arithmetic and geometric progressions)
2. Advanced Algebra:
- Complex numbers and their properties
- Higher-degree polynomials
- Systems of linear equations
- Exponential and logarithmic functions
- Algebraic inequalities
3. Advanced Geometry:
- Coordinate geometry and equations of lines and circles
- Advanced properties of triangles and circles
- Geometric inequalities
- Locus problems
4. Advanced Combinatorics and Probability:
- Advanced counting techniques (Pigeonhole principle, inclusion-exclusion principle)
- Binomial theorem
- Advanced probability problems
- Recurrence relations
For Open Section (Junior College / Grades 11 and 12) SMO Syllabus:
1. Higher Number Theory:
- Advanced properties of numbers
- Number theoretic functions (e.g., Euler’s totient function)
- Continued fractions
- Quadratic residues and non-residues
2. Advanced Algebra and Functions:
- Abstract algebra concepts (groups, rings, fields)
- Advanced polynomial theory (roots and coefficients, Vieta’s formulas)
- Functional equations
- Advanced inequalities (AM-GM, Cauchy-Schwarz)
3. Advanced Geometry:
- Transformation geometry (homothety, inversion)
- Advanced Euclidean geometry
- Non-Euclidean geometry concepts
- Projective geometry
4. Advanced Combinatorics and Probability:
- Graph theory and its applications
- Generating functions
- Advanced combinatorial identities
- Probabilistic method
Singapore Mathematical Olympiad (SMO) SMO Preparation Tips:
1. Practice Past Papers:
- It is important for participants to review SMO previous year papers to understand the level and exam pattern.
- Register for the SCO Olympiad exam, practice with supplementary questions, and enter real-time international competition.
2. Do follow Recommended Books for exam preparation:
- “The Art of Problem Solving” series by Richard Rusczyk
- “Mathematical Olympiad Treasures” by Titu Andreescu and Bogdan Enescu
- “Problems in Elementary Number Theory” by Titu Andreescu and Dorin Andrica
3. Join Math Workshop or Online Math conclave or register for SCO Olympiad online:
- Engage in various mathematics workshops and register for online Olympiad competitions such as SCO Olympiad or Art of Problem Solving (AoPS) for additional support and resources.
4. Attend Mathematics Workshops and Math Training Camps:
Participate in mathematical workshops and camps organized by schools or any mathematical forum. This will help in preparing for higher grade mathematical problems with real problem-solving techniques.
5. Focus on learning Mathematics Problem-Solving Techniques:
To become experts in math, it’s crucial to practice a variety of math problems. Over time, participants will learn and understand the proper techniques to solve challenging mathematical problems.
SCO Olympiad Exam Global Presence
Reference Link :
List of Olympiad exams in Singapore
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