Competitions · Mathematics · Math League
The Math League.
A contest series for grades 1 to 12, founded in 1977 and now entered by more than a million students a year. It is deliberately less austere than an olympiad: the problems are lively and drawn from ordinary situations, and because everything is in English, reading the question is part of the test.
At a glance
What the series is, and how it runs.
The Math League was founded by two American mathematics educators, Steven R. Conrad and Daniel Flegler, and first held in 1977. Their stated aim was to make students enjoy mathematics and use it on real problems rather than fear it.
- Organiser
- The Math League, founded 1977 by Steven R. Conrad and Daniel Flegler
- Who can enter
- Students in grades 1 to 12. A student may enter a level above their own year - a grade 5 student can register for grade 6
- Scale
- More than one million primary and secondary students take part each year, across the United States, Canada and internationally
- Three stages
- A China-region first stage, a China-region second stage for qualifying grades 3 to 9, and a summer finals event held in the United States
- First stage format
- Sat either on paper or online through the official Math League site, on a single Saturday in early December
- Language
- English throughout, which the organisers treat as part of what is being assessed rather than as an obstacle to it
- Online equipment
- A laptop or tablet with a camera for answering, plus a smartphone with a camera for invigilation. Video is monitored and recorded throughout, and messaging apps are prohibited
- What it is used for
- Results are accepted as supporting evidence in applications to North American secondary schools and universities
- The finals
- Held each summer in the United States, with the organisers working alongside Princeton University, Columbia University and Williams College
By year group
Four different papers across twelve years.
The youngest students sit a shorter paper of purely multiple-choice questions. From grade 3 upward the format is fixed at 75 minutes and mixes multiple choice with fill-in answers.
| Year groups | Time | Question types | Questions |
|---|---|---|---|
| Grades 1 and 2 | 45 minutes | Multiple choice | 45 |
| Grades 3 to 7 | 75 minutes | Multiple choice and fill-in | 35 |
| Grades 8 and 9 | 75 minutes | Multiple choice and fill-in | 30 |
| Grades 10 to 12 | 75 minutes | Multiple choice and fill-in | 30 |
Note what happens to the question count: the older papers have fewer questions in the same time, which is the clearest indication that they expect more thinking per problem rather than more speed.
The three stages
How a student moves through the series.
Each stage is a genuinely different kind of assessment, which is unusual - most series simply make the next paper harder.
First stage, December
A timed paper sat on one Saturday, on paper or online. The questions are deliberately flexible and close to everyday situations, meant to leave students understanding and enjoying mathematics rather than intimidated by it.
Second stage, January to February
Open book, and taken over weeks rather than hours: candidates download the questions after registering and upload answers before the deadline. Open to grades 3 to 9 who earned a certificate in the first stage.
Summer finals, United States
Held with Princeton, Columbia and Williams College, and set jointly with them. Students compete alongside entrants from the US and Canada and attend teaching from faculty at those institutions.
The second stage
An open-book round that works like research.
This is the most distinctive thing the series does, and it is worth understanding before entering: the second stage is not a harder version of the first.
Grades 3 to 6: think, do not rush
The questions differ in form from a conventional competition paper and are not especially hard. What they require is careful, sustained thought - the organisers make the point that genuinely important ideas are usually simple and close to ordinary life.
Grades 7 to 9: read, then solve
Candidates first read a mathematical topic written in English - number theory, for instance - and then answer a set of questions on it, rising in difficulty. The reading is the point; the questions test whether it was understood.
Research is allowed, including online
Students may look material up, including on the internet, and may ask experts. Very few contests permit this, and it changes what is being measured from recall to the ability to find and use unfamiliar mathematics.
But nobody may do it for you
The one hard rule is that no other person may do the work. The candidate has to complete the questions themselves and genuinely understand what they have done, which is what keeps an open-book round meaningful.
First-stage awards
Three certificates, and a place in the second stage.
The certificates are not cumulative - a student receives the highest one they qualify for. All three carry an invitation to the second stage.
The finals
Four rounds at the summer event.
The finals are split into elementary, middle and high-school groups, with the high-school group running at Stanford University and at Alphastar Academy in Silicon Valley.
Individual Round
Ten to fifteen questions worked one at a time, with seven to ten minutes allowed for each. Combined with the Speed Round, this decides the individual standing and the gold, silver and bronze medals.
