If your student took the AMC 10 or AMC 12 this fall, the next question is simple: did they qualify for the AIME? The rules are short, but a few details trip families up every year, such as who registers, who pays, and what happens if the student is under 13. Here is how qualification works for the 2027 AIME, what the scores mean in actual problems, and what to do if the answer was no.
What the AIME is
The AIME, the American Invitational Mathematics Examination, is the second stage of the American Mathematics Competitions sequence. It has 15 questions in two parts, 8 questions and then 7, and takes three hours in all. Every answer is a whole number from 0 to 999, so there are no answer choices to eliminate. Scores are small numbers, and solving even a few problems is a real result.
The 2027 AIME is on February 5 or 6, 2027, taken on a computer at a Pearson test center. There are no make-up dates. The registration deadline is February 1, 2027, and the fee is $85 plus tax, paid to Pearson after the MAA sends an invitation. Invitations go out by email in mid-December 2026, once AMC scores are final. Notice who registers: for the AMC, a school or site registers the student, but for the AIME the student's family handles registration and payment directly after the invitation arrives.
The qualifying scores
The MAA invites students who score 100 or higher on the AMC 10, or 85 or higher on the AMC 12. Two more rules apply. The student must be in grade 12 or below on AIME day and 19.5 or younger on the day of the qualifying AMC, and must be at least 13 on AIME day. That last rule matters for gifted younger students: a 7th grader who scores 120 on the AMC 10 has earned the invitation but cannot sit the AIME until age 13. Art of Problem Solving, through its USAMTS program, can also nominate a small number of additional students, so a family whose child narrowly missed the line should not assume that is the only route.
A fixed score is easier to plan around than a rank. You know the target before the contest, and you can work out in advance what it takes.
What 100 and 85 mean in problems
Each correct answer is 6 points, a blank is 1.5, and a wrong answer is 0. Because blanks earn points, the arithmetic is more forgiving than it first appears. Here are the combinations that matter.
On the AMC 10, 14 correct answers with the other 11 left blank is 84 plus 16.5, which is 100.5. That is enough. It also shows why 13 correct is not enough on its own: 13 correct with 12 blanks is 96. If the student attempts every problem, the line moves up, because 16 correct and 9 wrong is only 96 and it takes 17 correct to reach 102. A student who is careful about which problems to leave alone needs fewer correct answers than one who fills in every bubble.
On the AMC 12, 11 correct with 14 blank is 87. Ten correct with 15 blank is 82.5, just short. Take the student who answers 14 and guesses on the remaining 11: that is 84 if every guess misses, one point under the line. Leave even one of those blank and the score is 85.5.
Compare the two paths. The AMC 10 asks for about 14 clean solutions from an easier test. The AMC 12 asks for about 11 or 12 from a harder test. For a student who has finished precalculus, the AMC 12 line is often more reachable. For a student who has not seen trigonometry or logarithms, it usually is not.
A worked example: when guessing costs the invitation
Here is a pattern we see. A 10th grader finishes the AMC 10 with 14 solid answers and spends the last ten minutes on the 11 remaining problems. Five of them look vaguely familiar, so the student fills in a guess on each, and leaves six blank. Each guess has about a one in five chance of being right, so the student expects one of the five to land.
The expected points from one guess are 6 times one fifth, which is 1.2, below the 1.5 for a blank. Across five guesses, that is 6 expected points against 7.5 for leaving them blank. If the student is unlucky and all five are wrong, the score is 84 plus 9, which is 93. Left blank, the score is 100.5. The student did not lose the invitation to a hard problem. The student lost it to a bad risk. The rule of thumb that follows is to guess only when at least two of the five choices can be eliminated, which moves the odds to one in three and the expected value to 2 points.
A worked example: the kind of problem the AIME rewards
Because the AIME has no choices, a student has to get the exact number. Here is an original example of the style, not a real contest problem. How many three-digit numbers have digits that add up to 9?
Write the digits as a, b and c with a at least 1. Let a' be a minus 1, so a', b and c are non-negative and add up to 8. Counting the ways to split 8 among three digits is a stars and bars count: choose 2 divider positions among 10 spots, which is 45. No digit exceeds 9 in any of these splits, so nothing needs to be removed, and the answer is 45.
The lesson is the habit. A student who tries to list cases by hand will probably miss some. A student who recognizes the structure gets a clean answer. This is the kind of content gap that often separates a good score from a qualifying one: counting methods that school courses cover thinly.
What qualification does and does not do
It is a real achievement. Only a small fraction of students who take the AMC 10 or AMC 12 reach the AIME, and admissions readers at selective schools know the contest sequence. A line that says AIME qualifier tells a reader the student solved a large share of a hard test, which is more specific than participated in math competitions.
It does not decide an application. A strong score does not offset weak grades or a thin record outside the contest. And a student who did not qualify is not behind. For a student who does qualify, the next stage is the USAMO or USAJMO, by invitation based on AIME results, on March 20 and 21, 2027. Only a small group gets there, and we do not recommend planning around it.
If your student did not qualify
Start with the paper. Mark each problem as solved, close, or never started. A student who scored 78 with five problems that were close has a different path from one who scored 78 with five never started.
Next, decide whether the gap is care, content or time. If the mistakes are on problems 1 through 10, the gap is care, and that is the fastest to fix: slow down, check units, and reread the question. If the student solved the first fifteen cleanly and then stalled, the gap is content, and counting and number theory are the usual culprits. If the student ran out of time with problems half done, the gap is pacing, and timed practice fixes it.
Then plan to the next November, not to this contest. A reasonable calendar looks like this. From January to May, build content one topic at a time, two topics a month. Spend a week on each: read, do twenty problems, and redo the ones you missed three days later. In June to August, take one full timed test every three weeks and review it the same day. In the six weeks before the contest, take a full test every week, under real conditions: 75 minutes, no calculator, no notes. Keep a log of every missed problem and what kind of miss it was. After a month the log shows the pattern, and the pattern tells you what to study.
Common mistakes
Families make the same errors each year. They practice untimed for months and add the clock at the end, which builds a habit that falls apart at the real contest. They take a test and never review it, so the same gap shows up again. They chase the hardest problems when the first fifteen are where most of the score lives. And they guess on everything because a blank feels like giving up. A blank is worth 1.5 points, and it is often the correct choice.
For the AMC 12, add trigonometry, logarithms and complex numbers, but do not start there. A student who is weak on counting will be weak on the AMC 12 as well.
We are building a free AMC 10/12 diagnostic that shows a student's score against the AIME line. If you want to be told when it opens, join the list on our AMC 10 and 12 page. If you are still deciding between the two tests, read AMC 10 vs AMC 12.