What Are the Differences Between AMC10 and AMC12?
AMC10/12 are comparable to domestic high school and junior high school math competitions. AMC8 focuses on fostering interest and is equivalent to domestic primary school Olympiad math, forming the overall American math competition system.
IMO (International Mathematical Olympiad) represents the U.S. national team to compete with top math talents around the world. USAMO, comparable to CMO, is only open to U.S. citizens and essentially serves as a selection competition for the U.S. national team; winners represent the U.S. team in the IMO. AIME (American Invitational Mathematics Examination), comparable to provincial teams, is held in February of the following year with a full score of 15. A score of 7-10 can help apply for top 30 U.S. universities, and a score of ≥10 can qualify for USAMO and apply for Ivy League schools.
Every November, the top 2.5% of AMC10 participants and the top 5% of AMC12 participants advance to AIME and receive HR certificates. AMC8 is held every January, is non-selective, and serves as an introductory event for American math competitions.
Competition Format Comparison Between AMC10 and AMC12
AMC10 Math Competition Format
Suitable for: Students in 10th grade and below, and under 17.5 years old
Exam Duration: 75 minutes
Number of Questions: 25
Scoring: 6 points for each correct answer, 1.5 points for each unanswered question, 0 points for each incorrect answer; full score is 150
Exam Difficulty and Content: Junior high school 3rd grade and high school 1st grade curriculum content, including elementary algebra, basic geometry, elementary number theory, and probability problems
Exam Time: Every November
Difficulty Level: Intermediate, suitable for high school level
Awards: Perfect Score Award, Global Distinction Award, Global Achievement Award, AIME Qualification Certificate, Global Honor Roll, etc.
AMC10 mainly examines geometry, number theory, probability and statistics, permutations and combinations, etc., but does not involve calculus or trigonometric function knowledge. Some questions are relatively in-depth, such as logical reasoning questions, which require time to understand and master.
Number and Proportion of Questions in Each Module:
Algebra & Sequences: 8 questions, accounting for 32%
Combinatorics & Probability: 6 questions, accounting for 24%
Geometry: 8 questions, accounting for 32%
Number Theory: 3 questions, accounting for 12%
Core Test Points of Each Module:
Algebra: Equations and inequalities, functions and graphs, sequences and series, etc.
Geometry: Plane geometry (triangles, quadrilaterals, circles, etc.), solid geometry (polyhedrons, rotating solids, etc.), Pythagorean theorem, etc.
Number Theory: Prime and composite numbers, divisors and multiples, divisibility problems, remainder problems, etc.
Combinatorics and Probability: Permutations and combinations, counting principles, introductory graph theory, probability calculation, etc.
Functions: Coordinate system, position transformation, linear functions, circle equations, etc.
Solid Geometry: Point-line-plane relationships, 3D coordinate system, solid geometry drawing, regular polyhedrons, Euler's formula, special solid geometric figures, solid geometry skills, etc.
Analytic Geometry: Equations of lines and circles, parabolas, ellipses, hyperbolas, etc.
Inequalities: Linear inequalities, polynomial inequalities, quadratic inequalities, etc.
AMC12 Math Competition Format
Suitable for: Students in 12th grade and below, and under 19.5 years old
Exam Duration: 75 minutes
Number of Questions: 25
Scoring: 6 points for each correct answer, 1.5 points for each unanswered question, 0 points for each incorrect answer; full score is 150
Exam Difficulty and Content: All high school knowledge, including AMC10 content, plus logarithms, complex numbers, trigonometric functions, etc.
Exam Time: Every November
Difficulty Level: Advanced, suitable for high school students with high academic levels
Test Points: All knowledge points of AMC10, plus logarithms, calculation and graphs of trigonometric functions, complex numbers and other high school knowledge points
Awards: Perfect Score Award, Global Distinction Award, Global Achievement Award, AIME Qualification Certificate, Global Honor Roll, etc.
The questions and scope of the AMC12 exam overlap a lot with the AMC10 exam, mainly focusing on the four modules of algebra, geometry, number theory, and combinatorics. However, at the core knowledge level, it adds three knowledge modules: logarithms, calculation and graphs of trigonometric functions, and complex numbers, and these three modules are almost 100% tested in the AMC12.
Number and Proportion of Questions in Each Module:
Number Theory: 7 questions, accounting for 28%
Algebra: 6 questions, accounting for 24%
Geometry: 7 questions, accounting for 28%
Probability/Combinatorics/Logic: 5 questions, accounting for 20%
Core Test Points of Each Module:
Algebra: Various factorization methods and their wide applications, basic rules of exponential operations and solving equations.
