The American Math Competition, known as the AMC, is one of the most recognised math competition series in the world and a genuine pathway for Canadian students who want to take their mathematical ability beyond the school curriculum. Organised by the Mathematical Association of America, the AMC series runs from the AMC 8 for middle school students through to the AMC 12 for senior high school students, with top performers qualifying for the American Invitational Mathematics Examination and ultimately the International Mathematical Olympiad. This guide explains what the AMC is, which level is right for your child, why Canadian families participate, and how to get started with preparation.
What is the American Math Competition?
The American Math Competition is a series of multiple-choice examinations designed to develop mathematical problem-solving skills in students from middle school through to the end of high school. It is run by the Mathematical Association of America and has been identifying and nurturing mathematical talent for over seventy years.
Unlike school exams, the AMC does not test whether students have memorised a procedure. It tests whether they can reason through a problem they have never seen before, identify the underlying mathematical structure, and find an efficient path to a solution. This is a fundamentally different skill from performing well in a school math class, which is why students who are strong in school often find the AMC unexpectedly challenging the first time they sit it.
For Canadian students, the AMC provides an international benchmark. A strong AMC result tells a parent, a student, and a university admissions office something meaningful about a student’s mathematical ability that a school grade alone cannot convey.
Who organises the American Math Competition?
The AMC series is organised by the Mathematical Association of America, a non-profit organisation based in the United States. The MAA has run these competitions since 1950. The AMC serves as the first stage of the selection process for the USA Math Team that represents the United States at the International Mathematical Olympiad each year. Canadian students participate fully and their results are recognised alongside those of American students.
Can Canadian students take the AMC?
Yes. Canadian students are fully eligible to sit any level of the AMC series. Registration must go through a registered test centre — either a school that participates or an independent centre. Think Academy Canada is a registered AMC test centre and has hosted AMC competitions since 2021. Canadian students who perform well on the AMC 10 or AMC 12 qualify for the AIME on exactly the same basis as American students.
The AMC series explained
The American Math Competition series has three levels, each designed for a different stage of a student’s mathematical development. Understanding which level is appropriate for your child is the starting point for any preparation plan.
| Competition | Grade eligibility | Age limit | Questions | Time | Leads to |
|---|---|---|---|---|---|
| AMC 8 | Grade 8 and below | Under 14.5 | 25 | 40 minutes | AMC 10 readiness |
| AMC 10 | Grade 10 and below | Under 17.5 | 30 | 75 minutes | AIME (top 2.5%) |
| AMC 12 | Grade 12 and below | Under 19.5 | 30 | 75 minutes | AIME (top 5%) |
What is the AMC 8?
The AMC 8 is the entry-level competition in the series, designed for students in Grade 8 and below. It is a 25-question, 40-minute multiple-choice exam covering middle school mathematics including number theory, algebra, geometry, counting, and probability. There is no penalty for wrong answers, so students should attempt every question.
The AMC 8 is an excellent starting point for students who are mathematically curious and want to experience competition math for the first time. It is challenging enough to be meaningful and accessible enough that a well-prepared Grade 5 or 6 student can participate with confidence.
For more on the AMC 8, read AMC 8 Math Competition: The Complete Guide for Canadian Students and Parents!
What is the AMC 10?
The AMC 10 is for students in Grade 10 and below and covers high school mathematics up to Grade 10 level, excluding calculus. It is 30 questions in 75 minutes and uses a scoring system that rewards accuracy over guessing — a blank answer is worth 1.5 points while an incorrect answer scores zero.
The top 2.5% of AMC 10 scorers qualify for the American Invitational Mathematics Examination, making this the most significant qualification hurdle in the AMC series for most students. Strong AMC 10 performance is recognised by competitive university programmes including Waterloo, UofT, MIT, and Caltech.
If you’re interested in learning more about the AMC 10, read AMC 10 Math Competition: The Complete Guide for Canadian Students and Parents!
What is the AMC 12?
The AMC 12 is the most advanced level of the series, open to students in Grade 12 and below. It covers the full scope of pre-calculus high school mathematics including trigonometry, logarithms, complex numbers, and advanced number theory. The top 5% of AMC 12 scorers qualify for the AIME.
Students in Grade 9 and 10 who are eligible for both the AMC 10 and AMC 12 should generally sit the AMC 10 unless they have already covered pre-calculus topics. The AMC 12 requires a broader mathematical foundation that most Grade 9 and 10 students are still building – read AMC 12 Math Competition: The Canadian Parent’s Guide to find out more!
