SMT prep
The Stanford Math Tournament is a spring contest run by Stanford students, built from a Power Round, a Team Round, individual tests and a Guts Round, for teams of five or six.
SMT at a glance
- Individual tests
- A General Test for broad background, and Subject Tests in Algebra, Calculus, Discrete and Geometry.
- Team events
- A Team Round of short-answer questions and an 80-minute live-scored Guts Round.
- Power Round
- A proof-writing exam in which a team writes solutions together.
Who this is for
The General Test at SMT is meant for students without a specialized background, which makes the tournament a gentle first step outside the AMC. The Subject Tests are there when you want to go deeper in one area.
Do a General Test from a recent year on your own, then try a Subject Test in the area you like best.
The SMT circuit preset in Arena is built for it, and the General and Team rounds from recent years are in the bank.
What Lemmas has for SMT
- Problems in the bank
- 215
- Years covered
- 2022 to 2025
- Median difficulty, out of 100
- 38
The bank has 215 SMT problems from 2022 to 2025, divided among 15 papers. The median rating is 38, 10 points below the AIME's 48, with the middle half between 30 and 48.
The 15 SMT papers can be set in Arena with answers sealed until time is up, and the ratings follow the scale in how difficulty is measured.
The General Test, problem by problem
The General Test has 25 problems a year, and its median rating rises from 23 on problems 1 to 8 to 42 on problems 18 to 25.
- Problems 1 to 8, median rating
- 23
- Problems 9 to 17, median rating
- 33
- Problems 18 to 25, median rating
- 42
Team Round problems have a median of 49, which is higher than the General Test's 34, and the Subject Tests come in at 44.
SMT problems by subject
Geometry accounts for 71 of the 215 SMT problems here, and the next largest subject is Algebra with 53.
- Geometry, 33% of the bank
- 71
- Algebra, 25% of the bank
- 53
- Combinatorics, 22% of the bank
- 48
- Number Theory, 20% of the bank
- 43
From SMT to PUMaC
Every student at PUMaC chooses two of the four subjects, and SMT's General Test asks for no such choice. PUMaC also sorts teams into Division A and Division B, and it invites the top individuals in each test and division to a three-problem, proof-based Individual Finals.
Questions about SMT
How big is an SMT team?
A team has five or six students, and in person it also needs an adult chaperone.
What is the General Test?
An individual exam of short-answer questions for students without a specialized math background. It is the easiest way in.
Does Lemmas have SMT problems?
Yes. The bank holds recent SMT rounds, used under the tournament's own citation rules.
Where the SMT problems come from
The Stanford Math Tournament released its problems officially and allows reuse with a citation. Every SMT problem on Lemmas carries that citation and links back to the original.
SMT on the Stanford Math Tournament website (opens in a new tab)
Make an account and try your first problem.
Username, email and password. No card.