Competitions · Mathematics · AMC 10
AMC 10, the American Mathematics Competitions 10.
Twenty-five multiple-choice questions in seventy-five minutes, open to students in grade 10 and below anywhere in the world. It is the paper that decides who is invited to AIME, and through AIME to USA(J)MO and the olympiad route - which is why a score here is read as a position on a ladder rather than as a mark out of 150.
At a glance
What the paper is, and who may sit it.
Details below follow the published rules for the 2026 cycle. Hanlin is an MAA-authorised test centre and can register independent candidates as well as school groups.
- Organiser
- The Mathematical Association of America (MAA)
- Who can enter
- Students in grade 10 or below, who must not be older than 17.5 on the day of the contest. Nationality is not a restriction
- When
- Each November, in two sittings called the A paper and the B paper
- Format
- 25 multiple-choice questions, five options each. Sat online or on paper at a centre
- Duration
- 75 minutes, or three minutes a question
- Marking
- 6 marks for a correct answer, 1.5 for one left blank, 0 for a wrong one. 150 marks in total
- Calculators
- Not permitted
- Language
- Candidates sitting in China receive a bilingual Chinese and English paper
- A and B papers
- Two different papers of the same difficulty and scope. You may sit either or both. They are ranked and scored separately, and your better result is the one used for AIME qualification
- What it leads to
- A qualifying score earns an invitation to AIME, and from there the route runs to USAJMO and the national olympiad programme
Strategy
What the marking scheme is actually telling you.
The 1.5 marks for a blank answer is the single most consequential rule on the paper, and it is the one most often played badly.
A blank is worth a quarter of a right answer
Leaving a question blank scores 1.5 where a correct answer scores 6. A blind guess among five options averages 1.2, so answering at random is slightly worse than leaving the question alone. Ruling out one option makes the two exactly equal.
Eliminate, then commit
Once two options are ruled out, a guess among the remaining three averages 2 marks against the 1.5 you would keep by leaving it. The judgement to make under pressure is not whether you know the answer but how much you have ruled out.
Three minutes a question, unevenly spent
The paper is ordered roughly by difficulty. Banking the early questions quickly is what buys the time to think properly about the last ten, and most lost marks come from rushing the opening rather than from the closing questions.
The AIME line, not the total
For most candidates the mark that matters is the AIME cutoff rather than the maximum. That line has sat between roughly 93 and 105 in recent years, so the realistic target is a clean run through the first eighteen questions.
2026 cycle
Registration and contest dates.
China and the United States run on separate registration timetables, and the contest falls on a different calendar day in each because of the time difference.
| Stage | China | United States |
|---|---|---|
| Registration, A paper | 27 October 2026 | Early bird 30 September; regular 15 October; late 28 October 2026 |
| Registration, B paper | 3 November 2026 | Early bird 30 September; regular 15 October; late 28 October 2026 |
| Contest, A paper | Friday 6 November 2026, 17:00-18:15 | 5 November 2026 |
| Contest, B paper | Saturday 14 November 2026, 17:00-18:15 | 13 November 2026 |
| Scores released | 4 to 6 weeks after the contest | - |
| Cutoffs and certificates | 6 to 8 weeks after the contest | - |
Admission tickets for the China sittings are published closer to the date. Confirm every date against the organiser before relying on it.
Awards
Six individual awards and two school awards.
The MAA added the Top 10% and Top 25% Honor Rolls to widen recognition below the two long-standing global awards.
Score cutoffs
Where the lines have fallen since 2020.
Awards and AIME invitations are decided on the global distribution, so the mark required moves with the difficulty of each paper. Reading several years at once is more useful than reading any single one.
| Paper | AIME cutoff | Distinction (top 5%) | Honor Roll of Distinction (top 1%) |
|---|---|---|---|
| 2025 AMC 10A | 105 | 112.5 | 136.5 |
| 2025 AMC 10B | 99 | 105 | 133.5 |
| 2024 AMC 10A | 94.5 | 105 | 132 |
| 2024 AMC 10B | 105 | 114 (revised from 112.5) | 138 (revised from 135) |
| 2023 AMC 10A | 103.5 | 111 | 136.5 |
| 2023 AMC 10B | 105 | 112.5 | 135 |
| 2022 AMC 10A | 93 | 100.5 | 121.5 |
| 2022 AMC 10B | 94.5 | 100.5 | 114 |
| 2021 AMC 10A, autumn | 96 | 96 | 117 |
| 2021 AMC 10B, autumn | 96 | 96 | 120 |
| 2021 AMC 10A, spring | 103.5 | 112.5 | 132 |
| 2021 AMC 10B, spring | 102 | 108 | 126 |
| 2020 AMC 10A | 103.5 | 105 | 124.5 |
| 2020 AMC 10B | 102 | 103.5 | 120 |
Six cutoffs were revised after publication in 2024. The MAA stated that the revision changed awards and qualification only for AMC 12A candidates; other candidates were unaffected.
