Blog - American Mathematics Competition 8

2026 AMC8 Mathematical Competition Analysis: Score Cutoffs? Exam Format and Duration? Question Types? Key and Difficult Points? Common Mistakes? Preparation Strategies?

The AMC8 American Mathematics Competition is a global middle school mathematics contest organized by the Mathematical Association of America (MAA). It aims to stimulate students' interest in mathematics and develop their mathematical thinking and problem-solving skills. As the entry-level competition in the AMC series, it lays the foundation for participating in more advanced competitions such as AMC10/12 and AIME.

I. Exam Format and Duration

The AMC8 competition follows a format of completing 25 multiple-choice questions in 40 minutes. The scoring standard awards 1 point for each correct answer, with no penalty for incorrect or unanswered questions, resulting in a perfect score of 25. The exam is offered in a bilingual format (Chinese and English) and can be taken either online or offline.

II. Analysis of the 2026 AMC8 Exam

Overall Difficulty Assessment

The 2026 AMC8 competition presented characteristics of being "generally more difficult and highly targeted." There were differences between the Chinese and U.S. exam papers. The independent question-setting style for the Chinese region made the number theory and combinatorics sections more aligned with domestic Olympiad mathematics, placing higher demands on candidates.

Changes in Knowledge Point Distribution

The 2026 AMC8 showed significant shifts in the focus of knowledge points assessed, with core changes including:

The intensity of examining the combinatorics module increased, with its proportion of questions rising noticeably.

The difficulty of application problems increased overall, with question stems containing more complex information that required quickly extracting key conditions.

New high-level knowledge point question types, such as "defining new operations," were added to test on-the-spot adaptability.

The table below shows the distribution of main knowledge points in the 2026 AMC8:

Knowledge Module	Approximate Proportion of Questions	Change in Difficulty
Algebra	~24%	Relatively stable, but examination is more detailed and in-depth.
Geometry	~24%	Flexibility increased, with higher demands on spatial visualization.
Number Theory & Combinatorics	~20-25%	Difficulty noticeably increased, becoming a key factor for scoring.
Counting & Probability	Question count increased	Tests logical reasoning and combinatorial thinking.
Statistics-related questions	Relatively decreased

III. Innovation and Characteristics of Question Types

Diversified Presentation of Test Points: Questions increasingly require the comprehensive application of knowledge from multiple modules, emphasizing the flexible transfer and integrated application of knowledge points.

Enhanced Flexibility and Innovation in Questions: The proportion of innovative questions has significantly increased. Question stem design is closer to real-world scenarios, with noticeably rising complexity.

Mathematical Thinking and Problem-Solving Strategies Become Key: Rote memorization of knowledge is no longer sufficient to handle the exam. Solid logical thinking and efficient problem-solving strategies are essential.

IV. Predicted Score Cutoffs for the 2026 AMC8

Based on analyses from multiple educational institutions, the predicted award score cutoffs for the 2026 AMC8 are as follows:

Award	Predicted Cutoff Score	Corresponding Number of Incorrect Answers	Key Requirements
Distinguished Honor Roll (DHR, top 1% globally)	21 points	At most 4 questions incorrect	Must avoid losing points on details like missing process steps or incorrect units.
Honor Roll (HR, top 5% globally)	17-18 points	7-8 questions incorrect	Zero mistakes on basic questions, minimal point loss on medium-difficulty questions.
Achievement Roll (AR)	15 points	Within 10 questions incorrect	For students in grade 6 and below.

V. Analysis of Common Mistakes and Key/Difficult Points

Common Mistake-Prone Question Types

Complex Application Problems: Large amount of information in the question stem; requires quickly extracting key conditions and building a solution model.

Geometry-Integrated Problems: Integrates understanding of shapes into complex problem scenarios, emphasizing comprehensive application skills.

Define-a-New-Operation Problems: Tests the ability to learn and quickly apply new knowledge in a timely manner.

Key and Difficult Modules

Number Theory and Combinatorics: Difficulty of prime factorization and integer properties increased; need to master the short division method for quickly solving LCM and GCD.

Geometry Module: Added problems involving dynamic analysis of 3D nets and combination of the Pythagorean theorem with practical applications; strengthened calculation of areas of irregular shapes.

Algebra and Probability: Strengthened combination of probability and statistical data with real-world scenarios, such as quadratic function modeling.

VI. Preparation Strategies

Preparation Suggestions by Grade Level

Preparation strategies should be tailored according to the characteristics of students at different grade levels:

Grade Level	Suggested Prep Duration	Learning Focus
Lower to Middle Primary (Grades 3-4)	Around 18 months	Establish a systematic framework of mathematical knowledge; cultivate interest in math and foundational thinking skills.
Upper Primary (Grades 5-6)	Around 12 months	Systematically master all knowledge points required for the competition; strengthen logical reasoning and problem-solving skills.
Middle School (Grades 7-8)	6-8 months	Targeted strengthening of weak areas; optimization of problem-solving strategies; improvement of test-taking skills.

Key Preparation Points for Each Knowledge Module

Algebraic Operations: Strengthen calculation accuracy and speed, paying special attention to mixed operations with fractions, decimals, and percentages.

Geometric Figures: Start from the properties of basic shapes to develop spatial imagination and figure analysis skills.

Fundamentals of Number Theory: Deeply understand core concepts like divisibility properties and prime number characteristics; master common number theory methods.

Counting and Probability: Establish a systematic system of counting methods; understand the essential difference between the Addition Principle and the Multiplication Principle.

Optimizing Test-Timing Strategy

Time Allocation: Simple questions (Q1-15): ~1 minute each; Difficult questions (Q21-25): ~3 minutes each; Reserve about 5 minutes for checking.

Answering Techniques: Make good use of strategies like elimination and substitution. Mark time-consuming questions and prioritize ensuring the accuracy of basic questions.

Pre-exam Preparation: Adapt to the 40-minute, 25-question pace through timed mock tests, and learn to allocate answering time reasonably.

The 2026 AMC8 competition has moderately increased the required depth of thinking while maintaining its traditional characteristics, reflecting trends in the development of mathematics education. For students planning to participate, it is advisable to start systematic preparation early, focusing on a solid grasp of foundational knowledge and the comprehensive development of thinking skills. Through scientific planning and sustained effort, every student can showcase their mathematical potential on this platform.

Is the AMC 8 Math Competition Prestigious? How to Register for the 2026 AMC 8? Schedule? Key Points of the Syllabus? Difficulty? Awards? Preparation Methods? Includes AMC 8 Handout

The AMC 8 (American Mathematics Competitions 8) is one of the most influential youth math competitions globally. Organized by the Mathematical Association of America (MAA), it aims to discover mathematical talent and cultivate mathematical thinking. This competition for eighth graders and below has become a key platform for outstanding students worldwide to showcase their mathematical abilities.

