Category: Blog

1. IGCSE System Students

Advantages: IGCSE Additional Math overlaps heavily with AMC10 in algebra, functions, and basic geometry; quadratic equations, inequalities, coordinate geometry, etc., are already covered.

Module	Issues	Countermeasures
Geometry	IGCSE geometry emphasizes calculation, lacks proof and construction training	Supplement: Power of a Point theorem, comprehensive similar triangle problems, auxiliary line techniques
Calculation ability	Reliance on calculators → slow manual calculation, prone to errors	Daily timed calculation training (e.g., quick squaring, factorization)
Competition mindset	Habit of "standard solutions," lacks flexible modeling ability	Focus on problems 16–25, learn strategies such as "extreme case method," "symmetry," "reverse construction"

Action Recommendation: Leverage IGCSE math foundation to quickly cover algebra modules, then focus on number theory + combinatorics + advanced geometry.

2. IB System Students

Advantages: IB Math AA/AI covers a wide range of knowledge and offers strong logic training; HL students are already exposed to some advanced topics (e.g., complex numbers, introductory calculus).

Student Level	Challenges	Recommendations
SL students	Lack depth in knowledge; number theory/combinatorics are almost untouched	Need systematic supplementation; focus on conquering the four AMC10 modules
HL students	Sufficient knowledge but tight schedule (IB workload is heavy)	Intensive preparation during summer break; avoid conflicts with IAs in November

Note: IB does not teach "congruence" or "recurrence counting" – high-frequency AMC10 topics that require dedicated supplementation.

3. AP System Students

Core Challenge: AP Calculus / Statistics have low alignment with AMC10; calculus is not tested at all in AMC10, creating a knowledge gap.

GapsSolutionsWeak algebraRevisit middle/high school algebra: polynomials, Vieta's theorem, inequalitiesMissing geometrySupplement plane geometry proofs, circle properties, triangle centers and linesNumber theory/combinatorics gapsLearn from scratch: modular arithmetic, pigeonhole principle, classification countingProbability transferApply probability concepts from AP Statistics to combinatorial problems (e.g., expectation models)

AMC8 Key Topics

Basic Arithmetic: Integer operations, fractions, decimals, percentages, ratios

Elementary Geometry: Pythagorean theorem, area/perimeter, angles, simple solid figures

Counting & Probability: Basic permutations and combinations, classical probability

Word Problems: Modeling real-life scenarios such as travel, work, concentration

Data Interpretation: Graph reading, mean, median

Limited Extensions: Simple linear equations, coordinate systems, quadratic function graph recognition

Characteristics: Emphasizes fundamentals, speed, and attention to detail. The first 15 questions are mostly extensions of school curriculum, while the last 10 questions begin to reflect differentiation in thinking.

AMC10 Key Topics

Advanced Algebra: Quadratic equations, inequalities, function properties, sequences

Advanced Geometry: Similar triangles, circle properties, coordinate geometry, trigonometric identities (excluding trigonometric functions)

Introduction to Number Theory: Prime factorization, modular arithmetic, GCD/LCM

Probability & Statistics: Conditional probability, expected value, combinatorial counting (including inclusion-exclusion principle)

Logic & Strategy: Game theory, optimization, recurrence relations

Note: Does not include advanced high school topics such as trigonometric functions, calculus, complex numbers, vectors, etc., but places extremely high demands on logical reasoning and the integration of multiple knowledge points.

1. Expanding Knowledge Breadth: Supplement Core Middle School Modules

Quadratic functions and graph analysis

Geometric properties of circles (chords, tangents, inscribed angles)

Basic number theory (congruence, Fermat's Little Theorem concepts)

Advanced combinatorial counting (permutations vs. combinations, classification discussion)

2. Upgrading Your Thinking: From "Calculating Correctly" to "Thinking Thoroughly"

AMC8 approach: Know the formula → plug in numbers

AMC10 approach: Understand the essence of the problem → build a model → choose the optimal solution

Example: AMC10 often tests strategies such as "simplification through symmetry," "analysis of extreme cases," and "reverse construction."

3. Practicing with Past Papers: Familiarize Yourself with the Style of A and B Versions

AMC10 offers both A and B versions each year. Although the difficulty fluctuates slightly, the question types are consistent. Recommendation: Complete 2 sets each of the A and B versions from the last 5 years, summarizing high-frequency test points (e.g., Question 23 of the 2024 B version tested recurrence sequences combined with modular arithmetic).

AMC8

Builds mathematical confidence for upper elementary students

Serves as a reference for international school admissions and class placement

Lays the computational and thinking foundation for AMC10

AMC10

Top 2.5% receive an AIME invitation, the first step toward USAMO

Recognized STEM ability credential for Oxbridge, Ivy League, G5, and Top 30 US universities

Reference for scholarships at top Canadian universities such as Waterloo, University of Toronto, and UBC