Academic Year Mathematics
Courses during the school year for high-performing math students in grades 1–12. Before enrolling in Academic Year courses, you will need to request a consultation.
Math Level 1Students develop their number sense and begin to learn about place value. They are introduced to addition and subtraction and are encouraged to approach numerical problems in clever ways. Additionally, they manipulate shapes, compare numbers, and examine ways to measure physical objects. We use puzzles and games to build skills and establish student understanding of mathematical concepts and problem solving.View Course
Math Level 2Students build foundational problem-solving skills which they will use throughout their math education. They will expand their understanding of the number system and place value, develop fluency adding and subtracting multi-digit numbers, and explore the properties of special types of numbers such as odds and evens. Each lesson includes challenging word problems and engaging puzzles that guide students toward a deep understanding of the material.View Course
Math Level 3Students develop fluency with multiplication and division, including using the distributive property to simplify calculations. They are also introduced to fractions to expand their understanding of numbers. In addition, students explore two-dimensional shapes, estimation, the use of variables to write expressions and equations, and other topics. We regularly incorporate word problems to teach students how to translate between writing and mathematics, and puzzles to teach higher-order strategic thinking.View Course
Math Level 4Students master multiplication and division of multi-digit numbers and build upon their understanding of addition and multiplication to include fractions. They also explore a wide variety of other topics, including properties of special two-dimensional shapes, symmetry, logic, factors, and probability. Students expand their understanding of numbers to include decimals and negative integers, and they learn to create and employ mathematical models via challenging word problems.View Course
Math Level 5Students master the key topics they'll need to succeed in an AoPS Prealgebra course. They will complete their study of the arithmetic of fractions, decimals, and negative integers. They are also introduced to topics in geometry, number theory, statistics, and beginning algebra through lessons on three-dimensional solids, factors and multiples, statistics, sequences, and ratios. Critical problem-solving skills, mathematical modeling, and deductive reasoning are reinforced with thought-provoking word problems and puzzles.View Course
PrealgebraPrealgebra begins by formalizing the rules of arithmetic that students learned in elementary school, building on a rigorous foundation as they move into algebra. We then survey a wide range of topics, including number theory, algebra, geometry, counting, statistics, and probability. Each topic is introduced with compelling problems, including many drawn from major national math contests such as MATHCOUNTS and AMC 8. We place special emphasis on challenging word problems throughout the course.View Course
Algebra 1In Algebra 1, students engage with various expressions from an algebraic and geometric perspective. They learn to solve linear and quadratic equations as well as how to represent expressions in the Cartesian plane. Students are imbued with a deep understanding of the general concept behind functions and are introduced to several important types of functions. Students are also introduced to the rich field of complex numbers. As with previous courses, we continue to emphasize challenging word problems to train students how to apply their new tools. Advanced problems from contests such as MATHCOUNTS, AMC 8, and AMC 10 are included throughout the course.View Course
GeometryGeometry introduces students to spatial thinking. Students learn to dissect complex geometrical configurations, applying what they've learned to arrive at key insights and novel understandings. Geometry problems are also tackled analytically by placing them on the Cartesian plane. In addition, we build the foundations for precalculus and calculus by introducing students to trigonometry. Many of the challenging problems from this course come from contests such as MATHCOUNTS, AMC 10, and AMC 12, with a few problems coming from even more advanced contests to stretch the strongest students.View Course
Algebra 2In Algebra 2, students continue their study of algebraic functions and applications. We begin by reviewing key concepts from Algebra 1, then expand upon them to solve even more challenging problems. Students explore the rich field of polynomials and build foundations for calculus through the study of sequences and series. They are exposed to a variety of important algebraic forms and functions, and are equipped with the tools necessary for understanding new forms and functions they'll encounter in the future. We also lay the groundwork for navigating optimization problems with a study of inequalities. Many challenging problems in this course are drawn from contests such as AMC 10, AMC 12, AIME, and the Harvard-MIT Math Tournament.View Course
PrecalculusOur Precalculus class prepares students for a variety of college-level courses. Precalculus provides a deep exploration of trigonometry, complex numbers, and two- and three-dimensional vector spaces, with a special focus on how these areas of mathematics are related. This gives students a solid foundation for collegiate courses in calculus, linear algebra, multi-variable calculus, complex analysis, and physics. Many of the challenging problems of Precalculus come from contests such as AMC 12, AIME, and the Harvard-MIT Math Tournament.View Course
CalculusOur calculus class goes well beyond mechanics and calculators, and provides students a rigorous understanding of the fundamental operations of calculus, delivering a first-year calculus course like those students would find at a top-tier university. Students completing our calculus course will be in an excellent position to apply their new skills to physics, economics, engineering, and more advanced mathematics.View Course
Middle School Contest Math *Middle school math contests such as MATHCOUNTS are a launching pad for many of the best math students. In this course, we draw problems from premiere middle school contests such as MATHCOUNTS and the American Mathematics Competitions 8 (AMC 8), as well as beginning high school contests like the American Mathematics Competitions 10 (AMC 10). Students explore important new topics in counting, probability, and number theory, and learn to apply topics in algebra and geometry to advanced problems. Students should either have completed an Algebra 1 course or be currently enrolled in one to be successful in this course.View Course
High School Contest Math *AoPS has prepared students for the most prestigious high school competitions since 1993. Over the last decade, most winners of the USA Mathematical Olympiad (USAMO) have been AoPS students, including 15 USAMO winners in 2020, as well as the US team members that won the International Math Olympiad (IMO) in 2015, 2016, 2018, and 2019. In this course, students study strategies crucial for success on the American Mathematics Competitions 10 and 12 (AMC 10 and 12), the American Invitational Math Exam (AIME), the Harvard-MIT Math Tournament, and other major high school contests. This course is a challenge which builds on foundational knowledge that students should already have from their high school math courses. Students should expect to encounter difficult problems and topics. Students should either have completed an Algebra 2 course or be currently enrolled in one to be successful in this course.View Course
* Note for students who have previously taken this course:We alternate between two different versions of this course fromone year to the next. The two versions are roughly the samedifficulty, but include different lessons, practice contests,and homework. Therefore, students taking this course for twoconsecutive years will see different material in the secondyear than in the first.