With the 2026 AMC 8 approaching, this article provides a comprehensive guide covering its prestige, schedule, syllabus key points, difficulty, and preparation strategies.

1. Prestige of the AMC 8 Competition

The AMC 8 enjoys a high international reputation. Its value lies not only in the awards but also in the long-term benefits for students.

International Recognition: A globally accepted proof of mathematical ability, with over 300,000 participants annually. Excellent scores are highly regarded by top schools in countries like the US, UK, and Canada.

Value for Academic Advancement: In China, AMC 8 scores are a plus for admissions to key middle schools. For students planning to study abroad, it's a significant asset for applications to top US universities like MIT and Stanford.

Gateway to Advanced Competitions: The AMC 8 is the entry point to the US math competition system, leading to AMC 10/12, AIME, and USAMO.

Development of Thinking Skills: The preparation process systematically trains critical thinking and problem-solving abilities.

AMC 8 Award Settings and Standards

Award Type	Award Standard	Recognition Level
Perfect Score	Score 25 points	Global top level, extremely rare
Distinguished Honor Roll (Global Top 1%)	Rank in the top 1% globally	Proof of extremely strong mathematical ability
Honor Roll (Global Top 5%)	Rank in the top 5% globally	Possession of outstanding mathematical ability
Achievement Roll	Students in 6th grade or below scoring 15 points or above	Special recognition for younger students

2. How to Register for the 2026 AMC 8?

Exam Date: Friday, January 23, 2026 (17:00 - 17:40).

Registration Deadline: January 13, 2026.

Registration Methods:

1. Through Your School: If your school is an official test center, register through your teacher.
2. Through the ASDAN China Website/WeChat Mini-Program: Students from non-center schools can register via the official "ASDAN International STEM Assessments" channels.
3. Through an Authorized Partner Organization: If your school is not a center, you can register through an authorized partner.

Summary of AMC 8 Registration Information

Item	Specific Information
Eligibility	8th grade or below, and age ≤ 14.5 years on exam day
Fee	120 RMB/person
Exam Format	In-person, bilingual (Chinese/English) test paper provided
Channels	School, ASDAN website, authorized partner organizations

3. Schedule & Exam Format

Timeline: The contest is 40 minutes long with 25 multiple-choice questions. Scores are typically released within 4-6 weeks.

Format: 25 questions, 1 point each, no penalty for wrong answers. The Chinese test paper is bilingual.

Preparation Timeline: A preparation period of 3-6 months is ideal. Students with a strong foundation should start systematic preparation at least 3 months in advance.

4. Syllabus, Key Points & Difficulty

The AMC 8 covers four main areas: Algebra & Probability, Geometry, Number Theory & Combinatorics, and Word Problems & Logical Reasoning.

2026 AMC 8 Syllabus & Key Points Distribution

Knowledge Module	Proportion	Key Content	Changes & Difficulties
Algebra & Probability	40%-45%	Equations, basic functions, sequences	Increased modeling with quadratic functions, dynamic probability calculations; 30% more real-world scenario questions
Geometry	25%-30%	Plane geometry, Pythagorean theorem, area	Strengthened analysis of 3D shape nets, techniques for dissecting irregular shapes
Number Theory & Combinatorics	20%-25%	Prime numbers, factorization, counting principles	Increased difficulty in using short division for LCM/GCF, modular arithmetic with geometric sequences
Word Problems & Logic	Throughout	Ratios, percentages, logical reasoning	Increased complexity in problem statements, emphasis on chart analysis and interdisciplinary integration

Difficulty Levels:

Questions 1-10: Basic, comparable to the harder questions on regular school exams.

Questions 11-20: Intermediate, similar to the preliminary round of Chinese math competitions.

Questions 21-25: High difficulty, approaching the level of simpler questions in high school math leagues, requiring strong innovative thinking.

5. Award Settings & Criteria

Individual Awards: As listed in the table above (Perfect Score, Distinguished Honor Roll, etc.).

School Awards: Include "School Honor Roll" (sum of top 3 scores ≥ 66) and "School Merit Roll" (sum between 50-65). Note: These are only awarded to students who registered through their school.

Historical Score Reference: For reference, the 2024 cutoff for the global top 1% was approximately 22 points, and for the top 5% was about 18 points.

6. Practical Preparation Methods

A scientific preparation plan is key.

Knowledge Building Phase (3-6 months before): Systematically review the four main knowledge areas. Pay special attention to Number Theory and Combinatorics.

Problem-Type Training Phase (1-3 months before): Practice with past papers. Train by difficulty level: master basics, then tackle intermediate, and finally challenge high-difficulty questions.

Mock Testing Phase (1 month before): Take timed practice tests to adapt to the exam's pace and pressure. Practice "question-skipping技巧" – answer questions you're sure about first.

Utilize Resources: Use official past papers, master essential formulas and解题技巧, and take part in mock exams.

Sample Preparation Plan

Phase	Timeframe	Key Tasks	Goal
Foundation	3-6 months before exam	Systematic study of the four modules	Establish a complete knowledge system
Focused Breakthrough	1-3 months before exam	Targeted training on weak areas	Improve weaknesses, strengthen strengths
Mock Sprint	1 month before exam	Full模拟 tests, past paper practice	Adapt to exam pace, identify gaps

The true value of the AMC 8 lies not just in awards, but in the mathematical thinking and problem-solving skills developed during preparation, which form a solid foundation for future learning.

AMC8 2026 Season: Last-Minute Crash Guide, Detailed Syllabus, Key Focus Areas & Common Pitfalls

The 2026 AMC8 Mathematics Competition is set to kick off on January 23rd. With today being January 16th, only one week remains until the exam. This final preparation phase is crucial for all participating students.

This article provides a comprehensive last-minute crash guide, including syllabus changes, key focus area analysis, and preparation strategies to help you study efficiently in the final stage.

I. 2026 AMC8 Exam Schedule & Key Changes

The 2026 AMC8 Competition has undergone its most significant reforms in nearly five years, affecting multiple aspects such as exam format, question structure, and scoring criteria.

Basic Exam Information

Item	Details
Exam Date	January 23, 2026 (Friday)
Exam Duration	17:00-17:40 (40 minutes)
Registration Deadline	January 13, 2026
Exam Format	Dual-mode: Online + Offline
Number of Questions	25 multiple-choice questions
Scoring Criteria	1 point for each correct answer; no penalty for incorrect answers

Notable changes in the 2026 AMC8 syllabus:

The Geometry module accounts for 25%-30%, with newly added question types including 3D net analysis and architectural structure applications.

