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Introduction to Algebra B

Summary

Part of our introductory math series, Introduction to Algebra B builds on the foundations of Algebra A and extends into more complex topics beyond the standard school curriculum. Fundamental concepts of algebra, including quadratics, systems of equations, clever factorizations, complex numbers, functions, graphing, sequences and series, and special functions, are covered in this course.

This advanced math course is offered in two formats: a live online course or a self-paced course. Both formats include instructor feedback and a class message board for student support.

Introduction to Algebra B: Weekly Live

Length: 16 Weeks

Our live Introduction to Algebra B course brings together advanced problem solvers from around the world for 90-minute classes. Experienced instructors lead students to creatively problem-solve with quadratics, systems of equations, clever factorizations, complex numbers, functions, graphing, sequences and series, special functions, exponents and logarithms, and more.

Students learn from our Introduction to Algebra textbook and videos, while honing their skills on various types of engaging homework problems. They can also use the class message board to collaborate with their peers and reach out to instructors outside of class.

Live Online Course Features

16 live class sessions taught by our outstanding faculty in an interactive text- and image-based classroom designed for collaboration and motivated students
More than 100 supplementary videos by AoPS founder and Introduction to Algebra co-author Richard Rusczyk
Detailed instructor evaluation of students' written solutions to open-response problems designed to strengthen mathematical writing skills
Class message board where students can collaborate with their classmates or ask instructors and AoPS staff questions outside of class time
Weekly homework assignments including short-answer questions and open-response writing problems, on which students receive detailed feedback
Comprehensive reporting that allows students and parents to thoroughly track progress and performance throughout the course

Why AoPS?

Extraordinary Live Instruction from Accomplished Faculty

Our teachers were outstanding math students themselves, and many were winners of major math awards as well as recipients of degrees from schools like MIT, Harvard, Stanford, and Princeton. Our instructors understand from their personal experiences how to inspire and challenge eager learners, and they serve as role models for our students who aspire to similar success.

Active Learning

Students learn best by actively engaging with challenging problems. Our lessons start with thought-provoking questions, encouraging independent insights and problem-solving strategies. Instructors offer hints and guidance as needed and reinforce key concepts after problems are solved. To support diverse learning styles, we provide live classes, textbooks, videos, homework problems, and opportunities for discussion with instructors and peers.

Focus on Non-Routine, Challenging Problems

In today's world, many jobs previously requiring routine problem-solving are now handled by computers. To prepare students for the future, we focus on teaching them how to apply core principles to new, non-routine problems. This approach ensures that students develop essential skills for top-tier colleges and competitive careers, preparing them for lifelong learning rather than rote memorization.

Schedule: Introduction to Algebra B

The current and upcoming sections of this course are listed below. All sections cover the same course material.

Thursday
Feb 13 - May 29
7:30 - 9:00
PM ET
Feb 13 - May 29
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$485 (~$31/lesson)
$552 w/books
$485 (~$31/lesson)
$552 w/books
CLOSED
Sunday
Mar 2 - Jun 22
7:30 - 9:00
PM ET
Mar 2 - Jun 22
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$485 (~$31/lesson)
$552 w/books
$485 (~$31/lesson)
$552 w/books
CLOSED
Wednesday
Apr 16 - Jul 30
7:30 - 9:00
PM ET
Apr 16 - Jul 30
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$485 (~$31/lesson)
$552 w/books
$485 (~$31/lesson)
$552 w/books
ENROLL
Tuesday
May 6 - Aug 19
7:30 - 9:00
PM ET
May 6 - Aug 19
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$485 (~$31/lesson)
$552 w/books
$485 (~$31/lesson)
$552 w/books
ENROLL
Wednesday
Jun 4 - Sep 17
7:30 - 9:00
PM ET
Jun 4 - Sep 17
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$485 (~$31/lesson)
$552 w/books
$485 (~$31/lesson)
$552 w/books
ENROLL
Sunday
Jun 22 - Oct 19
7:30 - 9:00
PM ET
Jun 22 - Oct 19
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$485 (~$31/lesson)
$552 w/books
$485 (~$31/lesson)
$552 w/books
ENROLL
Friday
Jul 18 - Nov 14
7:30 - 9:00
PM ET
Jul 18 - Nov 14
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$485 (~$31/lesson)
$552 w/books
$485 (~$31/lesson)
$552 w/books
ENROLL
Fall 2025This course will be offered in Fall 2025. Click here to join our mailing list to be notified when the course schedule is available.
Don't see a schedule option that works for you? Check out the self-paced version of this class.

AoPS Holidays

There are no classes May 24 ‐ 26, July 4 ‐ 6, August 29 ‐ September 1, October 31, November 24 ‐ November 30, and December 20, 2025 ‐ January 2, 2026.

Who Should Take This Class?

Students are ready for this class if they have mastered square roots and fractional exponents, order of operations, linear equations and inequalities, ratio, and proportion. We recommend that students have experience with factoring quadratics prior to taking this course.

  • To determine if you’re ready for the course, students can take the diagnostic pretest.
  • To determine if you need this course or can move on to the next, students can take the diagnostic post-test.

Please note: Our algebra sequence will likely not match up exactly with your school's. Most students who have completed our Introduction to Algebra A course or a high-level honors Algebra 1 course in school are ready for this class. However, we encourage students to take our Introduction to Counting & Probability class before beginning this course. Visit our Recommendations page for help in choosing the right class.

Weekly Live vs. Self-Paced

Our weekly live class is designed for students who prefer a live group experience. In this format, students learn in an online classroom, engaging in real-time with their instructor and peers. For students interested in setting their own study schedule, we recommend considering the self-paced version of this course.

Lessons

Show All Topics
Lesson 1
Factorization
  • Factoring quadratics
  • Sums and products of roots of a quadratic
Lesson 2
Quadratics and Complex Numbers
  • Simon's favorite factoring trick
  • Introduction to complex numbers
Lesson 3
Completing the Square and the Quadratic Formula
  • Completing the square
  • Proving the quadratic formula
Lesson 4
Graphing Quadratics
  • Parabolas
  • Circles
Lesson 5
Quadratic Inequalities
  • Quadratic inequalities
  • Beyond quadratics
Lesson 6
Optimizing Quadratics and AM-GM Inequality
  • Quadratic optimization
  • The AM-GM inequality
Lesson 7
Functions
  • What is a function?
  • Adding, subtracting, multiplying, and dividing functions
Lesson 8
Composition and Inverses
  • Function composition
  • Inverse functions
Lesson 9
Graphing Functions
  • Transformations
  • Graphs of inverse functions
Lesson 10
Polynomials
  • What is a polynomial?
  • Adding and multiplying polynomials
Lesson 11
Exponential Functions
  • Compound interest
  • Logarithms
Lesson 12
Special Functions Part 1
  • Radicals
  • Absolute value
Lesson 13
Special Functions Part 2
  • Floor and ceiling
  • Rational functions
  • Piecewise-defined functions
Lesson 14
Sequences & Series Part 1
  • Arithmetic sequences
  • Arithmetic series
  • Geometric sequences
Lesson 15
Sequences & Series Part 2
  • Geometric series
  • Telescoping series
Lesson 16
Challenging Problems Day
  • Self-similarity
  • Symmetry

Required Textbook

Introduction to Algebra By Richard Rusczyk
A thorough introduction for students in grades 6-9 to algebra topics such as linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and more!
Related courses: Introduction to Algebra A and Introduction to Algebra B
View Details

This is a course that never runs out of interesting problems to tackle and goes far beyond other Algebra 2 courses I've seen in the past.