Why it matters
What an AMC 10 score is read as.
It is the entry point to the American olympiad ladder, and the first internationally comparable mathematics result most students hold.
The gateway to AIME
AMC 10 exists to select for AIME, and AIME in turn selects for USAJMO and the national olympiad programme. Nothing else on a school transcript places a student on that ladder, which is why the cutoff matters more than the raw mark.
A result that travels
The same two papers are sat worldwide on the same days and ranked against one global distribution. A percentile earned in Shanghai means what it means in Chicago, which is not true of a school grade.
Read directly by admissions
Several selective US universities provide a dedicated field for AMC results in their application systems, so a strong score is read as submitted rather than having to be argued for in an essay.
Two chances in one season
Because the A and B papers are separate and only your better result counts toward AIME, sitting both converts a single bad morning from a lost year into a discarded score.
Preparation
How Hanlin prepares students for AMC 10.
Hanlin is an MAA-authorised centre and has arranged AMC sittings for more than 7,000 students across successive seasons.
Real papers, in order
Preparation runs on past papers rather than imitation questions. Working several seasons in sequence shows how the difficulty is banded across the twenty-five and where each year quietly moved the hard questions.
Reaching above the level
Candidates aiming at the top awards work AMC 12 problems as part of preparation. Practising against a harder paper is what makes the AMC 10 questions feel like the routine ones on the day.
Timed papers, invigilated
Full papers are run under contest conditions, including the online setup. Candidates consistently score higher testing at home than in the contest, and the gap is pacing and pressure rather than mathematics.
Where the marks actually go
A diagnostic sorts the four topics into secure and leaking, so revision time is spent where the score changes. Most students lose more to the middle of the paper than to the final five questions.
Why Hanlin
Hanlin has been entering students for AMC 10 for years, and publishes what they got. The record is further down this page.
Programme formats
Five ways this is taught.
Group size is the whole difference between these. It decides how much of the tutor's attention a student gets and how far the course can bend to them, so it is worth choosing rather than accepting.
| Format | Group size | What it suits |
|---|---|---|
| One-to-one | One student | Content, pace and emphasis set by what this student actually needs rather than by a syllabus. The only format that can be rebuilt mid-course. |
| Small group | Three to eight | Opens at three. Frequent discussion, and the tutor can slow down or move on according to what the group has absorbed. Most students chasing a higher award are taught in this one. |
| Class | Eight to twelve | Taught by the subject lead or a medal coach. Less back-and-forth, so it suits a student who will say when something is unclear. |
| Large class | Ten to twenty | For students in the middle of the placement range, and a way to try a competition before committing. Students often move to a small group or to one-to-one afterwards. |
| Past-paper class | No cap | Past papers worked through in sequence in the weeks before the sitting. Free to students already enrolled. |
Course tiers
Which course, and on what evidence.
Every tier for AMC 10 is entered from a placement paper rather than from a year group. These are the actual standards.
| Course | Hours | Who it is for |
|---|---|---|
| Foundation | 80 hours | School mathematics to roughly grade 8-10 and four to nine correct on the placement paper. For a student new to competition mathematics |
| Full course | 60 hours | Eight to fourteen correct on the placement paper. Builds the AMC 10 syllabus from the ground up with AIME qualification as the target |
| Intensive | 40 hours | A mock score above 90, or fifteen or more correct. Adds harder problems and the groundwork for the AIME |
| Sprint | 30 hours | Around twelve correct on a real paper. A short structured run at the top 5% in the weeks before the sitting |
| Past-paper class | 20 hours | Ten years of papers worked through. Free to students already enrolled |
Ask for the placement paper before choosing a tier. It takes an hour and it settles the question.
How it runs
Six steps, four people on your side.
The same process for every student, so that nothing depends on one tutor remembering to do it.
Step 1Pre-course assessment
A placement paper before anything is booked, so the course tier is chosen on evidence rather than on a year group.
Step 2Tutor matching
A subject tutor is matched to the result, and their full background is provided before you agree to it.
Step 3Plan and group
A study group opens with four people on one student: the tutor, a planner, a supervisor and an academic manager.
Step 4Scheduled teaching
The teaching office sets the timetable around the competition date and school term, and teaching begins.
Step 5After-class reports
What was covered, and how the student handled it, reported after every lesson.
Step 6Homework follow-up
The teaching assistant and the form teacher both check that homework is done, which is where most preparation quietly fails.
Free resource pack
AMC 10 past papers and preparation pack
The same material our own AMC 10 students work from. Scan the code, say what you need, and an advisor sends it.
Tell an advisor which competition and year group, and the material comes back the same day. Free, and you do not have to enrol in anything. If we do not already hold what you need, we will go and find it.
- PDFTen years of AMC 10 A and B papers, with answer keys
- PDFAIME qualification cutoffs, year by year
- PDFThe syllabus on one page, with the placement paper we set
- PDFRegistration checklist and the dates for the current cycle
Teaching team
Who would teach it.
