Commonly used equivalent infinitesimal:
Basic derivative formula:
Summary of two knowledge points in advanced mathematics.
Chapter 1: Function and Limit.
1. Understand the concept of function and master the representation method of function.
2. The functional relationship in simple application problems will be established.
3. Understand the parity, monotonicity, periodicity and boundedness of functions.
4. Master the nature and graphics of basic elementary functions.
5. Understand the concepts of compound function and piecewise function, inverse function and implicit function.
6. Understanding the concept of function continuity (including left continuity and right continuity) will distinguish the types of function discontinuity.
7. Understand the concept of limit, the concepts of left limit and right limit of function, and the relationship between the existence of limit and left and right limit.
8. Master two criteria for the existence of limit, and use them to find the limit, and master the method of using two important limits to find the limit.
9. Master the limit properties and four algorithms.
10. Understand the concept of infinitesimal, master the comparison method of infinitesimal, and find the limit with equivalent infinitesimal.
Chapter 2: Derivative and differential.
1. Understand the concepts of derivative and differential, understand the relationship between derivative and differential, understand the geometric meaning of derivative, find the tangent equation and normal equation of plane curve, understand the physical meaning of derivative, describe some physical quantities with derivative, and understand the relationship between function derivability and continuity.
2. Mastering the four algorithms of derivative and the derivative law of compound function, mastering the derivative formula of elementary function, and knowing the invariance of the four algorithms of differential and the first-order differential form, we can find the differential of elementary function.
3. Find the derivative and inverse function of the function determined by implicit function and parametric equation.
4. Know the derivative of piecewise function, understand the concept of higher derivative, and know the higher derivative of simple function.
Summary of two knowledge points in advanced mathematics.
The math problem-solving part of the college entrance examination mainly examines seven main knowledge:
First, functions and derivatives. This paper mainly examines the related concepts such as set operation, function definition domain, range, analytical formula, limit, function continuity, derivative and so on.
Second, plane vector and trigonometric function, trigonometric transformation and its application. This part is the focus of the college entrance examination, but it is not difficult. It mainly contains some basic or intermediate problems.
Thirdly, sequence and its application. This part is the key and difficult part of the college entrance examination, which mainly produces some comprehensive questions.