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 (~$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 a 1:13 staff to student ratio, with a maximum of 40 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 exam assigned for homework
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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