High school mathematics compulsory one key knowledge summary one, collect related concepts
The meaning of 1. set
2. Three characteristics of elements in a set:
The certainty of (1) element is as follows: the highest mountain in the world.
(2) The mutual anisotropy of elements, such as the set of happy letters {H, a, p, Y}.
(3) The disorder of elements: for example, {a, b, c} and {a, c, b} represent the same set.
3. Representation of assembly: {…} For example, {basketball players in our school}, {Pacific Ocean, Atlantic Ocean, Indian Ocean, Arctic Ocean}
(1) The set is expressed in Latin letters: A={ basketball players in our school}, B={ 1, 2, 3, 4, 5}.
(2) Representation of sets: enumeration and description.
Note: Common number sets and their expressions: XKb 1. Com
The set of nonnegative integers (i.e. natural number set) is recorded as n.
Positive integer set: N* or N+
Integer set: z
Rational number set: q
Real number set: r
1) enumeration: {A, b, C...}
2) Description: describes the common attributes of the elements in the set, and is written in braces to indicate the set {x? r | x-3 & gt； 2}，{ x | x-3 & gt； 2}
3) Language description: Example: {A triangle that is not a right triangle}
4) Venn diagram:
4, the classification of the set:
The (1) finite set contains a set of finite elements.
(2) An infinite set contains an infinite set of elements.
(3) The empty set does not contain any elements.
Example: {x | x2 =-5}
Second, the basic relationship between sets
1. "Inclusive" relation-subset
Note: There are two possibilities that A is a part of B (1); (2)A and B are the same set.
On the other hand, set A is not included in set B, or set B does not include set A, which is marked as AB or BA.
2. "Equality" relationship: A=B(5≥5 and 5≤5, then 5=5)
Example: let a = {x | x2-1= 0} b = {-1,1} "Two sets are equal if their elements are the same".
Namely: ① Any set is a subset of itself. Answer? A
② proper subset: If a? B and a? B then says that set A is the proper subset of set B, and it is denoted as AB (or BA).
3 if a? B，B？ C, then a? C
4 if a? At the same time? Then A=B
3. A set without any elements is called an empty set and recorded as φ.
It is stipulated that an empty set is a subset of any set and an empty set is a proper subset of any non-empty set.
4. Number of subsets:
A set with n elements, including 2n subsets, 2n- 1 proper subset, 2n- 1 nonempty subset and 2n- 1 nonempty proper subset III. Set operation.
Intersection, Union and Complement of Operation Types
Define a set consisting of all elements belonging to A and B, which is called the intersection of A and B, and it is marked as AB (pronounced as' A crosses B'), that is, AB={x|xA, and XB}.
A set consisting of all elements belonging to set A or set B is called the union of A and B, and it is marked as AB (pronounced as' A and B'), that is, AB={x|xA, or xB}).
The above is a compulsory knowledge point of senior one mathematics shared with students today. Senior one is the most basic year of senior three. Only by laying a solid foundation and adding bricks and tiles, will it not be loose, especially the knowledge points of senior one mathematics. There are many in each chapter. Learn to preview and summarize, and it will be easier and easier to learn in the future!
What are the learning methods of high school mathematics? 1. Read your notes first, then do your homework. Some high school students think. I heard what the teacher said clearly. But why is it so difficult to do the problem by yourself? The reason is that students' understanding of what the teacher said did not reach the level required by the teacher. Therefore, before you do your homework every day, you must take a look at the relevant contents of the textbook and the class notes of that day. Whether you can stick to this point is often the biggest difference between good students and poor students. Especially when the exercises are not matched, there are often no questions in the homework that the teacher just talked about, so it is impossible to compare and digest them. If we don't pay attention to this realization, it will cause great losses over time.
2. Strengthen reflection after doing the questions. Students must make it clear that the topic they are sitting on is definitely not the topic of the exam. But to use ideas and methods to solve the problems we are doing now. Therefore, we should reflect on every question we have done. Sum up your gains. To sum up, this is a question of what content and how to use it. Make knowledge into pieces, problems into strings, accumulate over time, and build a scientific network content and method system.
3. Take the initiative to review, summarize and improve. It is very important to summarize the chapters. In junior high school, it is the teacher who gives the students a summary, which is meticulous, profound and complete. In the third year of senior high school, I made my own summary, but the teacher not only refused to do it, but also said where to take the exam, where to take the exam, leaving no review time, and did not clearly point out the time to make the summary.
What are the answering skills in high school mathematics? 1. Choose a topic and avoid sea tactics. Only by solving high-quality and representative problems can we get twice the result with half the effort. However, the vast majority of students have not been able to distinguish and analyze the quality of the questions, so they need to choose exercises to review under the guidance of teachers to understand the form and difficulty of the college entrance examination questions.
2. Analyze the problem carefully, and analyze it before solving any math problem. Analysis is more important than more difficult topics. We know that solving mathematical problems is actually to build a bridge between known conditions and conclusions to be solved, that is, to eliminate these differences on the basis of analyzing the differences between known conditions and conclusions to be solved. Of course, in this process, it also reflects the proficiency and understanding of the basic knowledge of mathematics and the flexible application ability of mathematical methods.
3. Make a summary of the topic. Solving problems is not the goal. We test our learning effect by solving problems, and find out the shortcomings in learning, so as to improve and improve. So the summary after solving the problem is very important, which is a great opportunity for us to learn.