Category: Blog

I. Detailed Explanation of High-Frequency AMC 10 Topics (by Module)

The AMC 10 consists of 25 questions with a stepwise difficulty increase: Questions 1–10: Basic Questions (curriculum extensions), Questions 11–20: Intermediate Questions (requiring technique and synthesis), Questions 21–25: Difficult Questions (competition-level thinking, often testing number theory/combinatorics). The following are the seven core modules and their key test points, based on an analysis of past five years' past papers:

1. Comprehensive Algebra
Core content: Quadratic functions, equations and inequalities, sequences, polynomials, multiplication formulas, and identity transformations.
High-frequency difficulties: Polynomial divisibility problems; simplification of symmetric expressions; substitution methods; constructing equations.
Advice: At least 6–8 questions in the first 15 are from algebra—key to securing your score!

2. Functions and Coordinate Geometry
Core content: Properties of linear/quadratic function graphs; equations of circles; coordinate transformations; area calculation of polygons.
Problem-solving tools: Shoelace formula (quickly calculates the area of any polygon); Pick's theorem (area of lattice polygon A = I + B/2 - 1).
Note: Function questions are often combined with geometry and appear in the 16–22 question range.

3. Comprehensive Plane Geometry
Core content: Triangles, quadrilaterals and polygons, trigonometric functions.
Area methods: Partition-complement method, equal-area transformation, common side theorem.
Key skills: Drawing auxiliary lines (e.g., altitudes, midpoints, constructing similar shapes); recognizing hidden conditions (e.g., "isosceles triangle," "right angle").
Tip: Geometry questions often appear in the 10–20 range and are key for differentiating scores in the middle segment.

4. Circles and Solid Geometry
Core content: Circle properties: inscribed angles, chord-tangent angles, perpendicular chord theorem, intersecting chords theorem; Solid geometry: Volume and surface area of rectangular prisms, prisms, cylinders, cones; Euler's formula (V - E + F = 2, occasionally seen in challenging problems).
Difficulties: Spatial visualization ability (especially for solid net diagrams); multiple points concyclic on a circle; angle transformation.
Trend: In recent years, circle problems have placed greater emphasis on comprehensive application, often combining trigonometry and algebra.

5. Combinatorics
Core content: Addition principle and multiplication principle; permutations (ordered) vs. combinations (unordered); special models: path counting, coloring problems, round-robin tournament systems.
Common errors: Double counting or omissions; considering order or not (e.g., "select 3 people to form a team" vs. "select 3 people to sit in a row").
Techniques: Drawing tree diagrams, case analysis, reverse exclusion (inclusion–exclusion principle).

6. Probability and Statistics
Core content: Classical probability (equally likely events); geometric probability (ratio of length/area/volume); conditional probability ("given that… find…" type problems); expected value (occasionally seen in recent years).
High-frequency scenarios: Rolling dice, drawing cards, random walks, game outcomes.
Key point: Conditional probability is a frequent guest in difficult problems (e.g., 2023 AMC 10B Question 24).

7. Number Theory
Core content: Divisibility, congruences, digit problems, parity, floor function [x], defined new operations.
Typical position: Appears frequently in questions 21–25, key to distinguishing the top 1%!
Difficulty: Requires flexible problem transformation (e.g., converting "last two digits are the same" to a congruence modulo 100 problem).

II. How Long Does It Take to Prepare for the AMC 10? – Planning Based on Foundation and Target Score

Student Type	Math Foundation Characteristics	Recommended Preparation Cycle	Core Tasks
Weak Foundation	No systematic junior high competition training; high school algebra/geometry not completed	6–12 months	1. Supplement core junior high competition topics (number theory/combinatorics) 2. Complete high school compulsory 1–2 3. Begin AMC 10 topic-specific training
Average Foundation	Completed high school curriculum; some competition exposure	3–6 months	1. Strengthen the four major AMC 10 modules 2. Categorized practice with past papers (focus on questions 1–20) 3. Build problem-solving templates
Solid Foundation	Award in AMC 8/junior high league competition; comprehensive high school knowledge	1–3 months	1. Focus on difficult questions 21–25 2. Summarize high-frequency techniques (e.g., symmetry, extreme principle) 3. Timed mock exams to maintain proficiency

Preparation Depth Based on Target Score

Target	Score Range	Required Ability	Recommended Cycle
Experience Participation	70–90 points	Master the first 15 basic questions	1–3 months
Top 25% (AIME Threshold)	95–110 points	Stably complete the first 20 questions, some of questions 21–23	3–6 months
Top 5% (Honor Roll)	≥120 points	Comprehensive mastery of all modules, ability to solve questions 24–25	6–12 months
Top 1% (Distinguished Honor Roll)	≥135 points	Competition-level thinking, high speed and accuracy	8–12+ months of long-term accumulation

For more information about AMC 10/12 competition courses, please contact us.

