BMT 2022

Berkeley Math Tournament 2022

Saturday, November 5, 2022

Welcome to Berkeley Math Tournament 2022! BMT 2022 will be in-person, with various satellite tournaments and an informal, online rerun. The tournament will consist of 3 main rounds — Power, Guts, and General/Focus.

Registration will open on Tuesday, September 20th, 2022.

BMT is open to high school students in grades 12 or below. In particular, there is no lower age limit to compete in BMT; middle schoolers and advanced elementary students are welcome to compete. Our middle school tournament will also be held in the spring. Coaches can register up to 6 students per team. There are no restrictions on how many teams/students a single coach can register. You do not have to be local to the Bay Area or California to register for BMT.

Registration Information

Registration, Waivers, and Pricing

Registration PeriodPrice Per Student
9/19 – 10/15Normal Registration$20
10/15 – 10/31Late Registration$30 and there is no guarantee of contest swag.
*For students facing financial hardship, please contact for a fee waiver*
As long as students register during normal registration, they will receive BMT shirts and swag as well as T-shirts and other company giveaways from our sponsors. We will not honor refunds during late registration.

We are now using a new registration portal. Coaches may register up to 6 people per team, and ContestDojo will allow them to assign and modify teams up until tournament day. All contestants are required to have their parent/guardian sign UC Berkeley’s consent waivers through this portal. Contestants will NOT be allowed to take the contest without having a signed liability and consent to treatment waiver. Any questions about managing the teams on the portal should be directed to us at

Student Eligibility

  1. Students must be in grade 12 or below to be eligible for BMT. Middle school students in particular, are encouraged to participate. 
  2. Students do not have to be local to the California Bay Area or the U.S. to participate in BMT. Please see “Satellites” and “BMT Online” for other options on tournaments. 
  3. Coaches/Institutions may register multiple teams. We ask that for every 2 teams, there is at least 1 parent chaperone.
  4. Due to room capacity constraints, we will cut-off registration at around 1000 students on a first-come, first-serve basis. 


Students may register as a team of 1, however, it is beneficial to compete on a team of at least 4 due to our scoring guidelines. For students who do not have a full team, we organized a “Team Finder” document. Follow all outlined steps in the document.

BMT Rounds

Power Round

90 mins

The Power Round is a proof-based team round. Contestants will answer a series of questions centered around a single topic not typically seen in competitive mathematics, culminating in incredible results in the field of that chosen topic. For all questions (unless stated otherwise), you will need to provide a rigorous mathematical justification for your assertions in full sentences. The topic for the Power Round will likely be at an undergraduate level, but no substantial previous mathematical background is expected.

General Round

90 mins

The general round is an individual round consisting of questions across the various subjects that comprise the focus rounds. This round is highly recommended for students with less prior contest experience.

Focus Rounds

60 mins

There are four focus rounds of 10 questions across four subjects — Algebra, Geometry, Discrete Math, and Calculus. Each student can participate in two rounds of focus exams.

Guts Round

75 mins

The guts round consists of 9 sets of 3 problems across various subjects in math. The key feature of this round is that each set must be turned in before the next set is given. All teams can see a live scoreboard with their standings


The tiebreakers will be held for the top scoring students in each of the individual rounds. Tiebreaker qualifies will be announced at the end of the Guts round, and will be a 15-minute test. The test will consist of three questions for the focus rounds, and five questions for the general round, and be scored primarlily on correctness and secondarily on submission time, That is, an earlier submission will be worth more than a later one with the same number of correct answers, but less than a later one with more correct answers.

Students may choose 2 Focus rounds to take (from Algebra, Geometry, Discrete, and Calculus) OR the General Round.


PowerFocus x 2GeneralGuts
Important DetailsProof-BasedStudents may choose 2 Focus rounds to take (from Algebra, Geometry, Discrete, and Calculus) OR the General RoundOnce answers to a set are submitted, they cannot be edited
LocationAssigned Classrooms – See Tournament GuideAuditorium
# of QuestionsTBA10 Each25 total27 total
Duration90 mins60 mins each90 mins75 mins
% of Score30%40%30%
Important Scoring NotesN/AThe General Round will only count for half as many points as the Focus combinationsN/A
Collaboration?YesNo, students will work individuallyYes

Acceptable Answers

Students are responsible for familiarizing themselves with the acceptable test formatting document and common notation document for details on how their answers should be submitted. Answers not submitted in the listed formats will be graded as incorrect, even if equivalent.


