Math Competitions Explained
AMC 8, MATHCOUNTS, AMC 10/12, and AIME are not four separate hobbies — they are one ladder a student climbs over roughly six years. Here is what each contest asks, who can enter, and what changed for the 2026–27 season.
Who Competes in What
Eligibility is set by grade and by age, not by ability. A strong 6th grader can sit the AMC 10 alongside 10th graders — and many of our students do.
Eligibility by grade
Bars show the grades each contest is open to.
The 2026–27 Season
Everything downstream depends on November. A student who misses the AMC 10/12 has no path to AIME in February, because AIME is invitation-only off those two dates.
| Date | What happens |
|---|---|
| Thu, Nov 5, 20266:00 – 7:15 PM | AMC 10A and AMC 12A at Thinking Feet |
| Fri, Nov 13, 20266:00 – 7:15 PM | AMC 10B and AMC 12B at Thinking Feet A student may sit an A and a B exam, but never two contests on the same day. |
| Nov – Jan | MATHCOUNTS School Competitions, scheduled by each coach |
| Sun, Jan 24, 20273:00 – 4:00 PM | AMC 8 at Thinking Feet Each student sits the AMC 8 once per year. |
| Feb 1–28, 2027 | MATHCOUNTS Chapter Competitions, roughly 500 nationwide |
| Feb 5–6, 2027 | AIME, at Pearson testing centers No alternate dates and no make-up administrations. |
| Mar 1–31, 2027 | MATHCOUNTS State Competitions |
Contest dates follow the official MAA and MATHCOUNTS calendars for the 2026–27 cycle. Times shown are for sittings at Thinking Feet.
The Four Contests
AMC 8
Mathematical Association of America. For most students, the first real competition.
The AMC 8 stays inside middle school content but asks questions no textbook chapter prepares a student to answer directly: counting and probability, estimation, proportional reasoning, elementary geometry including the Pythagorean theorem, spatial visualization, and reading graphs and tables. The last several questions reach into beginning algebra, linear and quadratic functions, and coordinate geometry.
- Format
- 25 multiple-choice questions, 40 minutes
- Eligibility
- Grade 8 and below, under 15.5 years old on competition day
- Scoring
- 1 point per correct answer, maximum 25. No penalty for a wrong answer
- When
- National window January 21–27, 2027 — once per student. Thinking Feet sits it Sunday, January 24, 3:00–4:00 PM
- Calculator
- Not permitted
- Recognition
- Honor Roll for roughly the top 5%, Distinguished Honor Roll for roughly the top 1%, plus certificates for high scorers in grade 6 and below
Answer all 25 questions
There is no penalty for a wrong answer, so a blank is strictly worse than a guess. This sounds obvious and it is still the most common source of lost points for first-time competitors, who run out of time and leave the last five blank rather than spending the final ninety seconds guessing.
Sample problem sets
MATHCOUNTS
MATHCOUNTS Foundation. The only team contest of the four, and the only one with a live head-to-head round.
MATHCOUNTS runs as a four-level tournament — school, chapter, state, and national. Each level uses the same four rounds and takes about three hours in total. Schools may send up to 14 competitors: 4 who take both the team and individual rounds, plus 10 competing as individuals. Students whose school will not participate can register as non-school competitors.
The four rounds
- Sprint
- 30 problems in 40 minutes, no calculator. Speed and accuracy
- Target
- 4 pairs of problems, 6 minutes per pair, calculator assumed. Multi-step reasoning
- Team
- 10 problems in 20 minutes, calculator assumed. Only the 4-person team takes this officially
- Countdown
- Head-to-head, maximum 45 seconds per problem, no calculator. Optional at school, chapter, and state level
Advancement
- Eligibility
- Grades 6–8
- Chapter to state
- Top students advance at no additional fee
- State to national
- The top 4 individuals per state earn an all-expenses-paid trip to nationals
- Nationals
- 224 competitors form 4-person state teams and also compete individually for the national title
Sprint is where students separate
The Sprint round rewards something specific: a large stock of instantly available facts. A student who has to derive the area of a regular hexagon will not finish. A student who simply knows it will. That recall is trainable, and it is most of what our MATHCOUNTS preparation builds.
Sample problem sets
AMC 10 and AMC 12
Mathematical Association of America. The round that qualifies students for AIME.
These two contests share a date, a format, and a scoring system, and differ in syllabus. The AMC 10 covers elementary algebra, basic geometry, area and volume, elementary number theory, and elementary probability, and deliberately excludes trigonometry, advanced algebra, and advanced geometry. The AMC 12 covers the full high school curriculum including all of those, and excludes only calculus.
Both are offered as an A and a B version on separate dates. A student may take both, but may not take the AMC 10 and AMC 12 on the same day.
