The AMC 12 is the most advanced exam in the American Mathematics Competitions series, open to Canadian students in Grade 12 and below. Organised by the Mathematical Association of America, it consists of 30 questions in 75 minutes covering the full scope of pre-calculus high school mathematics. Top scorers – the top 5% – qualify for the American Invitational Mathematics Examination (AIME), one of the most prestigious math competition credentials a high school student can hold. This guide covers everything Canadian parents and students need to know about the AMC 12: what it tests, how it is scored, how it differs from the AMC 10, how to use past contests effectively, and what the competition pathway looks like beyond it.
What is the AMC 12?
The senior-level exam in the AMC series run by the Mathematical Association of America. It targets students in Grade 12 or below and covers the full range of pre-calculus high school mathematics, including topics that go well beyond standard school curriculum. It is held alongside the AMC 10 in November each year, in two versions – AMC 12A and AMC 12B – administered approximately one week apart.
Like the AMC 8 and AMC 10, the AMC 12 does not test whether students have memorised procedures. It tests how students think mathematically: whether they can reason through unfamiliar problems, apply concepts creatively, and find elegant solutions under time pressure.
For Canadian students, the competition is particularly relevant in Grade 11 and 12. Strong performance and especially AIME qualification are recognised by competitive university programmes, including Waterloo, UofT, MIT, Caltech, and Princeton, as meaningful evidence of mathematical ability.
Who can take the AMC 12?
Any student in Grade 12 or below who is under 19.5 years old on the day of the competition. There is no minimum grade: exceptionally strong Grade 9 and 10 students occasionally sit the AMC 12, though most students at that stage are better served by focusing on AMC 10 preparation first.
Students who have already sat the AMC 10 should note that they cannot sit both the AMC 10 and AMC 12 on the same date. AMC 10A and AMC 12A are held on the same day, as are AMC 10B and AMC 12B. Students choose which version to sit based on their current level and goals.
AMC 12A and AMC 12B
The competition is offered in two versions each year, approximately one week apart. AMC 12A and AMC 12B contain different questions but are designed to be equivalent in difficulty. Students may sit one or both. Sitting both gives students a second opportunity to achieve a strong qualifying score for AIME, and the better of the two scores is used for qualification purposes.
Format and topics
Exam structure
| Structure | Detail |
|---|---|
| Number of questions | 30 |
| Time allowed | 75 minutes |
| Format | Multiple choice (5 options) |
| Scoring | +6 correct, +1.5 blank, 0 incorrect |
| Maximum score | 150 |
| Where | In-person at registered test centres |
| When | November each year (two sittings: 12A and 12B) |
The scoring system rewards accuracy over guessing. A blank answer is always worth more than a wrong answer, so students should leave questions blank rather than guess randomly – particularly on the harder questions at the end of the paper.
Topics covered
The AMC 12 covers the full scope of pre-calculus high school mathematics. It includes everything on the AMC 10 and adds several advanced topic areas.
| Topic area | Key concepts |
|---|---|
| Algebra | Advanced equations, complex numbers, polynomial theory, logarithms |
| Geometry | Euclidean geometry, trigonometry, coordinate geometry, 3D geometry |
| Number theory | Modular arithmetic, Diophantine equations, prime factorisation, number bases |
| Combinatorics and probability | Permutations, combinations, expected value, recursive counting |
| Trigonometry | Identities, equations, applications in geometry |
| Pre-calculus concepts | Sequences and series, limits at an introductory level, conic sections |
| Logic and proof | Multi-step reasoning, elegant solution design, proof-style thinking |
The exam does not include calculus. However, students who have been exposed to pre-calculus topics including logarithms, trigonometric identities, and complex numbers will have a meaningful advantage.
How hard is the AMC 12?
It is harder than the AMC 10, primarily because of the additional topic areas and the greater depth required within each one. Questions 1 to 10 are broadly comparable to questions 10 to 20 on the AMC 10. Questions 21 to 30 are among the hardest multiple-choice math problems a high school student will encounter anywhere in the world.
The average score on the senior AMC is typically lower than on the AMC 10 relative to the maximum, reflecting the broader and deeper topic coverage. AIME qualification from the AMC 12 requires approximately the top 5% of scorers, compared to the top 2.5% from the AMC 10.
Scoring and AIME qualification
| Answer type | Points awarded |
|---|---|
| Correct | 6 points |
| Blank | 1.5 points |
| Incorrect | 0 points |
The maximum possible score is 150. The scoring system is identical to the AMC 10. Students should never guess randomly: leaving a question blank is the better choice when there is no basis for eliminating options.
AIME qualification from the AMC 12
AIME qualification from the senior AMC goes to approximately the top 5% of scorers. The exact cutoff varies each year.
| Recognition | Approximate threshold |
|---|---|
| AIME qualification | Top 5% of AMC 12 scorers |
| Honor Roll | Top 5% (same threshold as AIME in most years) |
| Achievement Roll | Score of 90 or above |
The AIME qualification cutoff from the AMC 12 is typically lower in terms of raw score than the AMC 10 cutoff, reflecting the harder paper. Historically the AMC 12 AIME cutoff has been around 85 to 100 out of 150, compared to 100 to 115 for the AMC 10.
