代数工具图标

LIVE 34: 代数工具

一、四19:00–20:15从9月12日 (美国东部时间)

报名课程 $459课程详细介绍

该模块直播课总计25小时,课时费约为(~$18/小时)。报名直播课将同时享受该模块对应录播课程(Pre-Recorded Course)一年有效,无限次回看。

课程日历

上课日期由彩色图例标识。点击任意上课日期了解当天课程内容。

图例

16节日挑战课程,每节课通过不同的数学问题学习新的知识内容

4节周挑战复习课程,集中解决周挑战测试中遇到的问题

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课程大纲

LIVE在线直播课程每个模块包含16次日挑战Session(第1课到第16课)+ 4次周挑战复习课(Weekly Challenge 1到4)共20节课程。每四节日挑战Session结束后将有一次周挑战复习课,学生需要在复习课前进入Pre-Recorded课程完成周挑战测验。

第1课

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

第2课

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

第3课

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

第4课

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

第5课

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

第6课

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

第7课

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

第8课

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

第9课

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

第10课

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

第11课

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

第12课

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

第13课

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

第14课

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

第15课

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

第16课

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

启明星助教老师

Lillian Xia 的头像
LILLIAN XIA

入选AIME资格赛 • 入选MPFG资格赛 • 喜欢打网球

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Jesse Brodtman 的头像
JESSE BRODTMAN

州级别数学竞赛项目领队 • 全国级别数学竞赛前六名 • USACO(美国计算机奥林匹克)铜牌满分获得者 •

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