#### 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.

#### Click to Unmute

### 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:

### 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

really well explained!

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.

really well explained!

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.

really well explained!

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.

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### 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 will offer the LIVE version of this course in Summer 2023.

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.