Asia Pacific Mathematics Olympiad (APMO) syllabus

The Asia Pacific Mathematics Olympiad (APMO) syllabus covers a wide range of topics in Mathematics and focuses on advanced problem-solving and critical-thinking abilities for students. It is one of the most prestigious Olympiad exams conducted in the Asia Pacific region.

Below is the list of the APMO syllabus :

Algebra:

Equations and inequalities

Polynomials and their properties

Systems of equations

Functional equations

Vieta’s formulas

Arithmetic and geometric progressions

Number Theory:

Properties of integers

Divisibility and modular arithmetic

Prime numbers and their properties

Diophantine equations

Fermat’s little theorem

Chinese remainder theorem

Geometry:

Euclidean geometry

Properties of triangles, circles, and polygons

Geometric transformations

Coordinate geometry

Trigonometry in geometrical contexts

Combinatorics:

Counting techniques: permutations, combinations

Binomial coefficients

Pigeonhole principle

Inclusion-exclusion principle

Graph theory basics: paths, cycles, trees

Recurrence relations and generating functions

Miscellaneous:

Basic set theory and operations

Mathematical induction

Basic calculus: limits, derivatives, integrals (basic level)

Logical reasoning and problem-solving strategies

Asia Pacific Mathematics Olympiad (APMO) syllabus

Preparation Tips:

Fundamental Concepts: The APMO is a prestigious exam requiring participants to master the fundamental concept of all the concepts of Mathematics.
Problem-Solving Practice: To succeed in exams like APMO, practice solving the previous year’s problems and practice with over 100,000 questions available on sites like SCO IMO.
Proof Techniques: A solid grasp of mathematical reasoning and proof techniques is crucial for this exam.
Time Management: Participating in Online Olympiad competitions like SCO IMO helps to be into real Olympiad competition and increase time management and accuracy.

The Asian Pacific Mathematics Olympiad (APMO) is an esteemed competition that demands students to demonstrate strong problem-solving and critical thinking skills, along with a profound grasp of mathematical principles.

Participants are encouraged to engage with advanced-level questions, as this will enhance their problem-solving abilities and their confidence in tackling intricate mathematical problems.