AMC 10 vs AMC 12: Which should your child sit?
This is a common question for students in Grade 9 and 10 who are eligible for both. The decision depends on mathematical background and AIME qualification strategy.
| AMC 10 | AMC 12 | |
|---|---|---|
| Grade eligibility | Grade 10 and below | Grade 12 and below |
| AIME qualification threshold | Top 2.5% | Top 5% |
| Topic scope | Up to Grade 10, no calculus | Full pre-calculus |
| Best for | Students without trigonometry or logarithms | Students who have covered pre-calculus topics |
| Strategy note | Lower cutoff percentage needed | More topics required but lower raw score cutoff |
A student in Grade 9 or 10 who has not yet studied trigonometry and logarithms will generally perform better on the AMC 10. A student in Grade 11 who has covered these topics may find it worthwhile to attempt the AMC 12 where the AIME qualification percentage is higher. Some strong students in Grade 10 sit both the AMC 10A and AMC 12B in the same year to maximise their chances of AIME qualification.
For more on the AMC 10, read AMC 10 Math Competition: The Complete Guide for Canadian Students and Parents.
AMC 12 past contests: How to use them effectively
Past contests are one of the most valuable preparation tools available. The MAA publishes past papers going back many years, and working through them systematically is the foundation of any serious preparation plan.
Where to find AMC 12 past contests
Past papers and solutions are available through the Mathematical Association of America and through the Art of Problem Solving community, which hosts detailed solution discussions for every past problem. Both AMC 12A and AMC 12B papers are available for every year going back to 2000.
2024 and 2025 papers are the most recent and reflect the current difficulty and topic distribution. These should form part of any final preparation in the months before sitting the competition.
How to use past papers effectively
Working through AMC 12 past contests is most effective when approached as a study tool rather than simply a practice test. The most productive approach involves four steps.
First, complete the paper under timed conditions: 75 minutes, no notes or calculator. Record which questions you attempted, which you left blank, and which you answered incorrectly.
Second, after the paper, review every question including the ones you answered correctly. For each question identify the topic area, the key insight required, and whether there is a faster or more elegant approach than the one you used.
Third, categorise your errors. Questions answered incorrectly will generally fall into one of three categories: topic gaps (the concept required was not known), reasoning errors (the concept was known but applied incorrectly), or time pressure errors (the approach was correct but ran out of time). Each category requires a different response.
Fourth, return to questions from your weakest topic areas and work through additional problems in that area before attempting the next past paper.
A structured approach is to complete one past contest per month, then spend two or three sessions reviewing it before attempting the next. Quality of review is more important than volume of papers completed.
What AMC 12 2024 and 2025 tell us about the current paper
The 2024 and 2025 papers reflect the current MAA approach to question design. In recent years the later questions have placed increasing emphasis on elegant multi-step reasoning and problems that combine geometry with algebra or number theory with combinatorics. Students preparing for the 2026 competition should ensure their preparation covers all topic combinations, not just individual topics in isolation.
How to prepare for the AMC 12
Mathematical prerequisites
Before beginning serious preparation, students should have a solid foundation in all AMC 10 topic areas plus introductory trigonometry, logarithms, and complex numbers. Students who have not yet covered these in school should build them before attempting AMC 12 past papers, as the gap in knowledge will make paper review unproductive.
Most students who perform competitively on the AMC 12 have two or more years of dedicated competition math preparation behind them, beginning with AMC 8 and AMC 10 work in middle school and early high school.
Building from AMC 10 preparation
AMC 10 preparation is the most efficient foundation for AMC 12 work. The reasoning skills, problem-solving approaches, and mathematical habits developed through serious AMC 10 preparation transfer directly to the AMC 12. Students who have achieved AIME qualification through the AMC 10 are well-positioned to sit the senior AMC, with additional preparation focused on the topics the AMC 12 adds: trigonometry, logarithms, complex numbers, and more advanced number theory.
Students who have not yet achieved consistent AMC 10 Honor Roll performance are generally better served by continuing AMC 10 preparation rather than switching to AMC 12 work prematurely.
Preparation timeline
| Stage | Focus | Timeline before AMC 12 |
|---|---|---|
| Foundation | AMC 8 and AMC 10 topics | 2 to 3 years before |
| Transition | AMC 10 past papers, trigonometry and logarithms | 12 to 18 months before |
| AMC 12 specific | AMC 12 past papers, advanced number theory, complex numbers | 6 to 12 months before |
| Final preparation | AMC 12 2024 and 2025 papers, timed mock conditions | 1 to 3 months before |
Where the AMC 12 fits in the competition pathway
It sits near the top of the North American high school math competition ladder.
| Competition | Who | What it leads to |
|---|---|---|
| AMC 8 | Grade 8 and below | Foundation for AMC 10 |
| AMC 10 | Grade 10 and below | AIME (top 2.5%) |
| AMC 12 | Grade 12 and below | AIME (top 5%) |
| AIME | Top AMC scorers | USAMO qualification |
| USAMO | Invitation only | USA IMO team selection |
| IMO | Invitation only | World championship |
What is the AIME and why does it matter?
