How to Qualify for AIME

Independently answer every single challenge question in the following AoPS books:

Prealgebra

Intro to Algebra

Intermediate Algebra

Intro to C&P

Intermediate C&P

Intro to Number Theory

Intermediate Number Theory

Intro to Geometry

Intermediate Geometry

(If your kid gets stuck along the way, that is where my lessons are a benefit. But no amount of lessons is a replacement for working through the books for hours and hours.)

This path may look simple, but simple does not mean easy. Actually putting in the effort to reach each of these goals is a tremendous accomplishment! I recognize that titles such as "Prealgebra" likely sound beneath your child's skill level. However, there is a very wide range of what different programs consider "introductory" material.

The example I like to give is with "Algebra 1."

This class is called "Algebra 1": https://www.mathhelp.com/algebra-1-help/?utm_campaign=purplemath&utm_source=_mh_alg1&utm_medium=course

This class teaches how to solve x+3=5 and plot (2,4).

This class is also called "Algebra 1": https://ocw.mit.edu/courses/18-701-algebra-i-fall-2010/pages/syllabus/

This class assumes prior proof-writing experience and teaches about discrete groups of isometries.

There is a WILD difference between these two courses. AoPS's algebra is somewhere in between that is geared specifically towards competition preparation. That is the material needed to do well on the AMC. If your child already has taken courses with the same titles as these AoPS books, great; that will speed up (but not replace) the process. Keeping this in mind, the path listed above represents around 1500 hours of work BEYOND the math education provided in the accelerated math of elite high schools. That is entirely doable (even if you feel like you're starting "late"), but can take very intelligent students years to complete.

Group classes (such as those provided by AlphaStar Academy and AoPS Online) can be a cost-effective resource for speeding up independent study. However, parents and students can easily fall into the trap of believing that participation (or simply enrollment in some cases) in a course leads to certain future success. Only the students who use every resource provided and practice extensively on their own to master the material are the ones who regularly qualify.

Parents often ask how many hours it will take until their student reaches a certain milestone. For example: "My student is in accelerated math. How long until he qualifies for USAMO?"

This is a challenging question to answer as a vanishingly small number of students ever achieve USAMO at all. No teacher, group class, or study plan is able to force students to complete these rigorous curricula. Students must feel inspired and excited throughout this multi-year journey. There will be good seasons when your kid gets a major win earlier than expected, and other times where the contest gets harder faster than your kid improves (which can feel awful in the moment). Qualifying for these competitions is a massive accomplishment as a result of years of intense effort.

With all this effort required, it might sound like an impossibility for a child to win such an award. Yet, roughly 6000 students per year qualify for AIME each year, including several of my own middle school students.

There are myriad benefits to students excelling at competitions. For starters, students who excel at one competition already have the problem-solving skills and discipline needed to excel at other competitions. My USA Computing Olympiad students tend to progress rapidly to Silver if they have previously qualified for AIME. I have likewise seen AIME qualifiers readily pick up gold awards on the National Latin Exam, not because Latin is at all their focus, but because they know how to study. And due to the substantial overlap of students across various disciplines, these top students from around the country network with one another starting at surprisingly young ages. That becomes a powerful job network upon reaching adulthood. Above all else, high achievement in these contests will give your students the mental fortitude and problem-solving foundation necessary to succeed in any future endeavors, from theoretical research to applied sciences.

Think of these contests as one building block in a much larger picture.