Summarize and sort out the knowledge points of senior one mathematics.
Union set: The set whose elements belong to A or B is called the union (set) of A and B, marked as A∪B (or B∪A), and pronounced as A and B (or B and A), that is, A∪B={x|x∈A, or X.
A set with elements is called the intersection of A and B, marked as A∩B (or B∩A) and pronounced as "A ∩ B" (or B ∩ A "), that is, A∩B={x|x∈A, X. Then because both A and B have 1, 5, A ∩ B = {1, 5}. Let's take another look. Both contain 1, 2, 3, 5, no matter how much, either you have it or I have it. Then say a ∪ b = {1, 2, 3, 5}. The shaded part in the picture is a ∩ B. Interestingly; For example, how many numbers in 1 to 105 are not integer multiples of 3, 5 and 7? The result is the subtraction set of each term of 3, 5 and 7.
Multiply by 1. 48. Symmetric difference set: Let A and B be sets, and the symmetric difference set A of A and B? The definition of b is: a? B =(A-B)∩(B-A) For example: A={a, b, c}, B={b, d}, then A? Another definition of B={a, c, d} symmetric difference operation is: a? B =(A∪B)-(A∪B) Infinite set: Definition: A set containing infinite elements in a set is called an infinite set finite set: Let N_ be a positive integer, and N_n={ 1, 2,3, ..., n}. If there is a positive integer n, the difference is: Note: An empty set is contained in any set, but it cannot be said that "an empty set belongs to any set". Complement set is a concept derived from difference set, which means that a set composed of elements belonging to complete set U but not to set A is called the complement set of set A, and it is denoted as CuA, that is, an empty set with CuA={x|x∈U and x not belonging to A} is also considered as a finite set. For example, if the complete sets U = {1, 2, 3, 4, 5} and A = {1, 2, 5}, then 3,4 in the complete set but not in A is CuA, which is the complement of A. CuA = {3,4}. In information technology,
Summary of mathematics knowledge points in senior one.
Summary of knowledge points
The knowledge in this section includes monotonicity, parity, periodicity, maximum, symmetry and images of functions. Monotonicity, parity, periodicity, maximum and symmetry of functions are the basis of learning function images, and function images are their synthesis. So understand the previous knowledge points, and the image of the function will be solved.
First of all, the monotonicity of the function
1, the definition of monotonicity of function
2. Judgment and proof of monotonicity of function: (1) Definition method (2) Analysis method of compound function (3) Derivative proof method (4) Image method.
Second, the parity and periodicity of the function
1, the definition of parity and periodicity of function
2. Methods to judge and prove the parity of functions.
3. The method of judging the periodicity of the function
Third, the function of image.
1, method of function image (1) method of tracking points (2) method of image transformation.
2. Image transformation includes images: translation transformation, expansion transformation, symmetry transformation and folding transformation.
Common inspection methods
This part is an indispensable part of Duan and the college entrance examination, and it is the focus and difficulty of Duan and the college entrance examination. There are multiple-choice questions, fill-in-the-blank questions and solutions, and the questions are more difficult. In solving problems, we can combine each chapter of high school mathematics, mostly advanced questions. More attention should be paid to the monotonicity, maximum and image of the function.
Misunderstanding reminder
1. To find the monotone interval of a function, the domain of the function is required first, that is, the principle that the domain of the function problem takes precedence is followed.
2. Monotone interval must be expressed by interval, not by set or inequality. Monotone interval is generally written as an open interval, regardless of the endpoint problem.
3. Multiple monotonous intervals cannot be connected by "or" and ","and can only be separated by commas.
4. To judge the parity of a function, we should first consider the domain of the function. If the domain of a function is not symmetric about the origin, then the function must be a odd function or even function.
5. As a function, it is generally to simplify the analytical formula first, and then determine the image as a function by tracing points or image transformation.
Summary of mathematics knowledge points in senior one.
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, so it is recorded as A B or B A.
2. "Equality" relationship (5≥5, and 5≤5, then 5=5)
Example: let a = {x | x2-1= 0} b = {-1,1} "The elements are the same".
Conclusion: For two sets A and B, if any element of set A is an element of set B and any element of set B is an element of set A, we say that set A is equal to set B, that is, A = B.
Answer? (1) Any set is a subset of itself. A
B Then say that set A is the proper subset of set B, and write it as A B (or B A)? B and a? ② proper subset: If A
c？ C, then a? B，B？ ③ If a
So A=B? At the same time? 4 if a
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.
set operation
Definition of 1. intersection: Generally speaking, the set consisting of all elements belonging to A and B is called the intersection of A and B. 。
Write A∩B (pronounced "A to B"), that is, A∩B={x|x∈A, x∈B}.
2. Definition of union: Generally speaking, a set consisting of all elements belonging to set A or set B is called union of A and B. Note: A∪B (pronounced as "A and B"), that is, A∪B={x|x∈A, or x∈B}.
3. The nature of intersection: A∩A = A, A∪φ=φ, a ∪ b = b ∪A, a ∪ φ = a, A∪B = B∪.
4. Complete works and supplements
(1) Complement set: Let S be a set and A be a subset of S (that is, a set composed of all elements in S that do not belong to A), which is called the complement set (or complement set) of subset A in S..
A}？ S and x? x？ Note: CSA is CSA ={x
(2) Complete Works: If the set S contains all the elements of each set we want to study, this set can be regarded as a complete set. Usually represented by u.
(3) Properties: (1) cu (cua) = a2 (cua) ∩ a = φ 3 (cua) ∪ a = u.
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