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Introduction to Algebra A

Summary

In this online class, students proactively engage with the fundamental concepts of algebra. Part of our introductory math series, Introduction to Algebra A builds on the foundations of both Prealgebra 1 and Prealgebra 2.

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

Introduction to Algebra A: Weekly Live

Length: 16 Weeks

Our live Introduction to Algebra A course brings together advanced problem solvers from around the world for 90-minute classes. Experienced instructors lead students to creatively problem-solve with exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, factoring quadratics, complex numbers, completing the square, and the quadratic formula.

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 with challenging short-answer problems, assigned readings, and practice on our adaptive online learning system, Alcumus
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 A

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

Wednesday
Jan 29 - May 14
7:30 - 9:00
PM ET
Jan 29 - May 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
CLOSED
Sunday
Feb 16 - Jun 8
3:30 - 5:00
PM ET  
Feb 16 - Jun 8
3:30 - 5:00 PM Eastern
2:30 - 4:00 PM Central
1:30 - 3:00 PM Mountain
12:30 - 2:00 PM Pacific
Click here to see more time zones
$485 (~$31/lesson)
$552 w/books
$485 (~$31/lesson)
$552 w/books
CLOSED

STARTING SOON

Sunday
Mar 23 - Jul 20
7:30 - 9:00
PM ET
Mar 23 - Jul 20
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
Monday
Apr 7 - Jul 28
7:30 - 9:00
PM ET
Apr 7 - Jul 28
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
May 11 - Sep 14
1:00 - 2:30
PM ET  
May 11 - Sep 14
1:00 - 2:30 PM Eastern
12:00 - 1:30 PM Central
11:00 - 12:30 PM Mountain
10:00 - 11:30 AM Pacific
Click here to see more time zones
$485 (~$31/lesson)
$552 w/books
$485 (~$31/lesson)
$552 w/books
ENROLL
Wednesday
May 14 - Aug 27
7:30 - 9:00
PM ET
May 14 - Aug 27
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
May 30 - Sep 26
7:30 - 9:00
PM ET
May 30 - Sep 26
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
Monday
Jun 2 - Sep 22
7:30 - 9:00
PM ET
Jun 2 - Sep 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
ENROLL
Sunday
Jun 15 - Oct 12
7:30 - 9:00
PM ET
Jun 15 - Oct 12
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
Thursday
Jun 26 - Oct 9
7:30 - 9:00
PM ET
Jun 26 - Oct 9
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
Jul 15 - Oct 28
7:30 - 9:00
PM ET
Jul 15 - Oct 28
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?

Before taking this course, students should master arithmetic with fractions, decimals, percents, negative numbers, and integer exponents.

Most students who have completed a typical Prealgebra course are ready for this course. Students finishing our Beast Academy curriculum should take Prealgebra 1 and Prealgebra 2 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. This course covers much of the algebra of a typical honors Algebra 1 course, some of the content of an honors Algebra 2 course, and some additional material not taught in most standard curricula. 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
Follow the Rules
  • Rules of arithmetic
  • Distribution and factoring with numbers
  • Exponent rules
Lesson 2
Fractional Exponents, Radicals, and Variables
  • Fractional exponents and radicals
  • Variables in expressions
  • Simplifying expressions
Lesson 3
Variables and Expressions
  • Distribution and factoring with variables
  • Expressions with fractions
  • Expressions with radicals
Lesson 4
Linear Equations
  • Solving linear equations
  • Word problems
Lesson 5
More Variables
  • Evaluating expressions with multiple variables
  • Manipulating expressions
Lesson 6
Linear Equations with Multiple Variables
  • Basic manipulations
  • Substitution and Elimination
  • Word Problems
Lesson 7
Ratio and Percent
  • Ratios
  • Parts and wholes
  • Percentages and arithmetic with percents
Lesson 8
More Ratios and Proportion
  • Working with units
  • Direct and inverse proportion
  • Joint proportion
Lesson 9
Common Errors and Challenging Problems
  • Exponents do not distribute over addition
  • Extraneous solutions and dividing by zero
  • Difficult problems
Lesson 10
Graphing Lines (Part 1)
  • Cartesian plane
  • Distance between two points
  • Graphs of equations
  • Going from lines to equations
Lesson 11
Graphing Lines (Part 2) and Introduction to Inequalities
  • Perpendicular and parallel lines
  • How graphing relates to systems of equations
  • Inequality manipulation and interval notation
Lesson 12
Graphing Inequalities
  • Two variable inequalities
  • Graphing to solve inequalities
  • Optimization and linear programming
Lesson 13
Quadratic Equations (Part 1)
  • Distributing
  • Factoring
Lesson 14
Special Factorizations
  • Vieta’s formulas
  • Difference of squares
  • Sum and difference of cubes
Lesson 15
Simon's Favorite Factoring Trick and Complex Numbers
  • Completing the rectangle
  • Introduction to complex numbers and arithmetic
Lesson 16
Quadratic Equations (Part 2)
  • Completing the square
  • The quadratic formula

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
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I really enjoyed this course...I don't think any other Algebra 1 would have kept me as busy and challenged as this one.