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LIVE 114: Algebra Tools

Su 12:00–1:15am from 3/3 (Your Time*)

Enroll $459Full Course Details

This LIVE course contains a total of 25 hours of live video instruction (~$18/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 8:00am in China.

Diagnostic Tests:

Will I understand?Will I learn new things?

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 exam assigned for homework

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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

Profile picture for Jessie Wang
JESSIE WANG

USAJMO Qualifier • MPFG Qualifier • Attended MATHCOUNTS State (TX) twice • Enjoys watching hockey

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Profile picture for Daniel He
DANIEL HE

USA(J)MO Qualifier • MATHCOUNTS team coach • Plays cello

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Refund Policy

No refund requests will be accepted after the student’s second LIVE session starts; Refund amount: 75% refund in the original payment method or 100% refund in course credits.