Algebra and Probability have the largest proportion (40%-45%), introducing more real-scenario modeling questions such as supermarket promotion models and carbon emission optimization problems.

Number Theory and Combinatorics have increased in difficulty, emphasizing in-depth understanding of prime factorization and integer properties.

II. Last-Stage Crash Preparation Plan

For the remaining one week, we have developed an efficient crash plan for you.

Phased Crash Schedule

Time Period	Key Tasks	Specific Implementation Methods
Days 1-2	Address Knowledge Gaps	Focus on reviewing error logs and practice weak question types targeting specific areas
Days 3-4	Mock Exam Training	Complete 1-2 timed mock exams daily using past papers, strictly limiting to 40 minutes
Day 5	Strengthen Problem-Solving Skills	Conduct specialized training on strategic techniques such as elimination method and substitution with specific values
Day 6	Develop Exam Strategies	Determine time allocation plans and answer sequences based on personal ability
Day 7	Light Review & Mental Preparation	Review error logs, adjust mindset, and avoid excessive practice with new questions

Preparation priorities vary for students with different target scores in the final week:

Target score around 15 (Global Honor Roll): Focus on the first 15 questions to ensure accuracy in basic questions; prioritize reviewing fundamental algebra content such as ratios, fraction calculations, and equation applications.

Target score 16-19 (Global Distinguished Honor Roll): While consolidating the first 15 questions, improve problem-solving abilities for questions 16-20; specifically break through weak modules in Geometry and Combinatorics.

Target score 23+ (Top 1% Globally): Master all knowledge points comprehensively, especially strategies for difficult questions (21-25); strengthen the application of advanced techniques in Number Theory and Combinatorics.

III. Comprehensive Analysis of AMC8 Core Focus Areas & Common Pitfalls

Understanding common question traps and difficulties is key to avoiding score loss.

3.1 Algebra Module (40%-45%)

Key Focus Areas: Ratio/fraction calculations, equations and application problems, quadratic function modeling.

Common Pitfalls:

Unit conversion traps: Check unit consistency for distance and area questions.

Misunderstanding of percentage applications: Confusion between "increasing by 20%" and "increasing to 120% of the original".

Improper variable setting in complex application problems, leading to difficulties in formulating and solving equations.

3.2 Geometry Module (25%-30%)

Key Focus Areas: Triangle properties, circles and polygons, area calculations, 3D net analysis.

Common Pitfalls:

Missing or double-counting certain areas when calculating the area of irregular shapes.

Insufficient understanding of similar triangle determination conditions.

Spatial visualization deficiencies leading to conversion errors in newly added 3D net questions.

High-Score Tip: For complex 3D net questions, use the "paper-folding method"—create simple models with scratch paper, mark corresponding vertices, and intuitively understand the relationship between unfolding and folding.

3.3 Number Theory & Combinatorics (20%-25%)

Key Focus Areas: Prime factorization, divisibility properties, permutations and combinations, geometric sequences.

Common Pitfalls:

Overcounting or undercounting in combinatorial counting, especially improper grasp of classification boundary conditions.

Slow prime factorization of large numbers, affecting problem-solving efficiency.

Failure to use the "total set minus complement set" approach for "at least" type permutation and combination questions.

IV. Practical Skills & Time Management Strategies

In the AMC8 exam, time management is equally important as problem-solving skills. With 25 questions to complete in 40 minutes, you have only about 1.5 minutes per question on average.

4.1 Golden Rule of Time Allocation

First 10 questions: Complete within 8 minutes. These questions are relatively simple and should be answered quickly and accurately.

Questions 11-20: Allocate 15 minutes. These questions are of medium difficulty and require steady progress.

Questions 21-25: Reserve 12 minutes. These are challenging questions that determine high scores.

Reserve the last 5 minutes for checking answers and filling in the answer sheet.

4.2 Efficient Problem-Solving Skills

Substitution with Specific Values: When encountering questions involving unknown relationships, substitute simple values to convert abstract relationships into concrete calculations and quickly derive answers.

Elimination Method: Use conditions such as parity and value ranges to eliminate contradictory options, narrow down the selection scope, and improve accuracy.

Geometry Reassembly Method: Decompose complex figures into regular shapes, find proportional relationships through recombination, and solve for area or length.

On the day before the exam, avoid excessive question practice. Focus on reviewing error logs and adjusting your mindset.

V. Pre-Exam Preparation & Mental Adjustment

For students taking the online exam, prepare the following equipment in advance:

Install the latest version of a browser and ensure the camera works properly.

Prepare a mobile phone as a secondary device, fixed at the rear side for proctoring.

Choose an independent and quiet space with only allowed tools such as blank scratch paper, a ruler, and an eraser on the desk.

When encountering difficult questions during the exam, do not panic. Mark them and skip to ensure you complete all questions you are confident about before returning to them. AMC8 scoring awards points for correct answers with no penalty for incorrect ones, so never leave any questions unanswered.

In the final sprint stage, precise review is more effective than broad coverage. Understand your strengths and weaknesses, develop reasonable answering strategies, and maintain a calm mindset to achieve your best performance in the AMC8 Competition.

Free AMC8 Comprehensive Preparation Materials Package

Participating students can download for free:

2000-2025 AMC8 Past Papers (Chinese & English) + Detailed Explanations

Formula Sheets + Vocabulary Lists

Preparation Books + Lecture Notes

Nearly 20 Years of AMC8 Past Paper Video Explanations + Last-Minute Crash Materials

AMC8 Introductory Lecture Notes + Compiled Lecture Notes

Recommended Booklists (Full set of 23 AOPS Black Books + Omegalearn Recommended Books + Preparation Series, etc.)

Free Collection Method:

Scan the QR code above to contact us, then send your needs in multiple messages as instructed in the right image, and we will send the relevant materials to you one by one. Wish your child a high score!

Additional Services:

After contacting us, you can:

Ask 1 specific question you care about most, and we will provide targeted suggestions.

Share your personal situation (e.g., target score), and we will highlight key points for you.

Join an exclusive study group to access a focused Q&A live stream.

Note: The actual materials received shall prevail.

Aim for the Top 1%! 2026 AMC8 Math Competition Award-Winning Essential Guide: Comprehensive Strategies for Pre-Exam Preparation, Exam Room Tactics, and Post-Exam Arrangements! With AMC8 Sprint Notes

The 2026 AMC8 Competition will officially start on January 23rd. For registered candidates, familiarizing themselves with the exam process and pre-exam preparation is crucial. This article will detail the pre-exam preparation, exam process, and post-exam arrangements for the AMC8 Competition to help candidates take the exam smoothly

I. Comprehensive Pre-Exam Preparation Guide

Preparing exam equipment and the environment is the foundation for a smooth exam experience. Candidates need to prepare a computer with a camera (Windows or Mac system) and a mobile phone or Pad as the proctoring device.

