Category: Blog

1. Knowledge Breadth

AMC8: Mainly consolidates elementary school mathematics foundations and inspires students' mathematical thinking; the problems are relatively easy, suitable for beginners.

AMC10: Adds advanced algebra (e.g., Vieta's theorem, Factor theorem), advanced plane geometry (congruent triangles, trigonometric applications), in-depth number theory problems (modular arithmetic, congruence equations, Diophantine equations), and combinatorics (permutations and combinations, probability models), etc.; the knowledge coverage is broader, requiring students to master mathematics up to the first year of high school and middle school level.

2. Depth of Thinking

AMC8: Focuses on the application of basic knowledge, with relatively straightforward problems; emphasizes basic training in logical reasoning.

AMC10: Places more emphasis on the integration of multiple knowledge points and flexibility in logical reasoning; a single problem may involve number theory, algebraic manipulation, and geometric construction, testing students' comprehensive application ability.

3. Time Pressure

AMC8: Exam duration is 40 minutes for 25 questions; time is relatively ample, suitable for beginners to get used to the competition pace.

AMC10: Exam duration is 75 minutes for 25 questions; the requirements for proficiency and strategic selection are significantly higher, with an average of only 3 minutes per question.

1. Expansion of Knowledge Breadth

Advanced algebra: e.g., Vieta's theorem, Factor theorem, etc.

Advanced plane geometry: e.g., congruent triangles, similar triangles, Power of a Point theorem, trigonometric applications, etc.

In-depth number theory: e.g., modular arithmetic, congruence equations, Diophantine equations, etc.

Combinatorics: e.g., permutations and combinations, probability models, recurrence relations, etc.

2. Enhancement of Depth of Thinking

Integration of multiple knowledge points: A single problem may involve the comprehensive application of multiple knowledge points.

Flexibility in logical reasoning: Requires students to have strong abstract thinking and creative problem-solving abilities.

3. Coping with Time Pressure

Timed practice: Improve answering speed and accuracy through timed mock exams.

Strategic selection: Learn to allocate time reasonably, prioritizing problems you are confident about.

1. Fill Knowledge Gaps

Practice test with past papers: It is recommended to have students take an AMC10 practice test to accurately assess their mathematical foundation.

Supplement knowledge points: If a student achieves a top 5% or top 1% score in AMC8, it indicates a solid mathematical foundation. They need to supplement missing AMC10 knowledge points, such as sequences, linear functions, permutations & combinations and probability, overall operations, and other high-frequency topics.

2. Practice Problems to Develop Problem-Solving Thinking

Categorized training: Conduct categorized training on AMC10 past papers, focusing on medium-difficulty problems to improve problem-solving approaches and accuracy.

Cross-knowledge thinking: From problem 16 onward in the AMC10 competition, flexibility increases, and a single problem may involve multiple knowledge points. Therefore, while practicing, summarize thought processes and cultivate the ability to think from cross-knowledge perspectives.

3. Train Answering Techniques

Timed mock exams: Arrange timed mock exams to simulate the real exam environment, improving answering speed and accuracy.

Answering techniques: Master some common answering techniques, such as quick estimation, elimination method, special value substitution, etc., to help students save time.

1. Pre-AMC10 Express

Target Audience: G6-8 students

Course Content: Advance learning of four major middle school math topics: algebraic operations, functions and graphs, similar triangles, circles; advanced learning of two major in-school sections: algebra, geometry.

Course Duration: 120 hours

2. AMC10 Express Training

Target Audience: G9-10 students

Course Content: Systematically review AMC10 competition test points; train AMC10 problem-solving approaches and answering techniques.

Course Duration: 110 hours

3. Specific Class Settings

Class Name	Class Size	Hours
AMC10 Full Course	3-8 students	110 hours
Pre AMC10 Full Course	3-8 students	120 hours
AMC10 Foundation Course	3-8 students	50 hours
AMC10 Intensive Course	3-8 students	30 hours
AMC10 Sprint Course	3-8 students	30 hours
AMC10 Personalized Course	1V1/1V2/1V3	Customized

4. Course Features

Stratified, staged teaching: Different course offerings based on students' foundation levels.