Three of the twenty-two tutors on the published Hanlin roster - the ones whose subject this is.
Dr Zhang
PhD in theoretical mathematics from the University of Rochester and a postdoctoral fellow at the Shanghai Center for Mathematical Sciences at Fudan. An AMC-accredited coach, ASDAN-accredited for DMM and ITCCC, and an accredited UKMT BMO2 and PUMaC coach. His students have gone on to read mathematics and physics at Harvard, MIT, Princeton, Caltech and Cambridge.
Dr Zhuang
PhD in mathematics from the University of Denver, working in mathematical logic, after a first degree in applied mathematics at Southeast University. A repeat conference speaker on his research, with three years lecturing and assisting on undergraduate mathematics at Denver.
He
A Cambridge master's after a computer science degree with a mathematics minor at the University of Nebraska-Lincoln, and a US high school GPA of 4.13. Six years overseas and teaches entirely in English, across AMC, Math League, AP Computer Science and AP Calculus.
Student results
What Hanlin students got.
Taken from Hanlin's published record of student honours and rewritten in English. Figures are as the organisers reported them.
AIME qualifications, 2024-25
One line from Hanlin's published AMC 10 record. The rest of it is below.
AMC 10
- 2024-25235 AIME qualifications. 123 students in the top 5%, 30 in the top 1%, 3 perfect scores, 19 above 140 and 191 above 120
- 2023-24253 students qualified for the AIME, a 65% qualification rate. 170 in the top 5%, 45 in the top 1%, 12 above 140, 129 above 120
- 2022-23137 qualified, a 56% rate. 89 in the top 5%, 37 in the top 1%, 25 above 130
Earlier years
- 2021102 qualified, a 53.1% rate. 42 in the top 5%, 16 in the top 1%
- February 2021Highest AMC 10 score 135, with 58 students qualifying - a 44% rate
Hanlin reports AMC 10 and AMC 12 together, as one cohort sitting both papers.
The full record, across every subject and year, is on the student honours page.
Where it is taught
Hanlin learning centres.
Teaching runs from Hanlin's own centres in Shanghai, Shenzhen, Chengdu and Hangzhou, and online for students elsewhere.
Talk to an advisor
Everything Hanlin does for AMC 10, in one conversation.
Entry, planning, coaching and the past papers. An advisor will tell you which of these a student actually needs, including when the answer is none of them.
Competition entry and planning
Which competitions suit this student, in what order, and by when - then we handle the registration, including the ones that can only be entered through a school or a centre.
Competition coaching
Taught by full-time subject tutors, on a course tier chosen by placement paper rather than by year group.
International curriculum tutoring
IB, AP, A-Level, IGCSE and the US high school curriculum, taught alongside school and timed around the exam calendar.
Competition past papers, free
A large library of past papers, mark schemes and syllabus breakdowns across every competition on this site. No charge and no enrolment.
Scan to add an advisor
Say which competition or course you are asking about. Replies in Chinese or English.
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AMC 10, briefly answered.
What students and families ask before registering.
What is the difference between the A and B papers?
They are different papers of comparable difficulty and identical scope, and their cutoffs land close together - the gap between them is usually within 10 to 15 marks. The emphasis can differ. You may sit either or both, and only your better result counts toward AIME qualification.
Who is eligible for AMC 10?
Students in grade 10 or below who are not older than 17.5 on the day of the contest. There is no nationality restriction, and there is no minimum grade - strong students in grade 8 and below have their own award category on this paper.
Should I answer every question?
Not necessarily. A blank scores 1.5 and a wrong answer scores 0, so a completely blind guess among five options averages 1.2 and is slightly worse than a blank. Once you can eliminate one or two options, guessing becomes the better bet.
How do I qualify for AIME?
By reaching the AIME cutoff on either paper. The cutoff is set on the global distribution and has recently fallen between about 93 and 105 out of 150, so it moves each year with the difficulty of the paper.
Are my scores at home a good guide to the real thing?
They tend to run high. Practising at home carries less pressure and a more relaxed testing state than the contest itself, so treat a home score as an upper bound rather than a prediction.
What should I revise from?
Past papers and practice problems both work, since the point of either is to build reasoning and problem-solving habits. Candidates aiming high are advised to work some harder material, AMC 12 problems in particular.
Can I prepare for AMC 10 on my own?
It is harder than it looks. Beyond the mathematics, the paper demands answering technique and time management, and those are what first-time candidates most often find difficult without structured practice.
Can I use a calculator?
No. Calculators are not permitted on AMC 10.
When do results come out?
Scores are released four to six weeks after the contest. Award cutoffs and downloadable electronic certificates follow six to eight weeks after.
Related
Where AMC 10 sits.
The papers above and below it, and the invitational it selects for.
AMC 10 enquiries
Decide early whether you are sitting one paper or both.
Tell us the student’s year group and target - an AIME invitation, a global award, or a first comparable result - and an advisor will confirm the registration route and set a preparation schedule against the November dates.