The proctoring device should be fixed 0.5-1 meter behind the side of the computer, at a height of 1.2-1.5 meters, ensuring that the screen can cover the candidate's upper body, hands, and the computer screen. The exam must be conducted in an independent and quiet room. Only necessary stationery such as blank scratch paper, pencils, erasers, and straightedges can be placed on the desk; calculators are strictly prohibited.

AMC8 Exam Essential Items List

Item Category	Essential Items	Prohibited Items
Electronic Devices	Computer with camera, mobile phone/Pad (for proctoring)	Calculators, smart watches, mobile phones (other than proctoring devices)
Stationery	Black or blue signature pens, pencils, erasers, straightedges	Protractors, coordinate paper, compasses
Documents & Materials	Valid ID, blank scratch paper	Any books, notes, reference materials

In terms of software configuration, the exam computer must have the latest version of Google Chrome installed (Mac users are prohibited from using Safari), and the proctoring mobile phone must have the Tencent Meeting APP installed (users with non-Mainland China mobile phone numbers use VooV). Before the exam, be sure to close all irrelevant web pages and software on the computer, especially those with screen casting or live streaming functions, to avoid being judged as cheating by the system.

Mock exams are an indispensable part of pre-exam preparation. Candidates can complete mock exams between January 18th and 23rd to test the stability of equipment and the internet. The official equipment debugging time is from 18:00 to 19:30 on January 22nd; candidates can join the Tencent Meeting to adjust the position of the proctoring device.

II. Full Process on Exam Day

Regarding the exam schedule, the official 2026 AMC8 exam time is 17:00-17:40 (Beijing Time) on January 23rd. Candidates need to join the Tencent Meeting 1 hour in advance (16:00) to debug the proctoring device; log in to the online exam system 30 minutes before the exam (16:30); the exam will start promptly at 17:00.

AMC8 Exam Day Schedule

Time	Event	Notes
16:00	Join Tencent Meeting and debug equipment	Rename the participant name to "Exam Admission Ticket Number + Full Name"
16:30	Log in to the exam system and enter the pre-exam countdown page	Ensure the camera and microphone are working properly
16:45	Identity verification and listening to exam rules	Follow the invigilator's instructions
17:00-17:40	Official exam, 40 minutes duration	No login allowed 15 minutes after the exam starts

Before the exam begins, candidates need to complete the identity verification process and listen to the invigilator read out the exam rules. The camera should be adjusted at least 10 minutes before the exam to ensure a clear picture and that the candidate is always in the camera frame; avoid backlighting.

During the exam, candidates must strictly abide by the following regulations: no talking; no leaving the exam page or switching to other software; the candidate's hands and upper body (above the chest) must appear in the frame; the system will randomly take screenshots for information comparison. In case of unexpected situations such as internet or power outages, candidates can re-enter the exam room after recovery, and the system will automatically save the answered questions.

The AMC8 Competition consists of 25 multiple-choice questions, with 1 point for each correct answer and no points for incorrect or unanswered questions. Reasonable time allocation during the exam is crucial. The following time allocation strategy is for reference: the first 15 questions are relatively simple and can be answered quickly; the middle 5 questions are of moderate difficulty and require steady progress; the last 5 questions are mostly difficult, so candidates can first answer those they have ideas for.

III. High-Score Answering Skills

Mastering efficient answering skills helps improve scores. Here are some practical strategies:

Special Value Substitution Method: When encountering questions involving unknown quantity relationships, substitute simple values to convert abstract relationships into specific calculations and quickly get the answer.

Elimination Method: Use conditions such as parity and value ranges to eliminate contradictory options, narrow down the selection scope, and improve accuracy.

Geometric Patching Method: Decompose complex figures into regular figures, find proportional relationships through reorganization, and solve for area or length.

During the exam, candidates should prioritize easy questions first and ensure the accuracy of the first 15 questions, as these are relatively simple and should not be lost if possible. For difficult questions without immediate ideas, mark them and return to them after completing all other questions.

IV. Post-Exam Notes

After the exam ends, the system will automatically submit the paper. If there is a delay on the submission page, wait for 10 seconds. Before submission, candidates can check if the question numbers in the answer area have turned blue, which indicates that the system has automatically saved the answers.

Exam results will be announced 6-8 weeks after the exam. Candidates can log in to the "ASDAN International Academic Challenge" WeChat Mini Program, click [My Registration] - corresponding project - [Score Inquiry] to view their results.

In accordance with the requirements of the Mathematical Association of America (MAA), no one is allowed to disseminate or verbally discuss the exam content and answers on the internet, social media platforms, or chat software before 21:00 (Beijing Time) on January 29, 2026.

Sprint Preparation Suggestions: In the final days, it is recommended to maintain 2-3 hours of review time every day, focusing on reviewing wrong questions from previous years' real exams, especially high-frequency test points such as number theory and combinatorics. Ensure adequate sleep the day before the exam to meet the exam in the best state.

What are the main differences between AMC 8 and AMC 10/12? How to plan a learning path from AMC 8 to higher-level competitions?

As one of the most globally recognized mathematics assessments, the AMC (American Mathematics Competitions) series provides a progressive challenge platform for students of different ages and mathematical levels. Designed for students in different grades, AMC8, AMC10, and AMC12 are closely connected yet significantly distinct.

Understanding the differences between these three levels of competitions and formulating a scientific and reasonable learning path is crucial for achieving excellent results in mathematical competitions.

I. The Three-Level Leap of AMC8, 10, and 12: Understanding the Essential Differences

Founded by the Mathematical Association of America (MAA) in 1950, the AMC competition system has become one of the most trusted mathematics assessments worldwide. Its scores are highly recognized by numerous countries such as the United States, Canada, and the United Kingdom.

Although they belong to the same AMC series, AMC8, AMC10, and AMC12 differ significantly in multiple dimensions.

In terms of target participants and exam format, the three levels of competitions are designed for students of different age groups, with specific differences as shown in the following table:

Comparison of Participation Requirements and Exam Formats for AMC8, 10, and 12

Competition	Suitable Grades	Age Limit	Number of Questions	Exam Duration	Scoring Rules
AMC8	Grade 8 and below	Under 14.5 years old	25 multiple-choice questions	40 minutes	1 point for each correct answer, full score 25 points, no penalty for incorrect answers
AMC10	Grade 10 and below	Under 17.5 years old	25 multiple-choice questions	75 minutes	6 points for each correct answer, 1.5 points for unanswered questions, full score 150 points, no penalty for incorrect answers
AMC12	Grade 12 and below	Under 19.5 years old	25 multiple-choice questions	75 minutes	6 points for each correct answer, 1.5 points for unanswered questions, full score 150 points, no penalty for incorrect answers

In terms of knowledge scope and difficulty, the three levels of competitions also show an obvious gradient:

AMC8 covers primary and junior high school mathematics knowledge, including integers, fractions, decimals, percentages, ratios, number theory, daily geometry, area, volume, probability and statistics, logical reasoning, etc. The difficulty of the questions is relatively low, similar to the level of domestic primary school Olympiad mathematics.

