The AMC 10 is a 30-question, 75-minute multiple-choice competition covering algebra, geometry, number theory, and combinatorics — no calculus. The AIME qualification cutoff is typically between 93 and 105 points (out of 150), depending on the year. Most students who qualify practice 2 to 3 hours per week for at least 12 weeks using past exams and focused topic drills.
The AMC 10 is the main entry point into the North American math competition circuit. For Toronto students with strong math ability, it is one of the most meaningful competitions available — and one where structured preparation makes a measurable difference in scores.
What the AMC 10 Actually Tests
The AMC 10 is open to students in Grade 10 or below (under 17.5 years old). It runs twice each November — an A version and a B version — and students may sit both. The 30 questions increase in difficulty from front to back. Questions 1-10 are approachable for any strong math student; questions 20-30 require competition-specific techniques that are not taught in school.
Scoring: 6 points for correct, 1.5 points for blank, 0 for wrong. This scoring structure means that guessing randomly on a question you have no idea about costs you 1.5 points on average. Leaving it blank is always better than a random guess.
The AIME Cutoff and How It Works
The top 2.5% of AMC 10 scorers qualify for the AIME. The cutoff varies by year based on overall difficulty. Recent cutoffs have ranged from 93 to 105.5. A target score of 100+ gives a reasonable buffer in most years.
After the AIME, combined AMC and AIME scores determine who advances to the USAJMO (US Junior Mathematical Olympiad). For Canadian students, the AMC score also feeds into the Canadian competition circuit. Waterloo’s math department is known to notice strong AMC performance in applicants.
The Four Key Topic Areas
- Algebra: Equations, inequalities, sequences, and function properties. This is the highest-volume topic area, appearing in roughly a third of all questions. Strong algebraic manipulation is non-negotiable.
- Geometry: Plane geometry, similar triangles, area and perimeter, coordinate geometry. Geometry questions appear consistently in the mid-difficulty range (questions 10-20).
- Counting and Probability: Permutations, combinations, basic probability, inclusion-exclusion. These topics have predictable problem types that reward pattern recognition.
- Number Theory: Divisibility, modular arithmetic, prime factorization. Number theory problems often appear in the harder range and reward students who have seen the standard techniques.
A 12-Week Preparation Schedule
Start in late August for a November exam. This gives you enough time to cover all topic areas and take multiple full practice exams.
Weeks 1-3: Algebra and geometry fundamentals. Work through the first 15 questions of 2018-2021 exams. Grade every problem and read the official solution for any question you found difficult, even if you got it right.
Weeks 4-6: Counting, probability, and number theory. These topics have the best return on focused study time because the problem structures repeat year to year.
Weeks 7-9: Full timed practice exams (75 minutes, all 30 questions). After each exam, review every question you skipped or got wrong. Do not just read the answer — reconstruct the full solution yourself.
Weeks 10-12: At least two full exams per week. Separate practice on questions 20-30 from recent years. Build speed on the mid-difficulty range so you have time for the hard questions at the end.
Why Students Miss the Cutoff
Poor time management. Students who spend 8 minutes on a hard problem early in the exam run out of time for easier problems they could have answered correctly. The optimal strategy is to skip anything that takes more than 3-4 minutes and return at the end.
Arithmetic errors without a calculator. AMC 10 does not allow calculators. Many students who know the approach still lose points to computation errors. Build the habit of checking arithmetic during practice, not just the method.
Starting too late. Students who begin preparation in October — one month before the exam — rarely see meaningful score improvement. Ten to twelve weeks of consistent practice is the minimum for noticeable gains.
Only doing problems, not studying solutions. Reading the official AMC solution for problems you got wrong teaches you the specific techniques the competition tests repeatedly. Students who only check whether their answer matches and move on miss the learning opportunity.
Exploring Scholar runs AMC 10 preparation groups in Toronto each fall. Students work through past exams, learn competition-specific techniques, and get individual feedback on their errors. See our programs page for details.
Frequently Asked Questions
What is a good first-time AMC 10 score for a Grade 9 student?
For a Grade 9 student with no prior competition preparation, scoring between 60 and 90 on a first attempt is typical and normal. The important thing is to treat the first exam as a learning experience, review all the questions afterward, and prepare systematically for the next sitting.
Should my child take AMC 10A, AMC 10B, or both?
Taking both is generally recommended if your child is aiming for the AIME cutoff. The two versions have different question sets, and performance can vary. Both scores are valid for AIME qualification purposes, so sitting both maximizes the chance of hitting the cutoff in at least one.
What resources are best for AMC 10 preparation?
Past AMC 10 exams from the Art of Problem Solving (AoPS) website are the primary resource. The AoPS forums contain detailed solution explanations from multiple approaches. For a structured curriculum, the AoPS Introduction to Algebra and Introduction to Counting and Probability books cover the core material well.
Does the AMC 10 help with Canadian university applications?
For most Canadian programs, the direct impact is limited. However, qualifying for the AIME or scoring above the 90th percentile on the AMC 10 is worth noting in supplementary applications for math and computer science programs, particularly at Waterloo. For US university applications, strong AMC performance carries more explicit weight.
What is the difference between AMC 8, AMC 10, and AMC 12?
AMC 8 is for students in Grade 8 or below and tests middle-school math. AMC 10 is for Grade 10 and below, covering up to precalculus. AMC 12 is for Grade 12 and below and includes trigonometry, logarithms, and complex numbers. Students often start with AMC 8 in middle school and progress to AMC 10 and 12 in high school.
Preparing for the AMC 10?
Our instructors have helped Toronto students reach the AIME cutoff through structured preparation and targeted problem review. Spots fill quickly before the November exam.