Speed Round
Sixty fill-in questions in forty-five minutes - forty-five seconds a question. It is the opposite demand from the Individual Round, and sitting both in one event is part of the design.
Team Round
Ten to fifteen questions worked by a team of five over one to two hours. This is where the collaborative half of the finals begins, and where dividing the paper well matters as much as solving it.
Relay Round
Five questions passed down a team, each member needing the previous answer before they can start. Updated answers can be passed forward more than once, and the fifth question is the hardest.
Preparation
How Hanlin prepares students for Math League.
Two things separate this series from a domestic competition: the English, and the fact that later stages reward reading rather than drilling.
Reading mathematics in English
The second stage asks grades 7 to 9 to read a mathematical topic in English and then work on it. Practice therefore includes reading unfamiliar mathematical prose in English, which is a skill separate from solving problems in it.
Problems from ordinary situations
Questions are framed around real settings rather than abstract statements. The trainable step is turning a described situation into a mathematical one quickly, and it is where younger candidates lose most of their marks.
Two opposite speeds
Forty-five seconds a question in the Speed Round and ten minutes in the Individual Round demand different habits. Students who reach the finals practise both, because doing one well does not prepare you for the other.
Choosing the level
Entering a year above is permitted and sometimes right for a strong student, but it changes the paper and the field. That decision is settled against a past paper rather than by ambition.
Why Hanlin
Hanlin has been entering students for Math League 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 length for Math League is set after a placement paper. The gap between where a student is and what the paper asks for is what the course has to close, and that gap is not the same for two students in the same year group.
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
Past papers and preparation pack
The same material our own Math League 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.
- PDFPast papers, every year the organiser has released
- PDFWorked solutions, where the organiser publishes them
- PDFThe syllabus on one page - every topic, and how heavily it is examined
- PDFEntry 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.
Advanced from stage one, 2025
One line from Hanlin's published Math League record. The rest of it is below.
Math League
- 2025Stage one: one student in the top 8%, 5 in the top 25%, and an 85% advancement rate. Stage two: 8 in the top 8%, 7 in the top 25% and 15 through to the final
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 Math League, 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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Math League, briefly answered.
What students and families ask before entering.
Who can enter Math League?
Students in grades 1 to 12. A student may register for a year group above their own - a grade 5 student can sit the grade 6 paper - but the level determines both the questions and the field they are ranked against.
What is the first-stage paper like?
Grades 1 and 2 sit 45 multiple-choice questions in 45 minutes. Grades 3 to 7 sit 35 questions in 75 minutes, and grades 8 to 12 sit 30 questions in the same time, both mixing multiple choice with fill-in answers.
Can the first stage be taken online?
Yes. It can be sat on paper or online through the official Math League site. Online candidates need a laptop or tablet with a camera to answer on and a smartphone with a camera for invigilation; video is recorded throughout and messaging apps are not allowed.
Who qualifies for the second stage?
Students in grades 3 to 9 who earned an Honor Roll of Distinction, Honor Roll or Certificate of Achievement in the first stage - that is, anyone finishing in the top half of the field.
Is the second stage really open book?
Yes. Candidates download the questions and upload answers before a deadline weeks later, and may research the material including online and ask experts. The one prohibition is having someone else do the work.
What are the first-stage awards?
Honor Roll of Distinction for the top 8%, Honor Roll for the top 25% and Certificate of Achievement for the top 50%. They are not cumulative - a student receives the highest one they qualify for - and all three lead to the second stage.
What happens at the summer finals?
They run in the United States with Princeton, Columbia and Williams College, in four rounds: Individual, Speed, Team and Relay. Individual and Speed decide the individual medals; the team rounds decide the team standing and the Math League Cup.
Is the result useful for applications?
It is accepted as supporting evidence in applications to North American secondary schools and universities. Because the whole series runs in English, it also demonstrates working in the language rather than only mathematical ability.
Related
Other contests across this age range.
Series that also run from primary through to senior school.
Math League enquiries
The interesting round is the one nobody prepares for.
Most families plan for the December paper and are surprised by the open-book second stage, which rewards reading rather than drilling. Tell us the student’s year group and an advisor will map both stages against the season.