Online and offline synchronous classes: Convenient for students to choose the learning method that suits them.

Recorded sessions: Support repeated learning to ensure mastery of knowledge points.

Misconception 1: Thinking "a few practice tests will get an award"

Reality 1: Many tested topics aren't covered in school!

High-frequency AMC10 topics not covered in school include:

Inclusion-exclusion principle

Permutations & combinations (addition/multiplication principle, grouping/insertion method)

Congruences & modular arithmetic

Similarity in geometry, power of a point theorem, coordinate geometry

Recursive sequences, Vieta's formulas (comprehensive applications)

These topics are precisely concentrated in problems 16–25, the key scoring area!

Advice: If a student hasn't systematically studied the above topics, at least 3–6 months of targeted remediation is necessary.

Misconception 2: Treating AMC10 as "AMC8 upgraded"

Reality 2: The difficulty jumps dramatically!

Dimension	AMC8	AMC10
Problems / Time	25 problems / 40 min	25 problems / 75 min
Time per problem (avg.)	1.6 min	3 min
Difficulty of hardest problems	Middle school extension	Approaching AIME level
Depth of knowledge	Elementary + 7th grade	8th–10th grade + competition mindset

The truth: Problems 21–25 of AMC10 are almost a "chasm" for average students and require long-term training to overcome.

Misconception 3: Underestimating the intensity of competition

Reality 3: Average score is only 57 points, 90% of test-takers are "just participating"!

Perfect score: 150 points

Global average: ~57 points

AIME cutoff (2025): 105+ points

This means: You need to outscore 90% of global test-takers by nearly 50 points!

1. Foundation Building Phase (March–July)

Goal: Fill knowledge gaps, build a competition thinking framework.
Actions:
- Work on past papers from 2013–2018 (focus on problems 1–20).
- Focus on: algebraic identities and transformations, geometric auxiliary lines, elementary number theory.
- Do 2 full sets per week, analyze errors, and build a "knowledge – problem type" mapping table.

2. Skill Sharpening Phase (September–October)

Goal: Increase speed + conquer intermediate problems.
Actions:
- Work on past papers from 2019–2023 (timed full sets).
- Targeted practice: permutations & combinations, congruences, geometry optimization problems.
- Simulate test pacing: first 10 problems ≤15 min, problems 11–20 ≤35 min.

3. Final Sprint Phase (November, before the exam)

Goal: Fill gaps + solidify strategies.
Actions:
- Work on the most recent past papers from 2024–2025.
- Return to your error log, memorize high-frequency formulas (e.g., Pythagorean triples, difference of squares, combinatorial identities).
- Solidify test-taking habits: circle keywords, skip stuck problems, strategically leave blanks.

1. Golden time allocation ratio

Problems 1–10: ≤15 minutes (aim for perfect score)

Problems 11–20: ≤35 minutes (minimize mistakes)

Problems 21–25: ≤20 minutes (aim for 2 correct)

Last 5 minutes: check bubble sheet + recalc

2. Learn to strategically skip

AMC10 scoring rules: Correct: +6 points, Blank: +1.5 points, Wrong: 0 points.

Strategy: For uncertain problems, better to leave them blank! If you answer 16 correctly and leave 9 blank → 16×6 + 9×1.5 = 109.5 points → secure AIME qualification!

3. Use elimination to increase guess rate

Use:

Parity (e.g., the answer must be even)

Range estimation (e.g., side length cannot exceed 100)

Unit / dimension checks

Special value substitution (e.g., test with x = 0, 1, 2)

This can quickly eliminate 2–3 options, raising the chance of a correct guess from 25% to 50%!

4. Mindset management: Allow yourself to "not know"

When you encounter a stuck problem, remind yourself: "This problem is designed to filter people, it's normal to skip it." Prioritize ensuring 100% of the problems you know are correct — that's wiser than stubbornly grinding on one tough problem.