Who is eligible?
BAMO-12 is for anyone who is in grade 12 or below (full-time college students are not eligible, but if a high school student is taking some college courses while still in high school, that is OK).
BAMO8 is for anyone who is in grade 8 or below, unless they have previously scored a top award in BAMO-8.
Originally, BAMO was restricted to students in schools in the San Francisco Bay Area. In recent years, we have slowly expanded eligibility to include a few schools in the Pacific Northwest and Southern California. The number of students that we accomodate depends on how many people we have to grade the exams, so we cannot guarantee registration to all. Just ask!
How do I register?
Registration is done by schools or proctoring centers, such as math circles. We send out an email in December to schools/proctoring centers that have been involved with BAMO in the past to register students to take the exam. We also will have the registration questionnaire available on the web site in December. The school/proctoring site needs a designated proctor who will administer the exam on-site. If you wish to added to our email list, please click on this
What if I am a student at a school and I cannot find a proctor?
In this case, we will attempt to match you with a proctoring site nearby. Usually another school or math circle will accommodate you. Most years, we have several dozen sites.
What if I am home schooled? Can my parent or guardian be the proctor?
In this case, you will not be able to take the exam at home. You will need to find a nearby center to accommodate you.
The BAMO Exam
How many people take the BAMO exam?
During each of the past few years, nearly 500 people took BAMO-8 and about 200 took BAMO-12.
How do the BAMO-8 and BAMO-12 exams differ?
Both exams have 5 questions, with a four-hour time limit. The BAMO-8 problems are labeled A, B, C, D, E, in increasing order of difficulty. The BAMO-12 problems are labeled 1--5, in increasing order of difficulty, and generally the last three problems of BAMO-8 and the first three problems of BAMO-12 overlap, so that problems C, D, E in BAMO-8 are, respectively, problems 1, 2, 3 in BAMO-12.
What kind of problems are on the exam?
BAMO-8 problems include questions from logic, simple geometry, basic counting, and some algebra. BAMO-12 problems may involve more advanced algebra, such as complex numbers, and possibly trigonometry, along with more advanced geometric ideas and more adanced counting concepts (more formally, combinatorics). No problems use or involve calculus. Please see our archive of past problems and solutions for examples.
How hard are the problems?
The key word is "problem." A problem, in contrast to an exercise, is a mathematical question that requires investigation to solve. BAMO consists of, we hope, challenging and interesting problems. Usually the majority of the participants solve or make very significant progress on the first problem in their exam, but only a handful (perhaps 1 out of 50) make any progress with the last problem.
Why are those last problems so hard?
We have a very diverse group of participants. Many are inexperienced folks that are relatively new to problem solving mathematics. For these students, we want to provide interesting problems that are relatively easy to investigate and enjoy. But some participants are extremely experienced and highly skilled, including a few that are hoping to qualify for national or even international competitions. Therefore, some of our problems need to be so "hard" that they will separate the really experienced from the extraordinarily experienced people. We don't expect most participants to solve these problems during the time limit, but we try to make thse "hard" problems interesting to all. We hope that even if you haven't solved a problem during the exam that you continue to think about it and perhaps discuss it with others.
How are the problems graded?
Each problem is worth 7 points, so a perfect score is 35 points. Perfect scores are rare; perhaps one or two participants achieve this. The median score is usually around 7 points (i.e., about half the students solve more than one problem, and about half solve less than one problem).
If this exam is so hard, why should I take it? I won't win!
"Winning" is not the point! BAMO is a fun challenge. For most people, even people who love math, it is a new experience to spend four hours doing nothing but thinking deeply about mathematics. And you will meet other people who share your interests. And the awards ceremony, open to all participants, is another great experience.
Tell me more about the awards ceremony. Are there prizes?
A week or so after the graders finish their work, we have an awards ceremony (held at MSRI since 2006) that features a talk by an excellent mathematician, followed by announcements of the top scoring individuals and teams. Prize winners receive cash, books, certificates, sometimes trophies or mathematical scultpures. Winning teams get certificates for food. While it is certainly an honor to get an award, the real point of the awards ceremony is to celebrate mathematics itself. Here is list of past speakers.
Preparing for the BAMO exam
I'm a complete beginner. How do I get good at this stuff?
There's good news and bad news. The bad news is that mastery of mathematical problem solving, like any other meaningful endeavor, takes time and effort. The good news is that all you need is to love math; there are plenty of resources to help you learn more: local math circles, books, and a great online community. Read on!
Tell me more about math circles!
A math circle is a special kind of math club that features a problem-solving curriculum in a friendly, inclusive environment, facilitated often by professional mathematicians who are eager to share "folklore" with newcomers. There are literally hundreds of math circles around the country; click this
link for more information. The BAMO exam was created in tandem with the Berkeley Math Circle so that circle participants would have a contest to engage them. That does not mean that the Berkeley Math Circle, or any other math circle for that matter, is especially contest-focused. Different circles have different cultures, but they all have a love of math and collaborative problem solving in common.
Tell me more about an online community!
Students interested in becoming better problem solvers need a peer group, and math circles can provide that. But sometimes a math circle is inconvenient, so an online peer group is very helpful. The Art of Problem Solving (AoPS) is a gigantic international forum with many thousands of math-loving people, with numerous sub-communities and classes and lots of other helpful resources. If you haven't already joined, please visit AoPS to learn more about this remarkable community.
Tell me more about books!
Whether you do math online with a community like AoPS, or in a math circle, or on your own, you need to read. There are tons of books and other written resources out there, so sometimes it is good to have a small list of recommended books. Here are some suggestions.
AoPS publishes a number of excellent books at a variety of levels. Visit their bookstore for more details. In particular, the "Beast Academy" series is aimed at younger students.
Likewise, the Berkelely Math Circle has a link with suggested books at a variety of levels, including works written and edited by Zvezdelina Stankova, one of the founders of BAMO.
Paul Zeitz, one of the founders of BAMO, wrote The Art and Craft of Problem Solving for more advanced audiences (college students preparing for the Putnam Exam), but this book has become popular with high school students as well. Electronic versions can be found at the publisher's website and physical copies can be found from the usual websites. Additionally, Zeitz made a video course with the same title.