Why Canadian students take the American Math Competition
University admissions
For Canadian students targeting competitive university programmes, strong AMC performance carries genuine weight. The University of Waterloo and the University of Toronto both recognise competition math results as part of their assessment of applicants for engineering and mathematics programmes. Waterloo’s admissions process for mathematics and computer science considers performance in the Euclid contest, and the problem-solving skills developed through AMC preparation translate directly into strong Euclid performance.
For students with ambitions beyond Canada, the AMC is even more directly relevant. MIT, Caltech, Princeton, and other highly competitive American universities regard AIME qualification as meaningful evidence of mathematical ability. A student who qualifies for the AIME from a Canadian high school is demonstrating something that very few applicants can.
Problem-solving skills that transfer across subjects
The skills the American Math Competition develops are not confined to mathematics. A student who learns to approach an unfamiliar AMC problem systematically — breaking it into components, identifying what is known and unknown, testing approaches, and persisting through difficulty — develops a way of thinking that applies to physics, computer science, economics, and engineering.
This is one reason why competition math preparation has a disproportionate return compared to time spent on additional school math practice. The school curriculum covers what students need to know. Competition math develops how students think.
The competition pathway from AMC to IMO
The American Math Competition sits at the base of a clearly defined pathway that runs from middle school all the way to the International Mathematical Olympiad. Understanding this pathway helps parents see the AMC not as a single event but as an entry point into a broader mathematical journey.
| Stage | Competition | What it leads to |
|---|---|---|
| Entry | AMC 8 | Foundation for AMC 10 preparation |
| Junior | AMC 10 | AIME qualification (top 2.5%) |
| Senior | AMC 12 | AIME qualification (top 5%) |
| Invitational | AIME | USAMO qualification |
| National | USAMO | USA IMO team selection |
| International | IMO | World championship |
For Canadian students, strong AMC performance also feeds into the Canadian competition system. The Canadian Open Mathematics Challenge leads to the Canadian Mathematical Olympiad and ultimately Canada’s IMO team. AMC preparation and Canadian competition preparation are complementary — the problem-solving foundations are the same.
What does the American Math Competition test?
The AMC series tests mathematical reasoning rather than curriculum knowledge. The topics covered vary by level but the underlying demand is consistent: students must be able to think creatively about mathematical problems and apply concepts in unfamiliar ways.
AMC 8 topics
- Number theory: divisibility, primes, factors
- Basic algebra: expressions, equations, patterns
- Geometry: area, perimeter, angles
- Counting and probability: simple arrangements and likelihood
- Logic and multi-step reasoning
AMC 10 and AMC 12 topics
| Topic area | AMC 10 | AMC 12 |
|---|---|---|
| Algebra | Linear and quadratic equations, functions, sequences | Advanced equations, logarithms, complex numbers |
| Geometry | Triangles, circles, coordinate geometry | Trigonometry, 3D geometry, conic sections |
| Number theory | Divisibility, modular arithmetic | Diophantine equations, number bases |
| Combinatorics | Permutations, combinations, probability | Expected value, recursive counting |
| Pre-calculus | Not included | Introductory limits, polynomial theory |
The AMC 10 and 12 both reward students who can combine concepts across topic areas within a single problem. A question may appear to be about geometry but require algebraic reasoning to solve efficiently. This integration is what makes the AMC genuinely challenging and genuinely rewarding to prepare for.
How to prepare for the American Math Competition
Starting with the right level
The most common mistake families make is starting at a level that is too advanced for the student’s current foundation. A Grade 7 student who has never encountered competition math should begin with AMC 8 preparation regardless of how well they perform in school. Building the problem-solving habits and mathematical intuitions at AMC 8 level makes AMC 10 preparation significantly more effective later.
A useful rule of thumb: if your child is in Grade 6 to 8 and new to competition math, start with AMC 8. If your child has done some competition math preparation and is consistently performing well on AMC 8 practice papers, begin AMC 10 preparation. If your child is in Grade 11 or 12 and has covered pre-calculus topics, the AMC 12 is appropriate.
Using past papers
Past AMC papers are freely available through the Mathematical Association of America and the Art of Problem Solving community, which hosts detailed solution discussions for every past problem. Working through past papers systematically is the foundation of any serious AMC preparation plan.