The American Invitational Mathematics Examination is a 15-question, 3-hour competition open only to students who qualify through the AMC 10 or AMC 12. Unlike the AMC series, the AIME requires students to compute integer answers rather than select from multiple choice options, making it significantly harder. A strong AIME score is one of the most significant math competition credentials a high school student can achieve and is recognised by competitive university programmes worldwide.
The Canadian competition pathway
For Canadian students, strong AMC 12 performance feeds into the Canadian competition system as well. The problem-solving skills developed through AMC 12 preparation translate directly into strong performance on the Euclid contest run by the University of Waterloo, which is used in admissions and scholarship consideration for Waterloo and UofT engineering and mathematics programmes. AMC 12 preparation also builds the foundation for the Canadian Open Mathematics Challenge and the Canadian Mathematical Olympiad pathway.
Why Canadian families choose Think Academy for AMC preparation
Think Academy is one of the leading AMC preparation providers in North America, with a track record that speaks for itself.
Since 2021, Think Academy has served as an official AMC testing site, hosting AMC 8 and AMC 10 exams at multiple locations. Think Academy students have earned more than 1,700 AMC 8 medals and 700 AMC 10 medals. In the 2024 to 2025 academic year, nearly one in three Think Academy students qualified for AIME, four times the national average.
These results come from a structured approach to competition preparation that goes well beyond drilling past papers. Our curriculum uses a spiral advancement model, revisiting key concepts at increasing depth across multiple course levels. Classes are live and interactive, homework is marked and returned by teachers, and every session is recorded so students can review material at their own pace.
For students working toward the AMC 12, Think Academy’s AMC 10 courses build exactly the problem-solving foundation needed. The skills developed through structured AMC 10 preparation – creative reasoning, multi-step problem solving, and mathematical fluency across algebra, geometry, and number theory – transfer directly to AMC 12 level work. Students who complete Think Academy’s AMC 10 programme are well-positioned to make the transition to AMC 12 preparation independently or with additional support.
Think Academy competition winners were also recognised on a Times Square billboard in summer 2025, celebrating student achievement across AMC 8, AMC 10, and Math Kangaroo.
Start with a FREE math evaluation today to find your child’s current level and the right preparation pathway for their competition goals.
Frequently Asked Questions
What is the AMC 12 math competition?
A 30-question, 75-minute multiple-choice math competition for students in Grade 12 and below, organised by the Mathematical Association of America. It covers the full scope of pre-calculus high school mathematics and serves as a qualifier for the American Invitational Mathematics Examination. Top scorers – approximately the top 5% – are invited to sit the AIME.
What is the difference between AMC 10 and AMC 12?
Both are 30-question, 75-minute exams with the same scoring system. The AMC 10 is for Grade 10 and below and covers mathematics up to Grade 10. The AMC 12 is for Grade 12 and below and adds trigonometry, logarithms, complex numbers, and more advanced pre-calculus topics. AIME qualification requires the top 2.5% of AMC 10 scorers and the top 5% of AMC 12 scorers.
Can Canadian students take the AMC 12?
Yes. Canadian students are fully eligible through a registered AMC test centre: either a participating school or an independent centre. Think Academy Canada is a registered AMC test centre and has hosted AMC competitions since 2021.
Where can I find AMC 12 past contests?
Past papers and solutions are available through the Mathematical Association of America website and the Art of Problem Solving community. Both AMC 12A and 12B papers are available going back to 2000. The AMC 12 2024 and AMC 12 2025 papers are the most recent and most useful for current preparation.
What score do you need on the AMC 12 to qualify for AIME?
Approximately the top 5% of AMC 12 scorers qualify for AIME. The exact cutoff varies each year but has historically been around 85 to 100 out of 150. The official cutoff is published by the MAA after each sitting.
How hard is the AMC 12?
Significantly harder than school curriculum and considerably harder than the AMC 10. Questions 1 to 10 are broadly equivalent to the harder questions on the AMC 10. Questions 21 to 30 are among the hardest multiple-choice problems in any high school competition worldwide. Most students need two or more years of dedicated competition preparation before sitting the AMC 12 competitively.
Should my child take the AMC 10 or AMC 12?
Students who have not yet studied trigonometry and logarithms should sit the AMC 10. Students in Grade 11 or 12 who have covered pre-calculus topics may find the AMC 12 worthwhile, where the AIME qualification percentage is slightly higher. Some strong students in Grade 10 sit both AMC 10A and AMC 12B in the same year to maximise their chances of AIME qualification.
Does the AMC 12 help with Canadian university admissions?
Strong AMC 12 performance and AIME qualification are recognised by competitive university programmes as meaningful evidence of mathematical ability, including Waterloo, UofT, MIT, Caltech, and Princeton. For Canadian students specifically, the Euclid contest at Waterloo is the most directly relevant to domestic admissions, and competition preparation builds the skills that translate directly into strong Euclid performance.
This is really helpful, especially the part about AIME qualification. I’ve been researching that for my son.