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Introduction to Algebra B Self-Paced

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: Self-Paced

Length: 70 Lessons

In our self-paced Introduction to Algebra B course, students proceed at their preferred pace through a series of automated mathematical conversations. For the independently motivated learner, interactive automated instruction replaces live class meeting times.

Self-paced math classes offer live interaction through the class message board, where students can collaborate with peers and get support from instructors. We reinforce lessons with our Introduction to Algebra textbook and videos, as well as multiple types of homework problems.

Although many students complete Algebra B in 3–6 months, we offer unlimited class access for 9 months.

$485 $552 w/books

What's Included?

70 interactive lessons featuring lively, adaptive mathematical conversations to help students deepen their understanding
More than 100 supplementary videos from AoPS founder and Introduction to Algebra co-author Richard Rusczyk, providing expert insights and guidance
Scheduling tools that allow students to set their preferred study hours each week, ensuring that activities are aligned with their personal schedule
Class message board where students can collaborate with peers, ask questions, and receive support from instructors and teaching assistants outside of class time
Periodic homework assignments including challenging short-answer problems, assigned readings from our Introduction to Algebra textbook, and personalized practice through our adaptive online learning system, Alcumus
Detailed instructor evaluation of students' written solutions to open-response problems, designed to enhance mathematical writing and problem-solving skills
Comprehensive reporting that allows students and parents to track progress and performance throughout the course

Why AoPS?

Innovative Interactive Instruction

In our self-paced courses, students progress through interactive lessons that engage them in mathematical conversations, guiding them step-by-step and addressing common misconceptions. Students learn in various ways, so we offer multiple learning avenues: interactive lessons, a textbook, videos, diverse homework problems, and opportunities to engage in discussions with instructors and peers on the class message board.

Active Learning

Learning is not a spectator sport, and students learn best by tackling hard problems themselves. Our lessons start with challenging questions to help students develop new mathematical strategies. If students get stuck, our learning technology supplies helpful hints and adapts lesson structure to further reinforce key concepts.

Focus on Non-Routine, Challenging Problems

To prepare our students for the challenges of tomorrow, we teach them how to apply fundamentals to different types of problems, not just variations on the same problem they’ve seen before. Building a critical problem-solving skill set, our students are prepared for the rigors of top-tier colleges and internationally competitive careers.

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 (at least chapters 1-9) 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.

Self-Paced vs. Weekly Live

Our self-paced class is designed for students who prefer to set their own study schedule. In this format, students can engage with peers and receive support from staff through the class message board. For students interested in a live group experience with real-time interactions in an online classroom setting, we recommend considering the weekly live version of this course.

Chapters

Show All Topics
Chapter 10
Quadratic Equations - Part 1
  • Factoring quadratics
  • Sums and products of roots of a quadratic
    Chapter 11
    Special Factorizations
    • Difference of squares
    • Sum and difference of cubes
    • Simon's favorite factoring trick
    Chapter 12
    Complex Numbers
    • What are complex numbers?
    • Complex number arithmetic
    Chapter 13
    Quadratic Equations - Part 2
    • Completing the square
    • The quadratic formula
    Chapter 14
    Graphing Quadratics
    • Parabolas
    • Circles
    Chapter 15
    Quadratic Inequalities
    • Quadratic inequalities
    • Quadratic optimization
    Chapter 16
    Functions
    • What are functions?
    • Combining functions
    • Inverse functions
    Chapter 17
    Graphing Functions
    • Transformations
    • Graphs of inverse functions
    Chapter 18
    Polynomials
    • What is a polynomial?
    • Adding and multiplying polynomials
    Chapter 19
    Exponents and Logarithms
    • Exponential functions
    • Compound interest
    • Logarithms
    Chapter 20
    Special Functions
    • Radicals
    • Absolute value
    • Floor and ceiling
    • Rational functions
    • Piecewise-defined functions
    Chapter 21
    Sequences and Series
    • Arithmetic sequences and series
    • Geometric sequences and series
    • Telescoping series
    Chapter 22
    Special Manipulations
    • 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
    $485 $552 w/books

    The class gave me an excellent understanding of what was covered in the course, especially functions and parabolas. The methods that this class used has brought me very far in my mathematical knowledge. Compared to even the one of the best private schools in my city, this class is ridiculously far ahead of the other math courses. I would recommend this to anyone who has an urge to know more about algebra.