AP微积分BC考什么 高频考点汇总好啦

整体来看AP微积分BC的难度比AB要高出不少，所以复习时需要更用心。本文就为大家汇总一下微积分BC的常见考点，一起来看看究竟AP微积分BC考什么，让复习更有针对性吧。

AP微积分BC考什么、它和微积分AB的区别是什么？

AP微积分实际上分为两个科目，微积分AB和微积分BC。从学习内容上来看，微积分AB的知识点是被完全包括在微积分BC中的，相对难度会比较小。

对于社会科学、商科、管理类的学员，通常在大学里会需要完成两个学期以上的微积分课程，对于数学、计算机、工程、金融专业的学员更加是需要在此之后继续学习多元微积分的内容，因此推荐直接选择微积分BC。

AP微积分BC考试形式：

• 选择题45道，每道1.2分。

• 自由作答题6道,每道9分。

选择题答对得1.2分，答错或者不答题，不倒扣分。

AP微积分BC考什么？高频考点重点汇总

微积分的考试，函数是重点，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)

接下来让我们详细分解一下以上内容：

　　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.

AP微积分BC考什么相关信息就分享到这里啦。AP微积分BC的复习是非常重要的，因为考试的答题节奏很紧张，如果复习阶段没有训练好考试状态，将面临会答题也来不及答的无奈，更不用说冲刺知名大学要求的满分了。

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