One Article Clarifies the Difficulty Distribution of the Four Major Knowledge Modules in the AMC10 Math Competition!

I. Algebra Module (35%-40%)

1. Basic Level Topics (Easy Points)

Solving quadratic equations and discriminant analysis

Properties of linear/quadratic function graphs

Simple sequences (arithmetic/geometric)

Percent and ratio calculations

2. Intermediate Level Topics (Key to Improving Scores)

Absolute value and fractional inequalities

Recursive formulas for sequences

Polynomial factorization (grouping/cross multiplication)

Basic operations with complex numbers

3. Hard Level Topics (Core for High Scores)

Relationship between polynomial roots and coefficients (advanced Vieta's formulas)

Function iteration and composition

Scaling techniques for inequalities

Comprehensive application of parametric equations

Preparation Strategies

Must get full marks on basic questions: Ensure all basic questions are answered correctly.

Proficiently master problem-solving templates for intermediate questions: Through extensive practice, master problem-solving approaches for common question types.

Selectively tackle hard questions: Prioritize the accuracy of the first 20 questions; hard questions can be managed based on time constraints.

II. Geometry Module (25%-30%)

1. Basic Level Topics (Easy Points)

Perimeter and area calculations of triangles and quadrilaterals

Pythagorean theorem

Basic properties of similar triangles

Surface area and volume of solid geometry

2. Intermediate Level Topics (Key to Improving Scores)

Properties of circles (inscribed angles, tangents, chord-tangent angles)

Introduction to the five centers of a triangle

Geometric transformations (translation/reflection)

Coordinate geometry calculations

3. Hard Level Topics (Core for High Scores)

Comprehensive application of the power of a point theorem

Cross-sections and spatial angle calculations in solid geometry

Geometric constructions (auxiliary line techniques)

Advanced trigonometry (sum and difference formulas)

Preparation Strategies

Memorize geometric models: Such as cyclic quadrilateral models, similarity models, to improve recognition and application ability.

Practice drawing auxiliary lines for intermediate questions: Master the skill of constructing auxiliary lines through extensive practice.

Focus on spatial imagination and logical deduction for hard questions: Cultivate spatial visualization and logical reasoning skills.

III. Number Theory Module (20%-25%)

1. Basic Level Topics (Easy Points)

Divisibility, factors, and multiples

Prime and composite numbers

Greatest Common Divisor (GCD) and Least Common Multiple (LCM)

Base conversion (decimal to binary/hexadecimal)

2. Intermediate Level Topics (Key to Improving Scores)

Basic applications of congruence theorems: Understand the concept of congruence and its basic properties.

Introduction to Fermat's Little Theorem: Master the basic form and applications of Fermat's Little Theorem.

Digit characteristics: Understand the digit characteristics of numbers and their applications.

Formula for the number of factors: Proficiently use the formula to calculate the number of factors.

3. Hard Level Topics (Core for High Scores)

Solving indefinite equations (Diophantine equations)

Comprehensive applications of Euler's theorem

Number theory constructions and proofs

Complex operations in base conversion

Preparation Strategies

Requires specialized breakthrough due to limited exposure in class: Since number theory content is rarely covered in domestic curricula, dedicated study and practice are needed.

Basic and intermediate questions offer high cost-performance, prioritize mastering them: Basic and intermediate number theory questions are relatively easy to score and should be a review focus.

Hard questions are suitable for students targeting AIME to delve deeper: Students aiming for AIME need to intensively study number theory hard questions.

IV. Combinatorics Module (10%-15%)

1. Basic Level Topics (Easy Points)

Basic counting (addition/multiplication principles)

Simple probability calculations

Basic set operations

2. Intermediate Level Topics (Key to Improving Scores)

Permutation and combination problems with constraints (e.g., adjacent/not adjacent)

Recursive counting

Basic Inclusion–Exclusion Principle

Advanced classical probability

3. Hard Level Topics (Core for High Scores)

Complex applications of the Inclusion–Exclusion Principle

Combinatorial constructions and extremal problems

Expected value in probability

Competition-style combinatorial techniques (e.g., advanced pigeonhole principle)

Preparation Strategies

Ensure points on basic questions: Ensure all basic questions are answered correctly.

Summarize question patterns for intermediate questions: Through extensive practice, summarize problem-solving patterns for common question types.

Hard questions are flexible; consider skipping them if time is limited: For hard questions, decide based on time and actual circumstances.

V. AMC10 Math Competition Preparation Tips

1. Basic and intermediate questions account for over 80%; mastering the first 20 questions secures a high score: The first 20 questions are key to achieving a high score; ensure the highest possible accuracy. The core to advancing to AIME is getting all intermediate questions correct; the score on intermediate questions directly affects qualification.

2. Number Theory and Combinatorics are key modules for distinguishing performance: Especially number theory, as a "characteristic difficulty" of the AMC10. Since number theory content is rarely covered in domestic curricula, targeted reinforcement is needed. Combinatorics problems are highly flexible; summarize question patterns through extensive practice.

3. Overall Preparation Strategy

Systematically study the core knowledge points of the four major modules.

Solve over 1000 basic problems and maintain an error notebook.

Reinforce with past papers to become familiar with question types and improve speed and accuracy.

Conduct full mock exams weekly to optimize time allocation and adjust answering pace.

AMC10 Tutoring Courses

Our instructors are graduates of top universities worldwide, providing precise curriculum planning and full-course learning tracking to ensure you improve and win awards!

Class Type	Hours	Class Size	Start Date
Winter Break Class	30H	3–8 students	Consult teacher for details
Systematic Course	20H	1v1 / 3–8 student class	Consult teacher for details
Problem-Solving Class	20H	1v1 / 3–8 student class	Consult teacher for details

For more information about AMC10/12 competition courses, please contact us