Advanced Divison
Challenges
Advanced Division
Scope of Assessment
The Advanced Division is designed for students prepared for university-level reasoning and proof-based problem solving.
Assessment emphasizes:
Formal mathematical proofs
Abstract reasoning
Interdisciplinary integration
Scientific modeling at advanced depth
National Qualifying Round
Format
Online extended-response problems
Proof-based components
Focus Areas
Inequalities
Number theory fundamentals
Advanced algebraic reasoning
Conceptual physics analysis
Sample Questions
Solve:
$$x^4-10x^2+9=0$$
Evaluate:
$$\int_0^1 (4x^3-2x)\,dx$$
Local School Examinations
Format
Written proof-based assessment
Multi-step analytical problems
Focus Areas
Induction
Combinatorics
Advanced calculus concepts
Thermodynamics modeling
Sample Questions
Prove that for positive real numbers a,b,
$$\frac{a}{b}+\frac{b}{a}\ge2$$
Determine whether the series converges:
$$\sum_{n=1}^{\infty}\frac{1}{n^3}$$
International Finals
Format
Extended proof problems
Interdisciplinary modeling challenge
Academic symposium presentation (optional)
Focus Areas
Real analysis fundamentals
Discrete mathematics
Mathematical modeling
Advanced scientific integration
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:
$$\sum_{k=1}^{n}k^2=\frac{n(n+1)(2n+1)}{6}$$