Summary of Mathematics Knowledge Points in Volume 2 of Grade One.
intersection line
One vertex has a common * * *, one side has a common * * *, and the other side is an extension line opposite to each other. Such two angles are called adjacent complementary angles.
There are four pairs of adjacent complementary angles when two straight lines intersect.
There is a vertex with a common * * *, and both sides of the corner are opposite extension lines. These two angles are called antipodal angles.
Two straight lines intersect and have two opposite angles.
The vertex angles are equal.
Two straight lines intersect, and one of the four corners is a right angle, so the two straight lines are perpendicular to each other. One of the straight lines is called the perpendicular of the other straight line, and their intersection point is called the vertical foot.
Parallel lines and their determination
Property 1: Two straight lines are parallel and equal to the complementary angle.
Property 2: Two straight lines are parallel and the internal dislocation angles are equal.
Property 3: Two straight lines are parallel and complementary.
Properties of parallel lines
Property 1 Two parallel lines are cut by a third line, and the congruence angles are equal. To put it simply: two straight lines are parallel and have the same angle.
Property 2 Two parallel lines are cut by a third straight line, and their internal angles are equal. To put it simply: two straight lines are parallel and their internal angles are equal.
Property 3 Two parallel lines are cut by a third straight line and complement each other. Simply put, two straight lines are parallel and complementary.
translate
Translate one unit length to the left and you can get the corresponding point (x-a, y).
Translate b unit lengths upwards, and you can get the corresponding point (x, y+b).
By translating down by b unit lengths, the corresponding point (x, y-b) can be obtained.
The second volume of the first day of junior high school mathematics knowledge points
Polynomial divided by monomial
First of all, the monomial
1, an algebraic expression of the product of numbers and letters, is called a monomial.
2. The single numerical factor is called the single coefficient.
3. The index of all the letters in the monomial and the number of times called the monomial.
4. A single number or letter is also a monomial.
5. The coefficient of monomial with only letter factor is 1 or-1.
6. A number is a monomial, and its coefficient is itself.
7. The degree of a single nonzero constant is 0.
8. A single item can only contain multiplication or power operation, and cannot contain other operations such as addition and subtraction.
9. The coefficient of the monomial includes the symbol before it.
10, when the coefficient of the monomial is a fraction, it should be turned into a false fraction.
When 1 1 and the single coefficient is 1 or-1, the number "1" is usually omitted.
12, the number of monomials is only related to letters, and has nothing to do with the coefficient of monomials.
Second, polynomials
The sum of 1 and several monomials is called a polynomial.
2. Each monomial in a polynomial is called a polynomial term.
3. The term without letters in polynomial is called constant term.
4. A polynomial has several terms, which are called polynomials.
5. Every term of polynomial includes the symbol before the term.
6. Polynomials have no concept of coefficient, but have the concept of degree.
7. The degree of the degree term in a polynomial is called the degree of the polynomial.
Third, algebraic expressions.
1, monomials and polynomials are collectively called algebraic expressions.
2. Both monomials and polynomials are algebraic expressions.
3. Algebraic expressions are not necessarily monomials.
4. Algebraic expressions are not necessarily polynomials.
5. Algebraic expressions with letters in denominator are not algebraic expressions; It is a fraction to learn in the future.
Fourth, the addition and subtraction of algebraic expressions.
The theoretical basis of 1. Algebraic addition and subtraction is: the rule of removing brackets, the rule of merging similar items, and the multiplication distribution rate.
2. The key to the addition and subtraction of several algebraic expressions is to use the rule of brackets correctly, and then merge similar items accurately.
3, several general steps of algebraic expression addition and subtraction:
(1) List algebraic expressions: enclose each algebraic expression in parentheses and then connect it with a plus sign and a minus sign.
(2) Open brackets according to the rules for opening brackets.
(3) Merge similar items.
4, the general steps of algebraic evaluation:
(1) algebraic simplification.
(2) Substitution calculation
(3) For some special algebraic expressions, "whole substitution" can be used for calculation.
Learning methods and skills of seventh grade mathematics
1, get ready:
In the unit preview, we can read roughly, understand the learning content in the recent stage, read carefully in the classroom preview, pay attention to the formation process of knowledge, and record the concepts, formulas and laws that are difficult to understand, so that we can listen to the class with questions.
2. Listen carefully:
Listening to lectures should include listening, thinking and remembering. Listen, listen to the ins and outs of the formation of knowledge, listen to the key and difficult points, and listen to the answers and requirements of examples. Thinking, one is to be good at association, analogy and induction, and the other is to dare to question and ask questions. Taking notes means taking notes in class-methods, doubts, requirements and precautions.
3. Seriously solve the problem:
Classroom exercises are the most timely and direct feedback, and must not be missed. Don't rush to finish your homework, look at your notebook first, review your learning content, deepen your understanding and strengthen your memory.
4, timely error correction:
Classroom exercises, homework, tests and feedback should be consulted in time, the causes of wrong questions should be analyzed, and relevant calculation training should be strengthened when necessary. Ask your classmates and teachers if you don't understand. Don't let the problem hang in the air. Get into the good habit of doing things today.
5, learn to summarize:
Teacher Feng said: "Mathematics is closely related, and knowledge is closely related. Summing up by stages can not only play a role in reviewing and consolidating, but also find the connection between knowledge, so as to achieve a thorough understanding.
6, learn to manage:
Manage your notebook, exercise book, correction book, and all the exercises and papers you have done. Teacher Feng said that this is the most useful material for reviewing the final exam and must not be ignored.
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