Focus / General: To calculate the focus / general score, we will take the average of every team member’s score on their individual portion if the team has 4, 5, or 6 members. If the team has fewer than that many members, we will add 0’s until the team has reached at least 4 scores, of which we will take the average. While individuals are allowed to register a 1-person team, we highly encourage students without a team to use the Team-Finder to create a team of at least 4.

All scores for a given round will be normalized by either the top 10 students or the top 10% of all scores, whichever is bigger.

If a student takes the General Round instead of the two Focus rounds, their score will only count for half as many points as the Focus combination will.


Start Time (PT)Student EventsCoach + Parent Events
8:00 AMCheck-In
Wheeler Lobby
Bagels + Coffee
Dwinelle 145
8:30 AM
9:00 AMPower Round (90 mins)
See Tournament Guide
Po-Shen Loh Talk

Dwinelle 145
9:30 AM
10:00 AM
10:30 AM
11:00 AMFocus #1 (60 Min)
Focus #2 (60 Min)
See Tournament Guide
(90 Mins)
See Tournament Guide
Campus Tours

See Tournament Guide
11:30 AM
12:00 PM
12:30 PM
1:00 PMBreak
1:30 PMLunch
2:00 PM
2:30 PMGuts Round (75 Min)
See Tournament Guide
Campus Tours

See Tournament Guide
3:00 PM
3:30 PM
4:00 PM
4:30 PMActivities / Tiebreakers
See Tournament Guide
5:00 PM
5:30 PM
6:00 PMClosing Ceremony
Wheeler 150
6:30 PM

Student Activities

The following activities will be offered to students during the Activities / Tiebreaker period.

Combo Games – “I’m going to win! No wait, I’m going to lose!” Get lost in strategy and always being one or two moves ahead of your opponent in combinatorial games! Learn how to win at just a single glance (and how to jump ship when you’re going to lose) in fun combinatorial games! See Tournament Guide.

Dicey Duel – Battle against other competitors in this game of dice, luck and strategy. Players will participate in rounds against each other after building your optimal set of equipment. Test your ability to make the strongest class and turn the odds in your favor. See Tournament Guide,

Estimathon – A team-based contest that combines trivia, game theory, strategy, and mathematical thinking. Teams of ~3 will be under a time limit to work on a set of 13 Fermi-style problems.See Tournament Guide.

Integration Bee – Compete head to head against the best integrators around! Students will face off in a tournament style bracket, solving difficult integrals involving some clever tricks, to determine who will be the champion of all integrators. See Tournament Guide.

Parent Activities

Bagels + Coffee

BMT will be providing a light breakfast and coffee for parents and coaches throughout the day. In the lounge, parents + coaches will be served muffins, bagels, and coffee.

Po-Shen Loh Talk

Building Long-Term Success, Starting From Math

Life is long. The ~15 year period of contests, academics, and exams makes up a small fraction of that lifespan, but the decisions made during those years can significantly improve what the rest of life looks like. The speaker has closely observed the life journeys of 2 decades of math contest stars, starting from his cohort when he was on the International Math Olympiad team, to the present day. He has observed practical ways for many people to develop extraordinary math skills, which generalize into even more extraordinary technical abilities. However, he has also observed that those technical skills alone are not enough for the more complex game of life. In this talk, he will share some of these observations and advice.

The speaker is Po-Shen Loh (, a math professor at Carnegie Mellon University, and the national coach of the USA International Math Olympiad team. He uses math to devise new solutions to real-world problems and has appeared in national and international newspapers for several discoveries. These days, he runs a program that guides high school math stars to develop extraordinary communication and performance skills (, while teaching middle and elementary schoolers how to invent their own ways to think about math (

Campus Tours

BMT Staff will be offering a campus tour to parents while students are taking BMT. These tours will be all across the UC Berkeley campus, visiting some of the historical architecture and art found across campus.


The Parent + Coaches’ lounge will be located in Dwinelle 155, and will remain open from 8:00 AM to 4:00 PM, after the conclusion of the Guts round. Parents, coaches, and students wishing to remain on campus are welcome to find space in Wheeler 200 and 202.

