AP微积分BC考试知识点总结_ap微积分考点总结

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AP微积分BC考试知识点总结

AP微积分BC中用到的高中6大知识点总结，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.三立教育www.daodoc.com

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 三立教育www.daodoc.com

A polynomial in x is a function that is expreible 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 expreed 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 三立教育www.daodoc.com

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；三立教育www.daodoc.com

三、模考安排

第一次：课程中间，安排一次托福全真模拟考试及点评