The key is to treat past papers as study tools rather than just practice tests. For every question — including those answered correctly — students should be able to identify the topic area, the key mathematical insight required, and whether a faster or more elegant solution exists. If studying for the AMC 8, trying out American Math Competition 8 practice tests under this lens will be helpful. Similarly, when studying for the AMC 10, doing a few American Math Competition 10 practice tests while keeping this in mind makes a big difference in what students remember. This kind of deliberate review is significantly more effective than simply completing papers and moving on.
Structured preparation with Think Academy
Think Academy has prepared students for the American Math Competition since launching in North America in 2021. 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.
Think Academy’s AMC preparation courses use a spiral advancement model, revisiting key concepts at increasing depth across the course rather than covering each topic once and moving on. Classes are live and interactive, homework is marked by teachers, and every session is recorded for review.
The American Math Competition and Canadian school curriculum
One question Canadian parents often ask is how the AMC relates to what their child is learning at school. The honest answer is that the AMC requires mathematical thinking that goes well beyond the school curriculum at every grade level — but it builds on the curriculum rather than replacing it.
A student who is strong in school math has the necessary foundation to begin AMC preparation. What AMC preparation adds is the ability to apply that knowledge creatively in unfamiliar situations, which is precisely what the school curriculum does not train for.
The AMC is also accessible at a stage in a student’s development where competition math makes a real difference. A student who begins AMC 8 preparation in Grade 6 or 7 arrives at high school mathematics with problem-solving instincts that their peers who only followed the school curriculum do not have. This advantage compounds through Grade 11 and 12 functions, through university calculus, and into any quantitative field beyond school.
Interested in the Canadian school system? Read more here at Canadian School System: A Parent’s Guide to Elementary, Middle and High School!
Frequently Asked Questions
What is the American Math Competition?
The American Math Competition is a series of multiple-choice exams for students from middle school through to Grade 12, run by the Mathematical Association of America. The three levels — AMC 8, AMC 10, and AMC 12 — test mathematical reasoning and problem-solving at increasing levels of difficulty. Top scorers on the AMC 10 and AMC 12 qualify for the American Invitational Mathematics Examination.
Can Canadian students enter the American Math Competition?
Yes. Canadian students are fully eligible to sit any level of the AMC series through a registered test centre. Think Academy Canada has been an official AMC test centre since 2021 and hosts AMC 8 and AMC 10 exams for Canadian students.
What age is the AMC for?
The AMC 8 is for students under 14.5 in Grade 8 or below — strong students from Grade 4 upward can participate. The AMC 10 is for students under 17.5 in Grade 10 or below. The AMC 12 is for students under 19.5 in Grade 12 or below. There is no lower age limit on any level.
How does the American Math Competition help with university admissions?
Strong AMC performance, and particularly AIME qualification, is recognised by competitive university programmes as evidence of genuine mathematical ability. In Canada, Waterloo and UofT consider competition math results for engineering and mathematics admissions. Internationally, MIT, Caltech, Princeton, and other highly selective universities regard AIME qualification as a meaningful academic credential.
What is the difference between AMC 8, AMC 10, and AMC 12?
The AMC 8 is 25 questions in 40 minutes for Grade 8 and below, covering middle school mathematics. The AMC 10 is 30 questions in 75 minutes for Grade 10 and below, covering high school mathematics to Grade 10. The AMC 12 is 30 questions in 75 minutes for Grade 12 and below, covering the full pre-calculus curriculum. The AMC 10 and 12 both qualify top scorers for the AIME.
How do I register my child for the AMC in Canada?
Registration goes through a registered AMC test centre. If your child’s school does not offer the AMC, independent centres such as Think Academy Canada can register students. Create an account on the MAA website once a test seat has been secured through a centre.
What comes after the AMC?
Top scorers on the AMC 10 and AMC 12 qualify for the American Invitational Mathematics Examination. Strong AIME performance can lead to USAMO qualification and ultimately selection for the USA IMO team. For Canadian students, AMC preparation also builds the foundation for the Canadian Open Mathematics Challenge, the Canadian Mathematical Olympiad, and the Euclid contest at Waterloo.
How hard is the American Math Competition?
The AMC is harder than school curriculum at every level. The AMC 8 is accessible for well-prepared middle school students but requires problem-solving skills that go beyond what the school curriculum develops. The AMC 10 and 12 are significantly harder — most students find them challenging the first time regardless of their school performance. The AMC rewards preparation and deliberate practice far more than raw mathematical talent alone.