AMC10 covers the mathematics curriculum of Grade 9 and 10, including elementary algebra, basic geometry, elementary number theory, and probability, but excludes trigonometry, advanced algebra, and advanced geometry. In recent years, the exam has also added new question types such as coloring problems and chessboard problems, with an increasingly wide range of assessments and gradually increasing difficulty.

AMC12 is the most difficult among the three levels, covering the entire high school mathematics curriculum, including advanced algebra, advanced geometry, trigonometry, complex numbers, logarithms and logarithmic functions, etc. Both the difficulty of problem-solving and the requirements for skills have been significantly improved, putting forward higher requirements for students' mathematical thinking abilities.

It should be particularly noted that there is no direct promotion relationship between AMC8, AMC10, and AMC12. Students can choose the appropriate competition level according to their age and mathematical ability, without participating in sequence one by one.

II. From Introduction to Mastery: AMC Competition Learning Path Planning

A successful AMC competition journey requires systematic planning based on students' grades and mathematical foundations. The following is a reference learning path plan for students of different grades:

Grade-Based AMC Competition Learning Plan Recommendations

Grade Stage	Recommended Competition	Target Score/Award	Focus of Preparation
Grades 3-5	AMC8	Around 15 points (Global Honor Roll)	Cultivate interest in mathematics, consolidate primary school knowledge, and learn basic junior high school knowledge
Grades 6-8	AMC8	Top 5% globally (17+ points) or Top 1% globally (22+ points)	Systematically learn the four major modules of algebra, geometry, number theory, and combinatorics, and cultivate competition thinking
Grades 7-10	AMC10	Top 2.5% globally (approximately 120+ points)	Complete in-class mathematics learning before Grade 10, and strengthen comprehensive algebra, geometry, and elementary number theory
Grades 8-12	AMC12	Top 5% globally (approximately 100+ points) or AIME qualification	Master advanced content such as trigonometry, complex numbers, and advanced algebra, and strengthen the ability to solve complex problems

For lower-grade students (Grades 3-5), AMC8 is an ideal entry-level choice. The goal at this stage is not to pursue high scores, but to stimulate interest and build a foundation. It is recommended to set a target of around 15 points, and obtaining the Global Honor Roll is considered a success. During preparation, focus on consolidating primary school mathematics content, gradually learn junior high school knowledge, and cultivate basic competition thinking and abilities.

For middle-grade students (Grades 6-8), they can pursue higher awards in AMC8, such as the Honor Roll certificate for the top 5% globally or the Distinguished Honor Roll certificate for the top 1% globally. This stage requires systematic learning of the four major knowledge modules of algebra, geometry, number theory, and combinatorics, laying a solid foundation for the transition to AMC10/12.

A practical criterion for judging whether one can advance to AMC10 is: being able to stably score above 20 points in AMC8. For early high-scoring students, it is recommended to further prepare for AMC10, which is the core competition in the AMC series.

Preparing for AMC10 requires completing in-class mathematics learning before Grade 10 and reserving more than half a year for special preparation.

For upper-grade students (Grades 8-12), directly preparing for AMC12 is a more efficient choice. The knowledge points examined in AMC12 are broader and deeper than those in AMC10, adding almost mandatory content such as logarithms, trigonometry, and complex numbers.

The criterion for judging whether one is suitable for participating in AMC12 is: being able to answer about 18 questions correctly in AMC10.

Achieving the top 5% or 2.5% in AMC10/12 not only allows students to obtain honorary awards but also be invited to participate in the higher-level AIME competition, which is a very valuable qualification in college applications.

III. Detailed Explanation of High-Frequency Exam Questions: Master Core AMC Problem-Solving Skills

To achieve excellent results in AMC competitions, it is not enough to only master knowledge points; it is also necessary to be familiar with typical question types and problem-solving skills. The following are the high-frequency question types and problem-solving ideas for AMC8 and AMC10/12:

Typical Question Types and Solutions for AMC8

The difficulty gradient of AMC8 questions is obvious, usually divided into basic questions (1-10), medium-difficulty questions (11-20), and difficult questions (21-25). Different strategies are required for questions of different difficulty levels.

Algebra Problem Example: The product of two positive integers is 24, and their sum is 11. Find the larger number.

Problem-Solving Idea: Let the two numbers be x and y, with x > y. List the equations xy = 24 and x + y = 11. Solving the equations gives x = 8 and y = 3 (or x = 3 and y = 8), so the larger number is 8. This question examines integer factorization and the idea of quadratic equations with one variable.

Geometry Problem Example: Calculate the area of a lattice polygon.

Problem-Solving Idea: The area of a lattice polygon can be calculated by the division method or the complement method. Taking a question about calculating the area of a small kite as an example, the resulting area is 21 square inches. The test point is the area calculation of lattice figures, and Pick's Theorem or the division/complement method is often used.

Number Theory and Combinatorics Problem Example: Erase one number from 15, 16, 17, 18, 19 so that the sum of the remaining four numbers is a multiple of 4. Find the erased number.

Problem-Solving Idea: The total sum of the five numbers is 15 + 16 + 17 + 18 + 19 = 85. 85 divided by 4 leaves a remainder of 1. To make the sum of the four numbers a multiple of 4, it is necessary to erase a number that leaves a remainder of 1 when divided by 4. Check each number: 15 ÷ 4 leaves a remainder of 3, 16 ÷ 4 leaves a remainder of 0, 17 ÷ 4 leaves a remainder of 1, 18 ÷ 4 leaves a remainder of 2, 19 ÷ 4 leaves a remainder of 3. Therefore, 17 is erased. The test points are the properties of remainders when integers are divided by a certain number and the judgment of multiples.

Typical Question Types and Solutions for AMC10/12

The difficulty of AMC10/12 questions increases significantly, especially the last 5 questions (21-25), which are the key and difficult points for achieving high scores.

Algebra and Geometry Comprehensive Problem Example: The area of a rectangle is 24, and its perimeter is 20. Find the value of the square of the length plus the square of the width.

Problem-Solving Idea: Given that length × width = 24 and length + width = 10 (derived from the perimeter of 20). To find length² + width², recall the perfect square formula: (length + width)² = length² + 2 × length × width + width². Therefore, length² + width² = (length + width)² - 2 × length × width = 10² - 2 × 24 = 100 - 48 = 52. The core of such questions is to identify the algebraic relationship between geometric quantities.