AMC10 Preparation Courses

Our instructors are graduates from top global universities. With precise curriculum planning and comprehensive learning tracking, we ensure your score improvement and award-winning success!

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

I. AMC 10 Score Requirements for Different Award Goals

1. Applying to U.S. Top 30 Universities

Suggested Score: 120+ points. Top institutions like MIT and Stanford prefer students with AMC 10 scores of 135 or higher. Scoring in the top 2.5% (approximately 120+ points) or achieving AIME qualification is considered a significant academic achievement that can greatly enhance application competitiveness.

2. Planning to Apply for Mathematics/Computer Science Majors

Suggested Score: 130+ points. Mathematics and computer science majors are highly competitive; high scores better demonstrate students' logical thinking and problem-solving abilities. DHR (Distinguished Honor Roll, top 1% globally) typically requires 130+ points, proving both academic strength and the ability to handle complex problems.

3. Applying for Scholarships

Suggested Score: 140+ points. A high score (e.g., 140+) is a significant criterion for receiving full or merit-based scholarships. A score at this level indicates that the student possesses top-tier mathematical literacy and innovation skills, enabling them to stand out globally.

4. Applying to International Schools

Suggested Score: 110+ points. Many international schools (e.g., Beijing Keystone Academy) explicitly state that IBDP applicants with AMC 10 scores ≥ 110 can be exempted from math placement tests and directly enter advanced courses. Entrance exams for schools like Shanghai Guanghua Cambridge and Shenghua Zizhu often include original AMC 10 questions; thus, preparing for AMC 10 helps students become familiar with the style of these admission tests.

II. The Importance of AMC 10 for International Students

1. Alignment with International School Entrance Exams

High Consistency: The question types and difficulty levels of the AMC 10 are highly consistent with the entrance exams of international schools. Examples: Question 9 on the 2023 entrance exam of Shanghai Guanghua Cambridge was exactly the same as Question 19 on the 2023 AMC 10B; 50% of the math questions in Shenghua Zizhu's spring admissions test were original AMC 10 competition problems.

2. Assisting with IB/AL/AP Exam Preparation

High Content Overlap: The knowledge points tested in AMC 10 heavily overlap with the math sections of mainstream international curricula such as IB, AP, and A-Level. Students in grades 6-9 can build a solid foundation by preparing for AMC 10 in advance, clearing obstacles for future in-depth learning. Grade 10 students can use AMC 10 to sharpen their mathematical logic and problem-solving skills, supporting their progress in international coursework.

3. Boosting Applications to Top U.S. and U.K. Universities

Widely Recognized: Prestigious universities such as MIT, Stanford, and Columbia University have dedicated fields for entering AMC 10 scores in their application systems. A top 1% (DHR) score can help students stand out among a sea of applicants and increase their chances of admission.

III. AMC 10 Version A vs. Version B: How to Choose?

1. Overview

Versions A and B: The questions are different, and the exams are held about a week apart. However, the overall difficulty is similar, and the knowledge scope is the same, with only slight differences in focus and style. Score cutoffs are calculated independently, so choosing either version will not put you at a disadvantage in terms of ranking.

2. Specific Differences

Version	Characteristics	Suitable For
Version A	• More "stable," suitable for students with a solid foundation • Basic questions are more direct; cutoffs are typically lower	Students aiming to securely qualify for AIME, or those who want a high score without taking too many risks
Version B	• More "flexible," demands higher creative thinking • Contains more innovative question types in number theory and combinatorics	Students aiming for a very high score or DHR (top 5% globally), with prior competition experience and flexible thinking

3. Version Selection Strategies

Securely Qualifying for AIME: Prioritize Version A, or take both versions A and B. Version A's basic questions are more direct, and the cutoffs are typically lower, making it more favorable for students with a solid foundation. Taking both versions allows you to use your highest score as your final result, significantly increasing your chances of qualification.

Aiming for a Very High Score or DHR: Prioritize Version B. Version B has greater score differentiation; its innovative questions in number theory and combinatorics better showcase strengths, making it easier to stand out in the high-score range.

Transitioning to AMC 12 or Long-Term Preparation: Take Version A for AMC 10 and Version B for AMC 12. If you have a solid foundation, you can use the one-week gap between the two versions to consolidate your AMC 10 basics with Version A, then challenge AMC 12 difficulty. This allows you to secure a strong AMC 10 score while also getting an early taste of higher-level competition pacing.

AMC10 Preparation Courses

Our instructors are graduates from top global universities. With precise curriculum planning and comprehensive learning tracking, we ensure your score improvement and award-winning success!

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