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LIVE 34: Algebra Tools

M/Th 7:00–8:15pm from 9/12 (USA Eastern 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.

Calendar

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

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Lesson on new topic

Discuss exam assigned for homework

Sep 2022
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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

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LILLIAN XIA

MPFG Invite • AIME Qualifier • Enjoys playing tennis

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JESSE BRODTMAN

Leader of state-wide math competition program • Placed top 6 in national math competitions • Perfect score on USACO bronze

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