#### 代数工具

模块1的进阶。在MATHCOUNTS 和 AMC 8等数学竞赛中，代数问题出现的频率是其他领域问题的两倍。该课程将继续深入讲解代数知识内容，在代数基础（模块1）的基础上带领学生学习更加具有挑战性的代数内容。

想了解我们独具一格的教学方法？visit our home page first，来看看我们是如何打破线上数学课的固定框架的吧！

#### 点击开启麦克风

### 适合参加课程的学生

你是否正在上从5年级数学到代数的数学课程，并且已经了解代数基础课程中的内容？如果是的话，你已经具备了足够的能力来加入这门课。这门课将带你学习巧妙解决代数题目的方法，轻松应对比学校课本里更难的代数题目。

分级测试：

### 课程结构

每个模块的课程均包含 20节LIVE课程，分为16节【日挑战】课程和4节【周挑战测验】复习课程（学生需要在复习课前进入配套的Pre-Recorded课程完成周挑战测验）。每节课程都将由 2 位 Stars 共同授课。课程整体包含超过150个数学问题。

每节课中，学生都会学习解决全新的数学问题，老师们将通过启发式的教学引导和鼓励学生开创自己的解题方法。我们的LIVE课堂赞赏学生们提出自己的想法，鼓励每个学生和全班同学一起集思广益，构建各种不同的解题方法，更积极地参与数学发现。

【周挑战测验】包含20道数学问题，其中10题在正常难度范围内，而另外10题则非常具有挑战性。

### 回顾

really well explained!

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

really well explained!

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

really well explained!

This course shows you all the tips and tricks to not only to algebra but much more. They break it up into little pieces so you don't have to do much time every day. And whenever you have free time, boom! You can work on some math. This is coming from a fifth grader.

really well explained!

really well explained!

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### 课程大纲

**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