#### LIVE 32: Algebra Tools

화ㆍ수ㆍ목ㆍ금ㆍ월 7:30pm–8:45 from 7/12(미국 동부 시간)

이 LIVE 강좌에는 라이브 동영상 강의 25시간과 함께(시간당 21) 이 강좌를 통해 1년간 이용할 수 있는 Loh 교수의 녹화 동영상이 포함되어 있습니다.

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.

진단 시험:

### 캘린더

강조 표시된 날짜에 수업이 열립니다. 날짜를 클릭해 그날의 주제를 살펴보세요.

컬러 키:

새로운 주제 수업

숙제로 주어진 시험 토론

### 교육과정

20개의 강좌 모임은 수업 16개(아래 1일차부터 16일차로 표시됨) 및 숙제 시험 토론 4개로 나뉩니다. 수업 4강 이후 각 시험 토론 모임이 열립니다.

**1일차**

Percentage problems; decimals; ratios; difference of squares; distributive property; patterns in squares; exponents; scientific notation; estimation; expressions with two variables; multiplying binomials; special numbers

**2일차**

Interpreting word problems using algebraic expressions; number patterns; solving linear equations in two variables; integer equations; distributive property

**3일차**

Functions; averages; applications of variable expressions; order of operations; distributive property; simplifying expressions; rational functions; reciprocals; inverse functions

**4일차**

Sequences; algebraic methods and Fibonacci sequence; linear equations in one variable; rational expressions; functions; rational numbers and their decimal representations

**5일차**

Arithmetic and geometric sequences and their sums; averages; parity; prime factorization; divisibility; negative integers; sum of powers of 2; common ratio

**6일차**

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

**7일차**

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

**8일차**

Repeating decimals derived from geometric sequences and fractional form of; linear equations in one variable; sum of a convergent geometric sequence

**9일차**

Word problems; systems of linear equations in two variables; substitution method; rational equations; reciprocals; change of variables; averages; number line

**10일차**

Linear equations in three variables; substitution method; adding and subtracting equations; symmetry

**11일차**

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

**12일차**

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

**13일차**

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

**14일차**

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

**15일차**

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

**16일차**

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

### 동료 스타

**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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