Number Theory and Combinatorics Comprehensive Problem Example: Find the largest positive integer N such that there exist N distinct positive integers, where the sum of the exponents of 2 and 3 in the prime factorization of each number does not exceed 2.

Problem-Solving Idea: This question examines the combination of number theory and combinatorics. The key is to divide the problem into three cases: the sum of exponents is 0, 1, or 2. Then systematically calculate the number of numbers that meet the conditions in each case. Such questions require an accurate understanding of the meaning of the question and systematic analysis through classification and discussion.

Efficient Problem-Solving Skills

Mastering some efficient problem-solving skills can significantly improve scores in AMC competitions:

Specific Value Method: When the geometric figure is not uniquely determined, assume special conditions before calculation; consider extreme cases when finding the maximum or minimum value; assume the total number for proportion problems.

Measurement Method: For some geometry questions, draw the figure under special circumstances and directly obtain the answer by measuring the side length or angle (but question setters have intentionally avoided this possibility in recent years).

Finding Patterns: For sequence problems, start researching from simple cases; for remainder problems, find cyclic patterns.

Elimination Method: Eliminate options based on parity; eliminate options by considering the possible value range; for logical reasoning problems, test each option one by one.

Time Allocation Strategy

For the 40-minute AMC8 exam, it is recommended to spend about 15-20 minutes on simple questions (1-15), reserve 15-20 minutes for difficult questions (21-25), and leave 5 minutes for checking at the end.

For the 75-minute AMC10/12 exam, the first 15 questions should be answered quickly to ensure accuracy, leaving sufficient time for the subsequent difficult questions.

The road from AMC8 to AMC10/12 is full of challenges. AMC8 examines primary school mathematics and some junior high school knowledge, while AMC10/12 covers a wider range of high school mathematics content, such as trigonometry, complex numbers, and advanced algebra.

Scan the QR code to join the exclusive AMC8 study community! A wealth of preparation materials and trial courses await you!

Students preparing for the AMC8 can download the following for free:

2000-2026 AMC8 past exam papers (English and Chinese) + solutions + formula set + vocabulary list + preparation books + lecture notes, etc.

The 2026 AMC8 Math Competition Is About to Begin! Competition Date? Syllabus? Pre-Exam Preparations? High-Score Sprint Strategies? With Past Years' Real Questions

The 2026 AMC8 American Mathematics Competition is about to kick off! For participating students and parents, understanding the competition details and making a final sprint are crucial. This article will comprehensively analyze all the information about the 2026 AMC8 to help candidates face the challenge in the best possible state.

Real Questions for the 2026 AMC8 Now Available for Pre-Order!

2026 AMC8 real exam questions + answer explanations + video explanations will be sent to you within 24 hours after the exam ends. Scan the QR code to claim for free ⇓

I. Countdown to the Competition: Key Dates and Basic Arrangements

The 2026 AMC8 will be held on Friday, January 23, from 17:00 to 17:40, with a total exam duration of 40 minutes. Registration closed on January 13. Results are expected to be announced in late February, and certificates will be issued starting in March.

AMC8 is a mathematics competition open to students in Grade 8 (second year of middle school) or below, who must be under 14.5 years old on the competition day.

The exam uses a bilingual Chinese-English paper, with questions presented in English accompanied by Chinese translations, ensuring that language does not become a barrier to solving problems.

Overview of Basic Information for the 2026 AMC8

Item	Details
Exam Date	Friday, January 23, 2026
Exam Time	17:00–17:40 (40 minutes total)
Exam Format	Individual participation; online and offline options available
Question Type	25 multiple-choice questions
Scoring Rule	1 point for each correct answer; no penalty for incorrect answers; maximum score of 25
Eligibility	Grade 8 or below, and under 14.5 years old

II. Exam Format and Rules

The 2026 AMC8 will adopt a dual-mode of "online exams" and "offline test centers." Students choosing the online exam need to make technical preparations in advance:

Device Requirements

Prepare a computer with Windows (Win7 or above recommended) or macOS (10.15.7 or above) and a webcam.

A mobile phone is required as a proctoring device, placed 0.5–1 meter behind the computer at a height of 1.2–1.5 meters, ensuring full visibility of the student’s upper body, hands, and the computer screen.

Software Configuration

Install the latest version of Google Chrome on the computer.

The mobile phone must have Tencent Meeting installed, with audio and video functions enabled.

Exam Environment

Choose a quiet and independent space.

Only blank scratch paper, a ruler, an eraser, and other basic stationery are allowed on the desk. Calculators, smartwatches, protractors, and other tools are strictly prohibited.

The online exam simulation system will be available from January 18 to 23. It is recommended that candidates complete a mock exam in advance to test the stability of their equipment and network.

III. In-Depth Analysis of the 2026 Syllabus

The 2026 AMC8 has made significant adjustments to its syllabus, with greater emphasis on interdisciplinary applications and advanced logical reasoning abilities.

Distribution and Changes of Knowledge Modules in the 2026 AMC8 Syllabus

Knowledge Module	Proportion	New and Adjusted Content
Algebra and Probability	40%–45%	Strengthened integration of probability and statistical data with real-life scenarios (e.g., supermarket promotion models); quadratic function modeling (e.g., carbon emission optimization)
Geometry	25%–30%	Added dynamic analysis of 3D unfoldings; questions combining the Pythagorean theorem with architectural structural stability; enhanced calculation of areas of irregular shapes
Number Theory and Combinatorics	20%–25%	Increased difficulty in prime factorization and integer properties; mastery of short division for quickly solving LCM (Least Common Multiple) and GCD (Greatest Common Divisor) is required; new innovative topics such as the sum of geometric sequences

In terms of knowledge coverage, the AMC8 includes all elementary school mathematics knowledge and parts of junior high school mathematics knowledge (Grades 7–8), including but not limited to integers, fractions, decimals, percentages, ratios, number theory, geometry, probability, and statistics.

IV. Comprehensive Pre-Exam Preparation Guide

Preparations in the final days before the exam are crucial. A reasonable schedule can help candidates perform at their best.

For students taking the online exam: Log in to the online system at least 30 minutes before the exam. Before the official start, there will be identity verification and announcement of exam rules. No entry is allowed 15 minutes after the exam begins.

Pre-Exam Items to Prepare

Identification documents (admission ticket/ID card)

Blank scratch paper (it is recommended to prepare several sheets)

Basic stationery such as pencils, erasers, and rulers

Drinking water (avoid excessive consumption)

Sprint Strategies for Candidates with Different Foundations

Zero-based or weak-foundation candidates: Focus on reviewing high-frequency test points, such as basic arithmetic, number theory fundamentals, and simple geometric applications, to ensure high accuracy in the first 15 questions.

