Senior one mathematics sets up knowledge points and explains examples 1 to understand special concept elements.
A set is determined by an element. The representation, classification and operation of sets are also characterized by elements. So although there are many concepts and relationships in the set, as long as we grasp the core concept of element, the set problem will be solved. If you don't quite understand the concept of elements, the following courses and exercises can help you tide over the difficulties:
The concept and expression of compulsory 1 preparation course set in senior high school mathematics.
2. Grasp the special nature of mutual differences.
When solving the problem of set elements, we must pay attention to the fact that the elements in the set should be different from each other to avoid generating additional roots.
3, pay attention to the special set of empty sets
An empty set is a collection without any elements. We stipulate that an empty set is a subset of any set and a proper subset of any non-empty set. Therefore, when it comes to the relationship between sets, we should pay special attention to empty sets.
Senior high school mathematics required course 1 preparation course "the relationship between sets and the operation of sets"
4. Use special tools to draw Wayne diagram and number axis.
The representation methods of sets can be divided into enumeration method, description method and graphic method. Enumeration generally represents a finite set, and description generally represents an infinite set, which is used to write the final result. In the process of operation, the number axis is generally used to represent the set of continuous elements, and the Wayne diagram is used to represent the set of discrete elements. Graphic language can help us find the answer quickly and intuitively, and improve the speed of solving problems.
When a school held a sports meeting, there were 26 students in Grade One (1), 8 students in swimming competition, 8 students in track and field competition, 3 students in swimming competition and track and field competition, 3 students in swimming competition and ball competition, and no one participated in all three competitions at the same time.
Senior one mathematics set must recite knowledge points 1, meaning of set:
? Assembly? First of all, this word reminds us of what teachers often shout when they go to physical education class or have meetings. Everybody gather? . Math? Assembly? The meaning is the same, but one is a verb and the other is a noun.
So the meaning of a set is: some specified objects are gathered together to form a set, which is called a set for short, and each object is called an element. For example, the collection of Grade One and Grade Two, then all the students in Grade One and Grade Two form a collection, and each student is called the element of this collection.
2. Representation of sets
Generally, sets are represented by uppercase letters, and elements are represented by lowercase letters, such as set A={a, b, c}. A, b and c are elements in the set a, which is denoted as a? A, on the other hand, D does not belong to the set A, and is recorded as D? Answer.
There are some special sets to remember:
Non-negative integer set (i.e. natural number set) n positive integer set N* or N+
Integer set z rational number set q real number set r
Representation of collections: enumeration and description.
① enumeration method: {a, b, c}
(2) Description: Describe the common attributes of the elements in the collection. Like {x? r | x-3 & gt； 2}，{ x | x-3 & gt； 2}，{(x，y)|y=x2+ 1}
(3) Language description: Example: {A triangle that is not a right triangle}
For example: inequality x-3 >; The solution set of 2 is {x? r | x-3 & gt； 2} or {x | x-3 >；; 2}
Important: When describing a set, pay attention to the representative elements of the set.
A={(x, y)|y=x2+3x+2} is different from B={y|y=x2+3x+2}. There are array elements (x, y) in set A, while there is only element Y in set B. ..
Senior one mathematics exercises 1. Choose the appropriate method to represent the following sets:
(1) An integer set whose absolute value is not greater than 3;
(2) The set of real number solutions of equation (3x-5)(x+2)=0;
(3) The linear function y=x+6 is the set of all points on the image.
Integers whose absolute value of the solution (1) is not greater than 3 have seven elements, namely -3, -2,-1, 0, 1, 2,3, * *, which are expressed by enumeration as {-3, -2,-1, 0,0.
(2) Equation (3x-5)(x+2)=0 has only two real number solutions, 53, -2 respectively, which are expressed as {53,-2} by enumeration;
(3) The linear function y=x+6 There are countless points on the image, which are described as {(x, y)|y=x+6}.
2. It is known that set A contains three elements, a-2, 2a2+5a, 3, and -3? Find the value of a.
Solve by -3? A, a-2=-3 or 2a2+5a=-3.
(1) if a-2=-3, then a=- 1,
When a=- 1, 2a2+5a=-3,
? A=- 1 nonconformity.
(2) If 2a2+5a=-3, then a=- 1 or -32.
When a=-32 and a-2=-72, this is in line with the meaning of the question;
When a=- 1, it can be seen from (1) that it does not meet the meaning of the question.
To sum up, the value of real number A is -32.
3. the set of known numbers a satisfies the condition: if a? A, so 1 1-a? A(a？ 1), if a=2, try to find all the elements in a.
∵2? A, from the meaning of the question, 1 1-2=- 1? a；
By - 1？ A display 1 1-? - 1? = 12? a；
To 12? A display 1 1- 12=2? A.