Algebra Tools

Since algebraic problems appear twice as frequently as other subjects on MATHCOUNTS and AMC 8, this course makes a second pass at algebra, covering more advanced topics that Algebra Basics (Module 1) did not have time for.

If you haven't yet seen our revolutionary teaching method, visit our home page first, to shatter your expectations of what online math looks like.

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Who Is This Course For?

Are you taking any math class from 5th Grade Math through Algebra, and already know the content in our Algebra Basics class? If so, you are already ready to understand this course. It will teach many Algebra topics with creative methods that go beyond the curriculum.

Diagnostic Tests:

Will I understand?Will I learn new things?

Course Structure

This course contains 20 LIVE 1-hour video sessions, of which 16 are lessons, and 4 are exam review sessions that discuss the course's 4 practice 1-hour exams (homework). Each class is co-taught by 2 of our Stars. In total, there are over 150 problems.

Each lesson contains several problems which are meant to be unfamiliar to you, so that they inspire you to invent your own solutions. In our LIVE video class format, you propose your ideas, and we brainstorm together with you to construct a variety of alternative solutions using the class's own ideas. This actively involves you in discovering mathematics.

Each practice exam contains 20 problems, of which half are of average difficulty, and the other half are very challenging.

Reviews

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

RT

this is so good it is not boring and very engaging

AC

It’s great, I can understand and I am learning new ways of solving this question.

EC

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

MF

AMAZING

AQ

The class is going super smoothly and nicely. I can follow along easily and the teachers are all really nice.

NZ

It's good, everything make sense

EP

It's really suitable for people who find math boring at first (just like me), this course really gives me the passion for learning and exploring math!

PG

VERY GOOD AND INTERESTING!!!!!!

Syllabus

Day 1

Percentage problems; decimals; ratios; difference of squares; distributive property; patterns in squares; exponents; scientific notation; estimation; expressions with two variables; multiplying binomials; special numbers

Day 2

Interpreting word problems using algebraic expressions; number patterns; solving linear equations in two variables; integer equations; distributive property

Day 3

Functions; averages; applications of variable expressions; order of operations; distributive property; simplifying expressions; rational functions; reciprocals; inverse functions

Day 4

Sequences; algebraic methods and Fibonacci sequence; linear equations in one variable; rational expressions; functions; rational numbers and their decimal representations

Day 5

Arithmetic and geometric sequences and their sums; averages; parity; prime factorization; divisibility; negative integers; sum of powers of 2; common ratio

Day 6

Simplifying radicals and rational expressions; square roots; nested square root expressions; multiplying binomials; nonlinear equations in two variables; integer expressions; word problems; difference of squares; common denominator

Day 7

Exponents, multiplying and dividing exponents; n-th roots; derivation of definition of fractional powers; estimation; geometric sequences; common ratio; derivation of formula for geometric mean

Day 8

Repeating decimals derived from geometric sequences and fractional form of; linear equations in one variable; sum of a convergent geometric sequence

Day 9

Word problems; systems of linear equations in two variables; substitution method; rational equations; reciprocals; change of variables; averages; number line

Day 10

Linear equations in three variables; substitution method; adding and subtracting equations; symmetry

Day 11

Quadratic equations; factoring methods; multiplying binomials; distributive property; zero product rule; sum and product of the solutions of a quadratic and Viète's formulas; change of variables; reciprocals

Day 12

Derivation of Loh method of solving quadratic equations and applications to word problems; roots of an equation; ratios and proportion; area; sum and product of roots of a quadratic; golden ratio; difference of squares

Day 13

Graphing; definition of axes, origin, and coordinates; perpendicular angles and bisectors; rotation; system of linear equations with two variables; midpoints; slope-intercept form; slope of a line; x- and y- intercepts

Day 14

Graphing; intersection point of two lines; x- and y-intercepts; similar triangles; ratios; rotations of lines; systems of equations with two variables; sum of angles in a triangle; distance between a point and a line

Day 15

Right isosceles triangles; Pythagorean Thm; slope-intercept form of the equation of a line; coordinates; distance between two points; point equidistant from two other points; perpendicular bisector

Day 16

Graph of a parabola; tangent line to a curve; coordinates; slope and approximating slope; multiplying binomials; decimals; graph of the square root function; inverse functions; reflection of a curve

Enroll

We have LIVE and self-paced versions of this course. We strongly recommend the LIVE format, as it has been carefully designed to be so engaging that students fall in love with challenge. There has never been anything like it before. All times are listed in your local time zone.

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Su 12:30–1:45am from 11/10

Algebra Tools (Module 4)

view $519

For students who want to learn a subject sooner than a LIVE course matches their schedule, our self-paced version contains all of Prof. Loh's teaching on the subject (without live teaching). This is available on our self-paced course platform, where thousands of students have learned over the past 3 years.