AP微积分BC考试知识点总结

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

(f

。

g)(x)=f(g(x))

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.

上海新托福精讲班多少钱？

一、整体情况

培训对象：英语基础薄弱大学生或未接触过托福考试的高中生

培训目 的：

通过对托福基础听说读写的巩固及强化训练，

帮助学员提高 托福基础和应试技巧，

顺利通过考试。

目标分 数：

80-90

分

课程时长：根据学员需要而定

课程学费：依照学员学习水平而定

二、课程安排

课程课程：主讲托福词汇、托福语 法、托福听力、托福阅读、托福口语、托福写作；

辅导课程：梳理课程知识，解疑答惑，查漏补缺；

测评课程：托福全真模考及考试分析点评；