微积分中用到的高中知识主要是函数相关知识，主要有以下几方面内容：

　　1. 函数的定义、函数的图像、分段函数、绝对值函数、定义域和值域等;

　　2. 函数的运算及复合函数，函数图像的对称性;

　　3. x的n次幂的函数、反比例函数、多项式函数、有理函数、三角函数的定义、性质和图像分析;

　　4. 反函数和反三角函数的图像和性质;

　　5. 指数函数和对数函数;

　　6. 参数方程(只是Calculus BC所要求的内容)

　　这些基础内容的讲解将主要以做题带动讲解的方式，通过一定数量的例题引导，加速学生对基础知识的回忆，为后面的微积分学习打下一定的坚实基础。

　　1. 函数的基本知识

　　1.1. Definition

　　If a variable y depends on a variable x in such a way that each value of x determines exactly one value of y, then we say that y is a function of x.

　　1.2. The vertical line test:

　　A curve in the xy-plane is the graph of some function f if and only if no vertical line intersects the curve more than once.

　　1.3. The absolute value function

　　2. 函数的运算

　　2.1. Composition of f with g

　　Given functions f and g, the composition of f with g, denoted by f ο g, is the function defined by

　　The donation of f o g is defined to consist of all x in the domain of g for which g(x) is in the domain of f.

　　2.2. Symmetry Tests

　　a) A plane curve is symmetric about the y-axis if and only if replacing x by –x in its equation produces an equivalent equation.

　　b) A plane curve is symmetric about the x-axis if and only if replacing y by –y in its equation produces an equivalent equation.

　　c) A plane curve is symmetric about the origin if and only if replacing x by –x and y by –y in its equation produces an equivalent equation

　　3. 常见的函数

　　3.1. Inverse function

　　A variable is said to be inversely proportional to a variable x if there is a positive constant k, called the constant of proportionality, such that,

　　3.2. Polynomials

　　A polynomial in x is a function that is expressible as a sum of finitely many terms of the form cxn, wherec is a constant and n is a nonnegative integar.

　　3.3. Rational function

　　A function that can be expressed as a ratio of two polynomials is called a rational function.

　　4. 反函数

　　4.1. Inverse function

　　If the function f and g satisfy the two conditions：

　　g(f(x))=x for every x in the domain of f

　　f(g(x))=y for every y in the domain of g

　　then we say that f is an inverse of g and g is an inverse of f or that f and g are inverse functions.

　　4.2. The Horizontal Line Test

　　A function has an inverse function if and only if its graph is cut at most once by any horizontal line.

　　5. 指数函数、对数函数

　　5.1. A function of the form f(x)=bx, where b>0, is called an exponential function with base b.

　　5.2. The basic characteristic of exponential function

　　5.3. The basic characteristic of logarithmic function

　　5.4. If b>0 and b≠1, then bx and logbx are inverse functions.

　　6. 参数方程

　　6.1. Definition

　　Suppose that a particle moves along a curve C in the xy-plane in such a way that its x- and y- coordinates, as functions of time, are

　　x=f(t), y=g(t)

　　We call these the parametric equations of motion for the particle and refer to C as the trajectory of the particle or the graphs of the equations. The variable t is called the parameter for the equations.

(编辑：张剑乔)