Candidates with a solid foundation: Conduct targeted breakthroughs in weak modules and focus on practicing difficult content such as number theory and combinatorics.

Experienced competition participants: Conduct in-depth research on the final challenging questions, master advanced techniques such as modular arithmetic and counting principles, and practice the ability to solve a single problem through multiple methods.

Adjusting the schedule on the day before the exam is also important. Ensure adequate sleep to avoid overfatigue. On the exam day, maintain a light diet and avoid greasy food.

V. High-Score Sprint Techniques and Answering Strategies

Time management is the key to achieving a high score in the AMC8. With 40 minutes to complete 25 questions, candidates have only about 1.6 minutes per question on average, so reasonable time allocation is essential.

Golden Time Allocation Rule

Questions 1–15 (Basic Questions): Complete within 15–20 minutes. These questions usually directly test basic concepts, so high accuracy is a must.

Questions 16–22 (Intermediate Questions): Proceed steadily, as multi-step solutions may be required. If a question cannot be solved within 2 minutes, mark it and skip it temporarily.

Questions 23–25 (Challenging Questions): Reserve sufficient time, but do not dwell on a single question. If you have no idea how to solve a problem, make a bold guess.

Efficient Problem-Solving Techniques

Special Value Substitution Method: When encountering questions involving abstract relationships, substitute simple values to concretize the abstract relationships.

Elimination Method: Use conditions such as parity and value ranges to eliminate obviously incorrect options.

Geometric Recomposition Method: Decompose complex figures into regular shapes and find proportional relationships through recombination.

Guessing Strategy

Since the AMC8 does not penalize incorrect answers, no question should be left blank. Even if you have no idea how to solve a problem, choose an answer randomly. If you can eliminate 1 incorrect option, the correct rate increases from 20% to 25%; eliminating 2 options raises it to 33%.

In the sprint stage, focus on real exam questions, carefully study the past five years' papers, and compile a personal "list of error-prone points." On the exam day, maintain a calm mindset and do not panic when facing difficult questions. Remember that the AMC8 is designed to be challenging, and students around the world face the same test.

Scan the QR code to join the exclusive AMC8 study community, where you’ll find a wealth of preparation materials and trial courses waiting for you to explore!

Students preparing for the competition can download for free:

• 2000–2025 AMC8 real exam questions in both Chinese and English

• Detailed explanations

• Formula sheets

• Vocabulary lists

• Recommended preparation books

• Lecture notes and more

This document is just the “key.” After adding me, you can:

• Ask me 1 specific question you care most about at any time, and I’ll give you targeted advice.

• Tell me your personal situation (such as your goals), and I can help you identify the key points to focus on.

• Join the exclusive study group, where I’ll send you a link to a live Q&A session.

What are the main differences between the AMC 8 and the AMC 10/12? How can you plan a learning path from the AMC 8 to higher-level competitions? With typical high-frequency exam questions as examples.

As one of the most globally recognized mathematics competitions, the AMC (American Mathematics Competitions) provides a progressive challenge platform for students of different ages and mathematical levels through its tiered competition system. The AMC 8, AMC 10, and AMC 12 are designed for students in different grade levels, sharing close connections while also featuring significant differences.

I. The Three‑Level Leap from AMC 8 to AMC 10/12: Understanding the Fundamental Differences

The AMC competition system was founded in 1950 by the Mathematical Association of America (MAA) and has become one of the most globally trusted mathematics assessments, with its scores widely recognized in the United States, Canada, the United Kingdom, and many other countries. Although they belong to the same AMC series, the AMC 8, AMC 10, and AMC 12 differ significantly across several dimensions. In terms of participants and exam format, these three levels are designed for students of different age groups, with key differences summarized in the following table:

Comparison of Eligibility Requirements and Exam Formats for AMC 8, AMC 10, and AMC 12

Competition Program	Suitable Grade Level	Age Limit	Number of Questions	Exam Duration	Scoring Rules
AMC8	Grade 8 and below	Under 14.5 years of age	25 multiple-choice questions	40 minutes	1 point for each correct answer, 25 points total, no penalty for wrong answers.
AMC10	Grade 10 and below	Under 17.5 years of age	25 multiple-choice questions	75 minutes	6 points for each correct answer, 1.5 points for each unanswered question, 150 points total, no penalty for wrong answers.
AMC12	Grade 12 and below	Under 19.5 years of age	25 multiple-choice questions	75 minutes	6 points for each correct answer, 1.5 points for each unanswered question, 150 points total, no penalty for wrong answers.

Here’s a clear, natural English translation of your text:In terms of knowledge scope and difficulty, the three competition levels also show a distinct progression:

AMC8 covers elementary and middle school mathematics, including integers, fractions, decimals, percentages, ratios, number theory, everyday geometry, area, volume, probability and statistics, logical reasoning, and more. The questions are relatively easy, similar to the level of domestic primary school Olympiad competitions.

AMC10 covers the ninth- and tenth-grade mathematics curriculum, including elementary algebra, basic geometry, elementary number theory, and probability, but does not include trigonometry, advanced algebra, or advanced geometry. In recent years, the exam has also added new types of questions such as coloring problems and chessboard problems, making the content broader and the difficulty gradually increasing.

AMC12 is the most difficult of the three levels, covering the entire high school mathematics curriculum, including advanced algebra, advanced geometry, trigonometry, complex numbers, logarithms, and logarithmic functions. Both the problem-solving difficulty and the required techniques are significantly higher, placing greater demands on students’ mathematical thinking abilities. It is important to note that there is no direct advancement relationship between AMC8, AMC10, and AMC12. Students can choose the competition level that suits their age and mathematical ability without having to participate in each one in sequence.

II. From Beginner to Master: A Study Path Plan for the AMC Competitions

A successful AMC competition journey requires systematic planning based on a student’s grade level and mathematical foundation. Below is a reference study path plan for students at different grade levels:

Grade‑by‑Grade AMC Competition Study Planning Recommendations

Grade Level Stage	Recommended Competitions	Target Score / Award	Key Areas for Exam Preparation
Grades 3–5	AMC8	Around 15 points (Global Honor Roll)	Develop interest in mathematics, consolidate elementary school content, and learn basic middle school knowledge.
Grades 6–8	AMC8	Top 5% globally (17+ points) or Top 1% globally (22+ points)	Systematically study the four main modules of algebra, geometry, number theory, and combinatorics, and develop competition‑level thinking skills.
Grades 7–10	AMC10	Top 2.5% globally (approximately 120+ points)	Complete the in‑school mathematics curriculum through Grade 10, and strengthen skills in integrated algebra, geometry, and elementary number theory.
Grades 8–12	AMC12	Top 5% globally (approximately 100+ points) or qualification for AIME.	Master advanced topics such as trigonometry, complex numbers, and higher algebra, and strengthen the ability to solve complex problems.

