#### LIVE 32: Algebra Tools

Tu/W/Th/F/M 7:30–8:45pm from 7/12 (Your Time*)

This LIVE course contains a total of 25 hours of live video instruction (~$21/hour), plus 1 year of access to Prof. Loh's recorded videos from this course.

We’ve carefully designed our courses to maximize engagement. Each of our LIVE classrooms has at least one staff member for every 13 students. The typical class size is around 30 students.

* The official meeting time for this course is 3:30pm in New York.

Diagnostic Tests:

### Calendar

Classes will meet on the highlighted dates. Click on any date to view the topics for that day.

Color Key:

Lesson on new topic

Discuss homework challenge

### Syllabus

The 20 course meetings are split in 16 lessons (called Day 1 through Day 16 below), and 4 homework exam discussions. Each exam discussion meeting happens after 4 lessons.

**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

### Co-Stars

**KIRAN REDDY**

3-time MATHCOUNTS Nationals qualifier • USAJMO qualifier since 8th grade • Tennis state champion

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**ALON RAGOLER**

National MATHCOUNTS competitor for Washington • Perfect score on AMC 8 • Enjoys web development, playing instruments (piano + snare drum)

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