Stanford Math Tournament Preparation: SMT Guide

Stanford Math Tournament preparation involves one decision that most tournaments do not offer, and getting it right matters more than any amount of extra practice: whether a student should sit the subject tests at all.

A spring tournament with an online route

The Stanford Math Tournament is organised by Stanford students under SUMO, the Stanford University Mathematical Organization, and runs in spring, most recently in April. Teams are 5 to 6 students.

For students outside the United States the important structural fact is the entry route. The in-person tournament is for high school students residing in the United States, aged 14 or over, registering as a school or an established mathematics institution. International teams take part through SMT Online, which is open to students of all grades in any country.

That is not a reduced version to settle for; it is the tournament as offered to the rest of the world, and it removes the travel that makes most US tournaments impractical for an Indian or Singaporean team.

Two of four subjects, including Calculus

The Subject Tests are 10 problems in 50 minutes, short answer, in Algebra, Calculus, Discrete and Geometry, and students take two.

Calculus appearing here is worth noticing. Olympiad-track students usually arrive with strong algebra, discrete mathematics and geometry and no competition calculus at all, because the olympiad syllabus excludes it.

For a Class 11 or 12 student who has covered calculus at school, it is frequently the least contested of the four and often the better of their two choices. Part of serious Stanford Math Tournament preparation covers calculus as tournaments set it, which is not how textbooks set it.

The General Test is not a lesser option

SMT offers a General Test, 25 problems in 110 minutes, as an official alternative to the subject tests for less experienced competitors.

We recommend it more often than families expect, and we are direct about why. A student who is not yet at subject-test level will spend two 50-minute tests scoring a handful of marks, learn very little from it, and come away with the impression that tournament mathematics is not for them.

The same student on the General Test works 25 problems pitched where they actually are, finishes with a result they can read, and comes back the following year. Flattering a student into the harder paper serves nobody, least of all the student.

Eighty minutes of proof

The Power Round is 80 minutes of proof writing. That makes it a different discipline from PUMaC's week-long Power Round: there is no time to redraft, reconcile notation across a team, or sleep on a lemma.

Under that clock, the habit that pays is writing the argument correctly the first time, in order, with assumptions stated as they are used. A student who can produce a clean proof given a week cannot necessarily produce one in eighty minutes, and the two need separate practice.

For students on the Indian olympiad pathway, the 80-minute version is closer to what RMO asks for, which makes it unusually relevant practice.

Guts, and a detail worth not drilling

The Guts Round runs 80 minutes in series of four problems, submitted sequentially. The number of series has differed between sources and between years.

So prepare the format rather than a count: working in fours, deciding as a team when to submit an incomplete series, and keeping a reserve of time for the later ones. A team that has rehearsed exactly nine series and meets eight has rehearsed a number, not a skill.

The Team Round at speed

The Team Round is 15 questions in 50 minutes, short answer. At a shade over three minutes a question with six people, the binding constraint is coordination rather than mathematics.

Who takes what, how answers are checked without re-solving them, and how the team avoids two people working the same question while a third goes untouched. We practise the division explicitly, because teams almost never improvise it well and the cost is invisible until the scores come back.

What to cover

Algebra: polynomials, functional equations, inequalities and sequences, as covered in our algebra course.

Discrete: counting in bijection, recursion, graphs, probability and invariants. This is where many students are weakest and our combinatorics course does the most work.

Geometry: circles, cyclic configurations, power of a point, and coordinate and trigonometric methods.

Calculus: limits, differentiation, integration, series, and the problems tournaments set rather than the ones textbooks set.

Preparing for SMT Online specifically

If your team is entering through SMT Online, a few practical points are worth settling early rather than on the day.

Work past papers in the same format you will compete in. An online tournament adds submission mechanics, timing displays and sometimes a different way of entering answers, and attention spent on the interface is attention not spent on the mathematics.

Agree in advance how the team will communicate during collaborative rounds, and test it. A team scattered across a video call with no agreed protocol will lose several minutes to people talking over each other, which on a 50-minute Team Round is a meaningful share of the available time.

Finally, check the time zone. A spring tournament run on US Pacific time falls awkwardly for teams in India and Singapore, and a team sitting a 50-minute round at three in the morning is not being tested on its mathematics.

Who should enter and how to choose

Students at AMC 12 level and above for the subject tests; the General Test is the honest route for students not yet there. International students enter through SMT Online.

Team size is 5 to 6 on the current official page, and some third-party sources claiming up to eight do not match it. Dates, the Guts series count and registration details are set each year, so confirm them at stanfordmathtournament.org rather than relying on figures reproduced elsewhere.