For students in lower grades (Grades 3–5), the AMC8 is an ideal starting point. The goal at this stage is not to pursue a high score, but to spark interest and build a strong foundation. A recommended target is around 15 points, and earning the Global Honor Roll can be considered a success. When preparing, students should focus on consolidating elementary school math content, gradually learn middle school basics, and develop fundamental competition‑level thinking and skills.

For students in middle grades (Grades 6–8), they can aim for higher awards in the AMC8, such as the Honor Roll (Top 5% globally) or the Distinguished Honor Roll (Top 1% globally). This stage requires systematic study of the four core modules—algebra, geometry, number theory, and combinatorics—to build a solid foundation for transitioning to the AMC10/12.

A practical criterion for determining readiness to move up to the AMC10 is consistently scoring above 20 points in the AMC8. For early high‑scorers, further preparation for the AMC10 is recommended, as it is the core competition in the AMC series.

Preparing for the AMC10 requires completing at least the in‑school math curriculum up to Grade 10 and setting aside more than six months for focused, topic‑specific preparation.

For upper‑grade students (Grades 8–12), directly preparing for the AMC12 is a more efficient choice. The AMC12 covers a broader and deeper range of topics than the AMC10, adding nearly mandatory content such as logarithms, trigonometry, and complex numbers.

A good indicator of readiness for the AMC12 is the ability to correctly answer around 18 questions in the AMC10.

Achieving Top 5% or Top 2.5% in the AMC10/12 not only earns prestigious honors but also qualifies students for the more advanced AIME competition, which holds significant weight in university applications.

III. Detailed Explanation of High‑Frequency Exam Questions: Mastering Core AMC Problem‑Solving Skills

To achieve excellent results in the AMC competitions, it is not enough to merely master the knowledge points; students must also become familiar with typical question types and problem‑solving techniques. Below are the common question types and solution strategies for both the AMC8 and AMC10/12.

Typical AMC8 Question Types and Solutions

The difficulty level of AMC8 questions increases gradually, and they are generally divided into basic questions (1–10), intermediate questions (11–20), and challenging questions (21–25). Different strategies are needed for each difficulty level.

Example of an Algebra Problem: The product of two positive integers is 24, and their sum is 11. Find the larger number.

Solution Strategy: Let the two numbers be x and y, with x > y. Set up the equations xy = 24 and x + y = 11. Solving these gives x = 8 and y = 3 (or x = 3 and y = 8), so the larger number is 8. This question tests integer factorization and the concepts behind quadratic equations.

Example of a Geometry Problem: Calculate the area of a lattice polygon.

Solution Strategy: The area of a lattice polygon can be found using the dissection method or the complementary shape method. For example, in a problem asking for the area of a small kite, the result is 21 square inches. This type of question focuses on calculating areas of lattice figures, often using Pick’s Theorem or dissection/complementary techniques.

Example of a Number Theory and Combinatorics Problem: Remove one number from the set {15, 16, 17, 18, 19} so that the sum of the remaining four numbers is a multiple of 4. Find the number that was removed.

Solution Strategy: The total sum of the five numbers is 15 + 16 + 17 + 18 + 19 = 85. When 85 is divided by 4, the remainder is 1. To make the sum of the remaining four numbers a multiple of 4, we need to remove a number that also leaves a remainder of 1 when divided by 4. Checking each number: 15 ÷ 4 leaves remainder 3, 16 leaves 0, 17 leaves 1, 18 leaves 2, and 19 leaves 3. Therefore, the number to remove is 17. This question tests properties of remainders and divisibility.

Typical AMC10/12 Question Types and Solutions

The difficulty of AMC10/12 questions increases significantly, especially the last five questions (21–25), which are the key to achieving high scores.

Example of an Algebra and Geometry Combined Problem: A rectangle has an area of 24 and a perimeter of 20. Find the value of the sum of the squares of its length and width.

Solution Strategy: Given length × width = 24 and length + width = 10 (derived from the perimeter 20), we need to find length² + width². Recall the perfect square formula: (length + width)² = length² + 2×length×width + width². Therefore, length² + width² = (length + width)² – 2×length×width = 10² – 2×24 = 100 – 48 = 52. The core of such problems is recognizing the algebraic relationships between geometric quantities.

Example of a Number Theory and Combinatorics Combined Problem: Find the largest positive integer N such that there exist N distinct positive integers where the sum of the exponents of 2 and 3 in the prime factorization of each number is at most 2.

Solution Strategy: This question combines number theory and combinatorics. The key is to divide the problem into three cases: sums of exponents equal to 0, 1, or 2. Then systematically count the numbers that satisfy the conditions in each case. Such problems require precise understanding of the problem statement and systematic analysis through classification.Efficient Problem‑Solving Techniques

Mastering efficient problem‑solving techniques can significantly improve scores in AMC competitions:

Specific Value Method: When a geometric figure is not uniquely determined, assume special conditions and then calculate; when finding maximum or minimum values, consider extreme cases; in ratio problems, assume a total value for easier calculation.

Measurement Method: For some geometry problems, draw the figure under special conditions and directly measure side lengths or angles to obtain the answer (though recent examiners have tried to avoid making this possible).

Pattern Recognition: For sequence problems, start with simple cases; for remainder problems, look for cyclic patterns.

Elimination Method: Eliminate options based on parity; exclude options by considering possible value ranges; test options one by one in logical reasoning problems.

Time Management Strategy: For the 40‑minute AMC8 exam, it is recommended to spend about 15–20 minutes on easy questions (1–15), reserve 15–20 minutes for difficult questions (21–25), and leave 5 minutes for checking.

For the 75‑minute AMC10/12 exams, answer the first 15 questions quickly while ensuring accuracy to leave ample time for the later, more difficult questions.

The journey from AMC8 to AMC10/12 is full of challenges. The AMC8 tests elementary school math and some middle school knowledge, while the AMC10/12 cover a wider range of high school topics such as trigonometry, complex numbers, and advanced algebra.

Scan the QR code to join the exclusive AMC8 study community, where you’ll find a wealth of preparation materials and trial courses waiting for you to explore!

Students preparing for the competition can download for free:

• 2000–2025 AMC8 real exam questions in both Chinese and English

• Detailed explanations

• Formula sheets

• Vocabulary lists

• Recommended preparation books

• Lecture notes and more

This document is just the “key.” After adding me, you can:

• Ask me 1 specific question you care most about at any time, and I’ll give you targeted advice.

• Tell me your personal situation (such as your goals), and I can help you identify the key points to focus on.

• Join the exclusive study group, where I’ll send you a link to a live Q&A session.