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Prealgebra 2

Summary

Our Prealgebra 2 course builds off the concepts mastered in Prealgebra 1 by introducing percents and square roots, delving into a thorough exploration of geometric tools and strategies, and providing an introduction to topics in discrete mathematics and statistics, while continuing to facilitate discussion of general problem-solving strategies.

Prealgebra 2 is available both as a live course and as a self-paced course. Our self-paced courses allow students to advance through lessons on their own schedule, with automated interactive instruction replacing live class meetings. Both versions provide instructor feedback on student work, as well as office hours and a class message board for accessible support.

Required Text: Prealgebra

Prealgebra 2: 16 Weeks

Our live Prealgebra 2 course brings bright young mathematicians together to meet with an experienced instructor and assistants for 75-minute sessions. Students refine their skills with several types of homework problems and refer to our Prealgebra textbook and videos as resources. 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
Weekly homework assignments with challenging short-answer problems and practice on Alcumus, our adaptive online learning system
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 and ask their instructors questions
Office hours every day, where AoPS instructors and teaching assistants answer student questions live through the class message board
Weekly assigned readings in our Prealgebra textbook
Over 80 videos by AoPS founder and Prealgebra co-author Richard Rusczyk
Detailed reporting that allows students and parents to track their progression 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 the best universities in the nation. They understand from their personal experiences how to galvanize eager learners, and they serve as role models for students who aspire to similar success.

Active Learning

Students learn best by tackling hard problems themselves, not by watching others do the work. In our classes, instructors start with questions, challenging the students to find the key insights on their own. This helps students learn how to generate new ideas and develop new skills as needed, though teachers and assistants also provide hints and direct instruction when students get stuck. Once students have the solution, the instructors reinforce important concepts and strategies and move on to the next problem.

Focus on Non-Routine, Challenging Problems

Successful people in the next generation will need to develop new skills throughout their careers as their older skills become obsolete. To prepare our students for this challenging future, we show students how to apply fundamentals to different types of problems, not just variations on the same problem they’ve seen before. Our students will be ready for the rigors of top-tier colleges and internationally competitive careers because they have been taught how to learn.

Multiple Learning Avenues

Students learn in many ways, so we teach through multiple avenues. In addition to the live classes, our students can read the Prealgebra textbook, watch videos, solve many different types of homework problems, and participate in mathematical conversations with instructors and other students on the class message board.

Schedule: Prealgebra 2

The current and upcoming sections of our live Prealgebra 2 course are listed below. All sections cover the same course material.

Sunday
Oct 27 - Mar 2
7:30 - 8:45
PM ET
Oct 27 - Mar 2
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
CLOSED
Thursday
Nov 7 - Mar 13
7:30 - 8:45
PM ET
Nov 7 - Mar 13
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Monday
Dec 2 - Mar 31
7:30 - 8:45
PM ET
Dec 2 - Mar 31
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Wednesday
Jan 8 - Apr 23
7:30 - 8:45
PM ET
Jan 8 - Apr 23
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Sunday
Jan 19 - May 4
1:00 - 2:15
PM ET  
Jan 19 - May 4
1:00 - 2:15 PM Eastern
12:00 - 1:15 PM Central
11:00 - 12:15 PM Mountain
10:00 - 11:15 AM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Monday
Jan 27 - May 12
7:30 - 8:45
PM ET
Jan 27 - May 12
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Tuesday
Jan 28 - May 13
4:30 - 5:45
PM ET  
Jan 28 - May 13
4:30 - 5:45 PM Eastern
3:30 - 4:45 PM Central
2:30 - 3:45 PM Mountain
1:30 - 2:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Sunday
Feb 16 - Jun 8
7:30 - 8:45
PM ET
Feb 16 - Jun 8
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Tuesday
Mar 25 - Jul 8
7:30 - 8:45
PM ET
Mar 25 - Jul 8
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Sunday
Apr 13 - Aug 10
7:30 - 8:45
PM ET
Apr 13 - Aug 10
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 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?

This course is designed for students who enjoy math and have completed either our Prealgebra 1 course or its equivalent. Students can determine if their previous mathematical experience has prepared them for the course by taking the Prealgebra 2 "Are You Ready?" diagnostic test to see if they are prepared to take this course. Students who are finishing our Beast Academy curriculum should take our Prealgebra 1 course prior to taking Prealgebra 2. Students who wish to pursue studies at their own pace or cannot attend the live class times should consider our self-paced version of Prealgebra 2.

Lessons

Show All Topics
Lesson 1
Introduction to Percents
  • Definition of percent
  • Relationships among percents, fractions, and decimals
  • Percents of numbers
  • Basic percent word problems
Lesson 2
Percent Increase and Decrease
  • More percent word problems
  • Percentage increase and decrease
Lesson 3
Squares and Square Roots
  • Definition of square root
  • Equations with square roots
  • Non-integer square roots
Lesson 4
Arithmetic with Square Roots
  • Products and quotients of square roots
  • Simplification of square roots
  • Sums and differences of square roots
Lesson 5
Angles and Parallel Lines
  • Angle measurement
  • Parallel lines
Lesson 6
Angles in Polygons
  • Angles in a triangle
  • Angles in other polygons
Lesson 7
Perimeter and Area
  • Segments and perimeter
  • Rectangle and right triangle area
Lesson 8
More Triangles and Circles
  • Triangle area
  • Circumference of a circle
  • Area of a circle
  • Unusual areas
Lesson 9
Pythagorean Theorem
  • Pythagorean Theorem fundamentals
  • Pythagorean triples
Lesson 10
Special Triangles
  • Challenging Pythagorean Theorem problems
  • 30-60-90 and 45-45-90 triangles
Lesson 11
Quadrilaterals
  • Types of quadrilaterals
  • Quadrilateral area
Lesson 12
Basic Statistics
  • Average (mean)
  • Averages as a balancing act
  • Median, mode, and range
Lesson 13
Statistics, Graphs, and Charts
  • Limits of basic statistics
  • Types of graphs and charts
Lesson 14
Counting as Arithmetic
  • Numbers in lists
  • Venn diagrams
  • Multiplication principle
  • Casework
Lesson 15
Counting and Probability
  • Pairs
  • Introduction to probability
Lesson 16
Problem-Solving Strategies
  • Find a pattern
  • Make a list
  • Draw a picture
  • Work backwards

Required Textbook

Prealgebra By Richard Rusczyk, David Patrick, Ravi Boppana
Prealgebra prepares students for the rigors of algebra and also teaches students problem-solving techniques to prepare them for prestigious middle school math contests such as MATHCOUNTS, MOEMS, and the AMC 8. The text is written to challenge students at a much deeper level than a traditional middle school prealgebra course.
Related courses: Prealgebra 1 and Prealgebra 2
View Details

I really loved taking the Prealgebra courses! They were so insightful and helped me understand and think in ways that I normally don't. I like that when I ask for help with, say, a free-response question, the moderators/instructors/teachers don't just tell me what the answer is; they lead me to figure out the answer. A friend of mine told me about the course because she takes it too. I'm really glad she did, because it helps me understand, not just blindly accept, things that I didn't get before. Thank you, AoPS!