Day of Logistics



  • Honorable Mention certificates for the top 50% of individuals (sent via email with score reports)
  • Distinguished Honorable Mention certificates for the top 20% of individuals (sent via email with score reports)
  • Top 10 individuals will receive medals
  • Top individual will receive a plaque

Focus Rounds

  • Honorable Mention certificates for the top 50% (sent via email with Score Reports)
  • Distinguished Honorable Mention certificates for the top 20% (sent via email with Score Reports)
  • Top 5 Focus Round medals 
  • Top individual of each Focus Round will receive a plaque

Guts Round

  • Top 10 teams will receive certificates
  • Top 3 teams will receive plaques and medals

Power Round

  • Top 10 teams will receive certificates
  • Top 3 teams will receive plaques and medals


  • Top 3 teams will receive trophies, medals, and the BlackPenRedPen scholarships
  • Teams 4 – 10 will receive plaques

Room Assignments

BMT will give out room assignments to teams where they will take several tests during the day. Classroom assignments will be posted closer to the competition date.

Frequently Asked Questions

Are calculators or other reference material allowed?

Graph paper and calculators are prohibited, but protractors, rulers, and compasses are permitted. Blank white scratch paper will be provided for all participants. All answers must be exact, reduced, and simplified. Illegible answers will not be graded. Cheating in any form will not be tolerated, and failure to comply with all rules may result in immediate and irreversible disqualification.

Can middle school students compete? What if I don’t have a team?

Yes! BMT is open to any student in 12th grade or below, including those who haven’t entered high school. While students are allowed to compete as individuals under “LAST_NAME Homeschool” or some other variation, we highly recommend that students compete on a team of at least 3 due to our scoring guidelines. To calculate the overall Individual score, we will take the average of every team member’s score on their individual portion if the team has 4, 5, or 6 members. If the team has less than that many members, we will add 0’s until the team has reached at least 4 scores, of which we will take the average.

How are awards handled?

Awards will be physically presented to contestants at BMT 2022’s closing ceremony.

I’m in a different timezone or non-local and can’t compete live. What are my options?
  • Check out BMT Global! An informal week-long asynchronous contest with no awards or mini-events. This contest can be taken at any time – perfect for students who want to compete in a low-stakes environment.
  • There will also be BMT Satellite competitions held through our partners at ASDAN and SIMCC for competitors wishing to compete in an Asian time zone.
I’m having trouble picking between the General Round versus two Focus Rounds.

The General Round is highly encouraged for students who are new to the math competition atmosphere with little to no contest experience. As a result, the Focus combinations count for double the number of points a General Round does. The Focus combinations require more specialized knowledge of the following domains: 

  • Calculus: Differentiation, optimization, related rates, integration, sequences / series
  • Geometry: Areas and volumes, two and three dimensional Euclidean geometry
  • Algebra: Equations and summations, functions and inverses, theory of roots and polynomials
  • Discrete: Discrete probability, counting and combinations, modular arithmetic, divisibility and primes, base arithmetic, linear Diophantine equations,  geometric probability

Individuals seeking to maximize their scores should take the Focus combination that they are most comfortable with. Students can choose the General Round or Focus combination on the student portal the day of the test. 

Will lunch be provided?

Lunch is not provided for BMT 2022. Students, coaches and parents are free to find food in Berkeley. Restaurants can be found on the south side of campus (~5 minute walk from homerooms) and downtown (~15 minute walk from home rooms)

Where can I find parking / How can I get around Berkeley?

BMT will not be providing parking or travel arrangements for students — it is up to coaches and/or parents to handle travel logistics. There are a number of parking garages around the campus, including Underhill Structure, Lower Hearst Structure, and the RSF garage. In addition, UC Berkeley campus is very public transport friendly. If you are staying in Emeryville, Bus Line 36 will take you directly to campus, and the Downtown Berkeley BART station is next to campus

Can I take the Calculus Round if I am in AP Calc AB?

The Calculus Focus Round is written with the BC curriculum in mind, and sequences and series are likely to appear on the exam. Since these topics are not covered in the AB curriculum, it is strongly recommended to not take the Calculus Focus Round if you are taking AP Calc AB.