- Format
- 25 multiple-choice questions, 75 minutes
- AMC 10 eligibility
- Grade 10 and below, under 17.5 years old
- AMC 12 eligibility
- Grade 12 and below, under 19.5 years old
- Scoring
- 6 points correct, 1.5 points blank, 0 incorrect. Maximum 150
- Dates
- A: Thursday, November 5, 2026 · B: Friday, November 13, 2026. Both sittings at Thinking Feet run 6:00–7:15 PM
- Calculator
- Not permitted, and has not been since 2008
- Recognition
- Distinction for roughly the top 5%, Honor Roll of Distinction for roughly the top 1%, certificates for students performing well above grade level, and AIME qualification
The 1.5 points for a blank are a strategic instrument
A blank is worth 1.5 points. A pure guess among five choices is worth 6 × (1/5) = 1.2 points on average, so guessing blind is worse than leaving it blank. Eliminating even one choice flips the math: a guess among four is worth 1.5, and among three is worth 2.
Students who understand this convert a handful of points every year. Students who do not tend to either guess everything or leave everything, and both are wrong.
Sample problem sets
AIME
American Invitational Mathematics Examination. By invitation only, off the AMC 10/12.
AIME is the step where multiple choice disappears. Every answer is an integer from 000 to 999, which removes guessing entirely while keeping the exam machine-gradable. The problems are substantially harder than anything on the AMC 10 or 12, and they draw throughout on the same four areas: algebra, combinatorics, geometry, and number theory.
AIME has changed substantially for 2027
If you are working from guidance written before this cycle, parts of it are now wrong. The exam has moved to Pearson testing centers as a computer-based test, and the separate AIME I and AIME II are gone, replaced by a single competition window.
Qualification is now a fixed score rather than a percentile: 100 or above on the AMC 10, or 85 or above on the AMC 12. That is a real improvement for planning, because a student finally has a number to aim at during preparation instead of waiting for a cutoff announced after the fact.
Qualification for USAMO and USAJMO now rests primarily on AIME scores — AMC scores are no longer a factor.
- Format
- 15 questions in two 90-minute parts — 8 questions, then 7 — with a short break between
- Answers
- Every answer is an integer from 000 to 999
- Qualifying
- AMC 10 score of 100+, or AMC 12 score of 85+
- Age
- Students must be 13 or older. Younger qualifiers are not eligible in 2027
- When
- February 5–6, 2027 — once per student, no make-up dates
- Where
- Pearson Professional Centers, 200+ across the US and Canada
- Fee
- $85 plus tax, paid to Pearson. Financial assistance is available
- Materials
- Nothing may be brought in — no rulers or compasses. Laminated graph paper and fine-tip pens are provided
Two of the new rules deserve attention in preparation. Students cannot return to the first part once the second begins, so budgeting time across all 15 questions no longer works — the first 8 must be finished inside the first 90 minutes. And with no compass or ruler permitted, geometry has to be handled through coordinates, trigonometry, and synthetic reasoning rather than by drawing an accurate figure.
Sample problem sets
All Four Contests at a Glance
| AMC 8 | MATHCOUNTS | AMC 10 / 12 | AIME | |
|---|---|---|---|---|
| Grades | 8 and below | 6–8 | 10 and below / 12 and below | Qualifiers, age 13+ |
| Format | 25 questions, 40 min | 4 rounds, about 3 hrs | 25 questions, 75 min | 15 questions, 2 × 90 min |
| Answers | Multiple choice | Short answer | Multiple choice | Integer 000–999 |
| Calculator | No | Target & Team only | No | No |
| Scoring | 1 pt correct, max 25 | Varies by round | 6 correct / 1.5 blank / 0 wrong, max 150 | 1 pt correct, max 15 |
| 2026–27 date | Sun, Jan 24, 2027 | Nov 2026 – May 2027 | Thu, Nov 5 & Fri, Nov 13, 2026 | Feb 5–6, 2027 |
| Enrollment | Through Thinking Feet | School team or individual as non-school competitor | Through Thinking Feet | Invitation from AMC 10/12 score |
| Our levels | Comp Math L2–L3 | Comp Math L2–L3 | Comp Math L4–L5 | Comp Math L5 |
Level recommendations are a starting point. Placement is confirmed during a free assessment, based on skills rather than grade.
Sample Problem Sets
Download a set to see the kind of thinking each contest asks for. Problems and full worked solutions are provided separately, so students can attempt a set cold before checking their work.
AMC 8
Middle school topics approached the competition way — counting, proportional reasoning, and geometry without a formula to fall back on.
MATHCOUNTS
Sprint-style problems for speed and accuracy, plus Target-style problems that reward multi-step reasoning over raw pace.
AMC 10 / 12
Problems spanning both syllabi, including the trigonometry, logarithms, and complex numbers that separate the AMC 12 from the AMC 10.
AIME
Integer-answer problems with no choices to work backwards from, at the difficulty students meet after qualifying.
Not sure where your child fits?
Placement is based on skills, not grade. A free assessment puts your student in the right level and the right contests for this season — and November comes around quickly.
© Copyright Thinking Feet. All Rights Reserved.