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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: 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 several types of 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 one of 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 Richard Rusczyk.
Office hours held every day, where instructors and assistants provide live homework help, and a class message board, where students can ask questions and collaborate.
Weekly homework including short-answer questions and open-response writing problems, on which students receive detailed feedback.
Automated reminders for upcoming classes, reading assignments, and homework and thorough progress tracking

Why AoPS?

Live, Collaborative Instruction

Our instructors were outstanding math students themselves. Many won major math awards and earned degrees from schools like MIT, Harvard, Stanford, and Princeton. They understand from experience what our students need and serve as role models and mentors.

Active Problem Solving

The class sessions are lively interactive discussions. Students drive the narrative and ask questions right as they have them, learning complex concepts by actively solving problems, not by watching others.

Schedule: Introduction to Algebra A

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

Sunday
Oct 20 - Feb 23
7:30 - 9:00
PM ET
Oct 20 - Feb 23
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
Monday
Oct 28 - Mar 3
7:30 - 9:00
PM ET
Oct 28 - Mar 3
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
Friday
Nov 8 - Mar 14
7:30 - 9:00
PM ET
Nov 8 - Mar 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
Wednesday
Dec 11 - Apr 9
7:30 - 9:00
PM ET
Dec 11 - Apr 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
Jan 7 - Apr 22
7:30 - 9:00
PM ET
Jan 7 - Apr 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
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
ENROLL
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
ENROLL
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
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 November 25 ‐ December 1, December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, August 29 ‐ September 1, and October 31, 2025.

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.

Live vs. Self-Paced

Our live class is designed for students who wish to have a live group experience in an online classroom with instructors and peers. Students wishing to set their own schedule for their studies should should consider our self-paced version of Introduction to Algebra A.

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
View Details

Great class! I learned a whole lot! I don't think math has ever been fun before. AoPS is a great math curriculum for me. It is a more challenging than normal math, but not too challenging. I will definitely take another class!