Advanced Competitions

University-level reasoning, formal proof, and interdisciplinary scientific modeling for advanced competitors.

Scope of Assessment

Advanced Competitions are designed for students prepared for university-level reasoning and proof-based problem solving.

01Formal mathematical proofs

02Abstract reasoning

03Interdisciplinary integration

04Scientific modeling at advanced depth

Each category moves through a full competition sequence: online qualification, supervised school examination, and international finals.

Format: online extended-response problems with proof-based components.

Sample Questions

Solve: $$x^4-10x^2+9=0$$

Evaluate: $$\int_0^1 (4x^3-2x)\,dx$$

Format: written proof-based assessment with multi-step analytical problems.

Sample Questions

Prove that for positive real numbers a,b, $$\frac{a}{b}+\frac{b}{a}\ge2$$

Determine whether the series converges: $$\sum_{n=1}^{\infty}\frac{1}{n^3}$$

Format: extended proof problems, interdisciplinary modeling competition, and optional academic symposium presentation.

Sample Questions

Let $$a_{n+1}=\frac{1}{2}\left(a_n+\frac{7}{a_n}\right)$$ Show that the sequence converges and find its limit.

Prove that: $$\sum_{k=1}^{n}k^2=\frac{n(n+1)(2n+1)}{6}$$