Plane Geometry: Calculation of isosceles, equilateral and right triangles, basic trigonometric function calculation of special angles.
Number Theory: Divisibility theory, congruence theory, Fermat's little theorem and fundamental theorem of arithmetic, number theory proofs.
Permutations and Combinations: Counting principles, mastering permutation and combination principles and calculations, calculation of mean, mode, median and weighted mean.
Trigonometric Functions: Basic trigonometric knowledge and formulas, calculation and simplification of trigonometric functions, comprehensive application of trigonometric functions.
Sequences and Series: Solution methods of arithmetic and geometric sequences, learning skills to solve special sequences and series, solution methods of competition questions combining trigonometry, algebra and combinatorics.
Different Thresholds for Advancing to Higher-Level Competitions
Both exams allow advancement to AIME (American Invitational Mathematics Examination), but the advancement ratios are different:
AMC10: The proportion of advancing to AIME is about the top 2.5%, with a higher score line
AMC12: The proportion of advancing to AIME is about the top 5%, with a relatively lower score line
If a child has sufficient mathematical ability, taking the AMC12 math competition is easier to advance.
How to Choose Between AMC10 and AMC12?
If the child has not finished learning high school math: Prioritize AMC10, which is more suitable and easier to win awards
If the child has finished learning high school math and aims to apply for top universities: Choose AMC12, which has higher gold value
If time and energy permit: You can take both exams, one as a backup and the other as a sprint
Suggestions for Taking Both AMC10 and 12:
AMC10A + AMC12B
AMC10B + AMC12A
|
Competition Name
|
AMC8
|
AMC10
|
AMC12
|
|
Suitable for
|
Students in 8th grade and below, and under 14.5 years old on the competition day
|
Students in 10th grade and below and under 17.5 years old
|
Students in 12th grade and below and under 19.5 years old
|
|
Registration Time
|
Around January every year
|
Held every November, divided into two sessions: A and B, one week apart
|
Held every November, divided into two sessions: A and B, one week apart
|
|
Exam Time
|
40 minutes
|
75 minutes
|
75 minutes
|
|
Domestic Equivalent
|
Hope Cup
|
Junior High School League
|
High School League
|
|
Scoring Standard
|
Complete 25 multiple-choice questions (25 points) within 40 minutes: 1 point for each correct answer, no points deducted for incorrect answers
|
Complete 25 multiple-choice questions within 75 minutes: 6 points for each correct answer, 0 points for incorrect answers, 1.5 points for unanswered questions; full score is 150
|
Complete 25 multiple-choice questions within 75 minutes: 6 points for each correct answer, 0 points for incorrect answers, 1.5 points for unanswered questions; full score is 150
|
|
Exam Content
|
Mainly divided into three directions: primary school math, junior high school math, primary school Olympiad math
|
Junior high school and part of high school math in-class knowledge + extracurricular knowledge
|
High school math in-class knowledge + extracurricular knowledge
|
|
Awards
|
Perfect Score Award: 25 pointsGlobal Distinction Award: Top 1% globallyGlobal Achievement Award: Top 5% globallyGlobal Honor Roll: G6 and below with 15+ points
|
Perfect Score Award: 150 pointsGlobal Distinction Award: Top 1% globallyGlobal Achievement Award: Top 5% globallyGlobal Honor Roll: G8 and below with 90+ pointsAIME Qualification: Top 2.5% globally
|
Perfect Score Award: 150 pointsGlobal Distinction Award: Top 1% globallyGlobal Achievement Award: Top 5% globallyGlobal Honor Roll: G8 and below with 90+ pointsAIME Qualification: Top 5% globally
|
How Difficult Are AMC10 and AMC12?
How difficult are the AMC10 and 12 math competitions? How to judge if a child is suitable for learning? How much energy does it take to prepare?
Compared with in-school math:
AMC10 ≈ Domestic junior high school competition enhancement + a small amount of high school 1st grade math
AMC12 ≈ Domestic high school math league preliminary difficulty
In what ways is AMC12 more difficult than AMC10?
1. One more large block of knowledge
AMC12 adds: Trigonometric functions, logarithms, complex numbers, higher-order algebra. It is impossible to solve without learning high school math.
2. The questions are more tricky and the calculations are more complex
For questions in the same position, AMC12 is obviously more difficult to figure out.
3. The high score segment is more competitive
Many top students take the AMC12, making it more difficult to get high scores.
Gold Value of AMC10 and 12
The gold value of AMC12 is higher than that of AMC10. Because AMC12 is more difficult, covers more extensive and in-depth mathematical knowledge, and has more flexible questions, its difficulty is naturally higher than that of AMC10. Therefore, when applying for top universities, AMC12 scores are often more valued.
