Summary of knowledge points of senior two mathematics last semester 1
1, four propositions:
(1) Original proposition: If p is q; ⑵ Inverse proposition: If q is p; (3) no proposition: if p is q; (4) negative proposition: if q is p
Note: 1, the original proposition is equivalent to the negative proposition; Whether the inverse proposition is equivalent or not. To judge whether a proposition is true or not, we should pay attention to transformation.
2. Pay attention to the difference between whether the proposition is negative or not: the negative form of the proposition is; No proposition is. The negation of proposition or is "harmony"; The negative form of "and" is "or".
3. Logical connector:
(1) and: propositional form p q；; p q p q p q p
⑵ or (or): propositional form p q；; True, true, true, false.
(3) not: propositional form P. True false false true false.
The true and false characteristics of "or proposition" are "one truth, all false";
The true and false characteristics of the "and proposition" are "if one is false, it must be true";
The true and false feature of "non-proposition" is "one truth and one falsehood"
4. Necessary and sufficient conditions
The conclusion can be deduced from the condition, which is a sufficient condition for the conclusion to be established; If the condition can be deduced from the conclusion, then the condition is the necessary condition for the conclusion to be established.
5. Full name proposition and proper name proposition:
The phrase "all" refers to all in a sentence, which is usually called a full-name quantifier in logic and represented by symbols. A proposition containing all quantifiers is called a full name proposition.
The phrase "you yi" or "some" or "at least one" indicates an individual or part of something in a statement, which is usually called an existential quantifier in logic and is represented by symbols. Propositions containing existential quantifiers are called existential propositions.
Summary of knowledge points of senior two mathematics last semester II
A definition
Set is the most primitive undefined concept in high school mathematics, and only descriptive explanation is given. Certain different objects are brought together into a set. The objects that make up a collection are called elements.
Abstract representation of two sets
Use capital letters a, b and c to represent the set; Use lowercase letters a, b and c to represent elements.
The relationship between three elements and set
There are two kinds of relationships: ownership and non-ownership. Element a belongs to set a, denoted as aa; Element a does not belong to set a and is recorded as aA.
Naming of four kinds of sets
Finite set: a set with finite elements; Infinite set: a set containing infinite elements; Empty set: a set that does not contain any elements is called an empty set and is represented by; Natural number set: n; Positive integer set: N_ or n+; Integer set: z; Rational number set: q; Real number set: r.
Five sets representation
(1) enumeration: a method of listing elements with braces, such as {a, b, c}. Note: All collections in the form of enumeration often examine the differences between elements.
(2) Description: There are the following two description methods.
1. Code Description: The set of all solutions of equation 2x3x+2=0, which can be expressed as {x|x2-3x+2=0}. X is the code name of the element in the set, and the vertical line can also be written as a colon or semicolon. The function of the formula behind the vertical bar is to describe the conditions that the elements in the set meet.
2. Text description: Write a sentence to explain the nature of the elements in braces. Example {Integer greater than 2 and less than 5}; Once the set represented by descriptive methods appears, it is necessary to analyze the meaning of elements first, that is to say, to judge what elements are.
(3) Wayne's graphic method: graphically representing a set defines all the relationships between two sets. There are two limit cases for subsets:
(1) When A becomes an empty set, A is still a subset of B;
(2) When A and B are equal, A is still a subset of B. proper subset: If all the elements belonging to A belong to B, and at least one element in B does not belong to A, then the proper subset of A is called B, and it is called AB? Or ... Proper subset is also a subset, the difference is that.
For the same set, the number of proper subset is one less than the number of subsets.
(1) Find the number of subsets or proper subset. The set of n elements has 2n subsets and 2n- 1 proper subset;
(2) Investigation of empty sets: whenever it is mentioned that one set is a subset of another set, the set as a subset can be an empty set at first, and its equivalent forms mainly include.
Summary of knowledge points of senior two mathematics last semester 3
1, standard equation of circle:
Equation of a circle with center A(a, b) and radius r
2. The method of judging the relationship between a point and a circle: (1), the point is outside the circle (2), the point is on the circle (3) and the point is inside the circle.
4. General equation of1.2 circle
1, general equation of circle:
2, the characteristics of the general equation of the circle:
(1) ① The coefficients of x2 and y2 are the same and not equal to 0.
② There are no quadratic terms such as xy.
(2) There are three specific coefficients D, E and F in the general equation of a circle, so as long as these three coefficients are found, the equation of the circle is determined.
(3) Compared with the standard equation of a circle, it is a special binary quadratic equation with obvious algebraic characteristics, while the standard equation of a circle points out the coordinates and radius of the center and has obvious geometric characteristics.
4.2. positional relationship between1circles
1, use the distance from point to straight line to judge the positional relationship between straight line and circle.
4.2.2 positional relationship between circles
4.2.3 Application of Linear and Circular Equations
1, and use the plane rectangular coordinate system to solve the positional relationship between the straight line and the circle;
2. Process and method
Steps to solve geometric problems by coordinate method;
Step 1: Establish an appropriate plane rectangular coordinate system, express the geometric elements in the problem with coordinates and equations, and transform the plane geometric problem into an algebraic problem;
Step 2: Solve algebraic problems through algebraic operations;
Step 3: Transform the result of algebraic operation into geometric conclusion.
4.3. 1 space rectangular coordinate system
1, and the point m corresponds to a definite ordered real array, corresponding to a point in the space rectangular coordinate system. 3. The coordinates of any point M in space can be expressed by an ordered real array, which is called the coordinates of this point M in the rectangular coordinate system of space, and M is recorded.
Expanding reading: the learning method of senior high school mathematics
1. Start with the foundation of mathematics and refine it to review every knowledge point.
The starting point of mathematics review for liberal arts in senior three should be "low", and it is best to start with the most basic knowledge points. On the one hand, take textbook examples as the starting point; On the other hand, starting from textbook exercises, this is mainly because the content of liberal arts mathematics in the college entrance examination is based on textbooks. Only by fully understanding and understanding the "source" in the teaching materials can we draw inferences and be invincible in the sea of college entrance examination questions. In addition, you can also start with the exercises of middle (low) grade questions, such as multiple-choice questions, fill-in-the-blank questions, simple problem solving, etc., to ensure that questions with low difficulty and many basic knowledge points do not lose points.
2. Actively participate in class review, and the class logistics is reflective.
The preparation time for senior three is tight, and there are many things to master, so the capacity of classroom review is also quite large and the pace is fast. In order to achieve an efficient review effect, students should keep up with the teacher's rhythm, actively participate in it, and strive to achieve the effect of "checking for missing parts" and really play a role in the exam. Of course, besides reviewing in class, students also have more time to review after class. Many students think that math review is to do more problems and improve the efficiency of solving problems.
3. Master the speed and skills of solving problems
By understanding the information in the exam description and syllabus, we can clearly understand what, how and how to test liberal arts mathematics in the college entrance examination, and explore more problem-solving skills in a targeted manner. At the same time, in the general examination, as the strict requirement of "preview" of the college entrance examination, we should speed up the problem-solving in a limited time and summarize the problem-solving strategies of different types from repeated examination practice.