Every year, students at top private schools and advanced math programs across North America sit down for one of the most respected high school math competitions: the AMC 10 and AMC 12. For many families, the conversation starts with a question from their child’s teacher or a mention in the school’s math department newsletter. “Should my child be doing AMC?” and “How do we even prepare for it?” are questions we hear regularly from parents whose students attend schools like Upper Canada College, Havergal College, and Phillips Exeter Academy. This guide explains exactly what the AMC tests, who it is designed for, and how to build a preparation plan that gets real results.
What Are the AMC 10 and AMC 12, and Who Should Take Them?
The AMC 10 and AMC 12 are 25-question, 75-minute multiple choice math competitions administered by the Mathematical Association of America. The AMC 10 is intended for students in Grade 10 or below, while the AMC 12 is open to all high school students. Both serve as the first stage of the path to the USA Mathematical Olympiad (USAMO) and, for the strongest performers, the International Mathematical Olympiad (IMO).
The AMC is the right fit for students who enjoy math beyond the standard curriculum, especially those already taking accelerated or advanced courses. Students in IB programs, AP schools, or gifted math streams often find the AMC’s problem style both challenging and rewarding. A student does not need to be aiming for the Olympiad to benefit from AMC preparation; the problem-solving skills developed through AMC study make students significantly stronger in IB Math AA HL, AP Calculus BC, and first-year university mathematics.
When Should Your Child Start Preparing for the AMC?
Ideally, students should begin structured AMC preparation at least six months before the competition. The most competitive students often start in Grade 7 or 8. The AMC is held in November each year, so a student in Grade 9 or 10 should begin working through foundational topics in the spring or early summer before the exam year.
Here is a general preparation timeline that works well for most students:
- 6 to 12 months out: Build foundational skills in algebra, geometry, number theory, and combinatorics. Use AMC 8 and early AMC 10 problems from 2000 to 2010 for practice.
- 3 to 6 months out: Work through recent AMC 10 or AMC 12 past papers. Target problems 1 through 15 consistently before advancing to the harder problems near the end.
- 6 to 8 weeks out: Timed practice tests under exam conditions. Review every missed problem carefully, not just the answer but the underlying concept and where your reasoning went wrong.
- Final 2 weeks: Light review with a focus on speed and accuracy on problems you can solve reliably. Avoid trying to learn new topics this close to the exam.
According to experienced competition math educators, the most common mistake students make is skipping foundational review and jumping straight into hard problems. Building a solid base first leads to far better results on test day.
What Topics Does the AMC 10 and AMC 12 Cover?
The AMC 10 covers topics up to and including Grade 10 mathematics, which means no trigonometry, advanced combinatorics, or calculus. The AMC 12 has no such restriction and can include material from all of high school math, including pre-calculus and trigonometry. Both exams reward creative problem-solving and mathematical reasoning over rote computation.
The core topic areas for each exam are:
| Topic Area | AMC 10 | AMC 12 |
|---|---|---|
| Algebra and Functions | High emphasis | High emphasis |
| Euclidean Geometry | High emphasis | High emphasis |
| Number Theory | Moderate | Moderate |
| Combinatorics and Probability | Moderate | High emphasis |
| Trigonometry | Not included | Moderate |
| Logarithms and Complex Numbers | Not included | Moderate |
Students who do well on the AMC typically have strong intuition in geometry and are comfortable with counting arguments. These are areas where focused preparation can yield significant score gains in a relatively short time.
How Is the AMC Scored, and What Score Should You Aim For?
Both the AMC 10 and AMC 12 are scored out of 150 points. Each correct answer earns 6 points, while wrong answers and blank answers both receive 0 points. There is no penalty for guessing, so students should attempt every problem rather than leaving any blank.
The key benchmark for many students is the AIME qualification cutoff. This changes year to year but historically falls around 100 out of 150 on the AMC 10 (roughly 17 correct answers) and 90 out of 150 on the AMC 12 (roughly 15 correct answers). Qualifying for the AIME is a meaningful academic achievement that universities in the US and Canada recognize in competitive admissions.
Based on our work with students at top private schools and advanced programs, students aiming for AIME qualification typically need 12 to 18 months of consistent preparation. Students whose goal is to score above the 75th percentile can achieve that with 3 to 6 months of focused effort. Setting a realistic target score early makes preparation far more efficient.
What Study Resources and Methods Work Best for AMC Preparation?
The most effective AMC preparation combines structured topic study with extensive problem-solving practice. Here are the resources that competition math educators consistently recommend:
- Art of Problem Solving (AoPS) books: The Introduction to Algebra, Introduction to Geometry, Introduction to Number Theory, and Introduction to Counting and Probability volumes are the gold standard for AMC preparation. Students aiming for AIME qualification should move on to the Intermediate series after mastering the introductory material.
- AMC past papers: The AMC has over 20 years of freely available past papers. Working through timed past papers is the most direct and effective preparation method.
- AoPS online community: The Art of Problem Solving forums provide exceptional problem discussions and peer support that go well beyond what any textbook offers.
- One-on-one math competition tutoring: For students who need faster progress or have specific topic gaps, working with an experienced competition math tutor is the fastest path to meaningful improvement. A skilled tutor can identify weaknesses in a few sessions that might take months to uncover through self-study alone.
Students at schools with strong math teams, such as those at Crescent School, Upper Canada College, or Phillips Exeter Academy, often find that working through problems collaboratively with peers adds an important dimension to individual preparation.
Frequently Asked Questions About AMC 10 and AMC 12 Preparation
What is the difference between the AMC 10 and AMC 12?
The AMC 10 is open to students in Grade 10 and below and covers math through Grade 10, excluding trigonometry and advanced topics. The AMC 12 is open to all high school students and includes the full range of pre-university math. A student in Grade 10 or below can choose to take either exam; many strong math students take the AMC 12 for the additional challenge and the slightly lower AIME qualification cutoff.
How many questions are on the AMC, and is there a penalty for guessing?
Both the AMC 10 and AMC 12 have 25 questions and a 75-minute time limit. There is no penalty for wrong answers; blank answers and incorrect answers both receive 0 points. Students should attempt every problem since an educated guess gives a chance at 6 points and risks nothing.
What score do you need to qualify for the AIME?
The AIME qualification cutoff changes each year and is announced after the exam. Historically, students need approximately 100 out of 150 on the AMC 10 (around 17 correct answers) or 90 out of 150 on the AMC 12 (around 15 correct answers) to qualify. The AMC 12 cutoff is often lower in absolute points, which is part of why some high-achieving Grade 10 students choose to write it instead.
What grade should a student be in when they first take the AMC?
Most students take the AMC 10 for the first time in Grade 9 or 10. Highly motivated students with strong math foundations often write it as early as Grade 7 or 8 for the experience. Starting early gives students multiple attempts and more time to develop their skills over successive years.
Can a private tutor help with AMC preparation?
Yes, a qualified competition math tutor can make a significant difference. The right tutor will identify the specific topic gaps holding a student back, teach problem-solving strategies and shortcuts not covered in standard school curricula, and run timed practice sessions that build both skill and exam confidence. Students working with a dedicated AMC tutor typically progress faster than those preparing entirely on their own, particularly as problems grow more complex in the higher-numbered questions.
If your child is working toward AMC success or wants to develop serious competition math skills, Polaris Tutors has experienced competition math educators who have prepared students from advanced programs and top private schools across Canada and the United States. Contact us today to discuss how we can help your child build the problem-solving skills to compete at the highest level.