In the study day after day, everyone has recited all kinds of knowledge points, right? Knowledge point is the basic unit of transmitting information and plays an important role in improving learning navigation. So, what are the knowledge points? The following is a summary of senior three mathematics knowledge points compiled by Bian Xiao for everyone, for reference only, hoping to help everyone.
Senior three mathematics knowledge points induction article 1
Sorting out the knowledge points of mathematics in the first volume of senior three.
1, the concept of function zero: for a function, the real number that makes it true is called the zero of the function.
2. The meaning of the zero point of the function: the zero point of the function is the real root of the equation, that is, the abscissa of the intersection of the image of the function and the axis. Namely:
The equation has a real root function, the image has an intersection with the axis, and the function has a zero point.
3, the role of zero solution:
Find the zero point of a function:
(1) (algebraic method) to find the real root of the equation;
(2) (Geometric method) For the equation that cannot be solved by the root formula, we can relate it with the image of the function and use the properties of the function to find the zero point.
4. Zero point of quadratic function:
Quadratic function.
1)△& gt； 0, the equation has two unequal real roots, the image of the quadratic function has two intersections with the axis, and the quadratic function has two zeros.
2)△=0, the equation has two equal real roots (multiple roots), the image of the quadratic function intersects with the axis, and the quadratic function has a double zero or a second-order zero.
3)△
Summary of Mathematics Knowledge Points in Senior Three of People's Education Press
1. Definition:
Use the symbols >, =, 1? ; = 1? ;
Can be summarized as: differential method, commercial method, intermediate method and so on.
3. The nature of inequality
(1) symmetry: A >；; b？ ;
(2) Transitivity: a>b, b>c? ;
(3) additivity: a>b? a+cb+c，a & gtb，c & gtd？ a+c b+ d；
(4) Availability: a>b, c>0? Ac> BC; a & gtb & gt0，c & gtd & gt0? ;
(5) Multiplier: a>b>0? (n∈N，N≥2)；
(6) Prescription: a>b>0? (n∈N，n≥2)。
Review guide
1. "One skill" is the skill of difference method deformation: deformation is the key in difference method, and factorization or formula is often carried out.
2. "One Method" undetermined coefficient method: When calculating the range of algebraic expression, the known algebraic expression is used to represent the target expression, then the parameters are obtained by using the principle of polynomial equality, and finally the range of the target expression is obtained by using the properties of inequality.
3. "Two common attributes"
(1) Reciprocity:1a > b，ab & gt0? 3a & gtb & gt0,0; 40
(2) If a>b>0, m>, then 0
The properties of the true fraction of 1;
(b-m & gt； 0);
The fifth chapter summarizes the knowledge points of mathematics in senior three.
Solution set of inequality;
The value of 1 that can make the inequality hold is called the solution of the inequality.
All the solutions of an inequality with unknowns constitute the solution set of this inequality.
The process of finding the solution set of inequality is called solving inequality.
Determination of inequality:
1 Common inequalities are ">" inequality "2" in "a >"; "b" or "a"
3. There are many openings with different numbers, but few tips with different numbers;
When enumerating inequalities, we must pay attention to the key words of inequality relations, such as positive number, non-negative number, not greater than, less than and so on.
Senior three mathematics knowledge points induction 6
Properties of the equation:
The properties of 1 inequality can be divided into two parts: the basic properties of inequality and the operational properties of inequality.
The basic properties of inequality are:
( 1)a & gt； bb
(2)a & gt； B, b & gtca & gtc (transitivity)
(3)a & gt； ba+c & gt； b+c(c∈R)
(4)c & gt； 0, a & gtbac & gt BC
c
Binary-to-analog conversion (abbreviation for binary analogue convert)
Operational attributes include:
( 1)a & gt； b，c & gtda+c & gt； b+d .
(2)a & gt； b & gt0，c & gtd & gt0ac & gtbd .
(3)a & gt； b & gt0an & gtbn(n∈N，n & gt 1)。
(4)a & gt； b & gt0 & gt(n∈N，n & gt 1)。
It should be noted that there are two logical relationships between conditions and conclusions in the above properties: deductive relationship and equivalent relationship. Generally speaking, proving inequality is a series of deductive transformations based on conditions. Solving inequality is to implement a series of equivalent transformations. Therefore, we should correctly understand and apply the properties of inequality.
2. Regarding the investigation of the nature of inequality, there are mainly the following three questions:
(1) According to the given inequality conditions, use the properties of inequality to judge whether inequality is established.
(2) Using the properties of inequality, real number and function to judge the size of real number.
(3) Using the nature of inequality, judge the sufficient or necessary relationship between conditions and conclusions in inequality transformation.
High school mathematics highlights review knowledge points
Any a, b, marked AB.
AB，BA，A=B
AB={|A|, and |B|}
AB={|A|, or |B|}
Card (AB)= Card (A)+ Card (B)- Card (AB)
(1) proposition
If the original proposition is p, then q
If q is the inverse proposition of p
If p is q, there is no proposition.
If the negative proposition is q, then p.
(2)AB, A is a sufficient condition for B.
BA and a are necessary conditions for the establishment of B.
AB and A are the necessary and sufficient conditions for the establishment of B.
1. The set element has the certainty of 1; 2 mutual anisotropy; 3 disorder
2. Set representation 1 enumeration method; ② Description method; 3 Wayne diagram; Four-axis method
(3) Unit operation
1A∩(B∪C)=(A∪B)∩(A∪C)
2Cu(A∩B)=CuA∪CuB
Cu(A∪B)= CuA∪CuB
(4) the nature of the set
Number of word sets in N-tuple set: 2n
Proper subset number: 2n-1;
Nonempty proper subset number: 2n-2.
Induction of knowledge points of high school mathematics set
1, the concept of set
Set is the most primitive undefined concept in mathematics, which can only give a descriptive explanation: some formulaic and different objects are called sets together. The objects that make up a set are called elements, and the set is usually represented by uppercase letters A, B, C,. Elements are usually represented by lowercase letters A, B, C and.
A set is a definite whole, so it can also be described as a set composed of all objects with certain attributes.