Rational number 1, rational number: rational numbers are divided into positive rational numbers, 0 and negative rational numbers;
2. Number axis: The number axis is a straight line that defines the origin, positive direction and unit length.
3, the opposite number:
(1) There are only two numbers with different signs, and we say that one of them is opposite to the other; The antonym of 0 is still 0;
(2) Is the sum of opposites 0? a+b=0？ A and b are reciprocal.
4. Absolute value: the absolute value of a positive number is itself, the absolute value of 0 is 0, and the absolute value of a negative number is its inverse; Note: the absolute value means the distance from the origin of a point representing a number on the number axis.
5. Scientific notation: Write numbers greater than 10 in the form of a× 10n, where a is a number with only one integer bit. This notation is called scientific notation.
6. monomial: in algebraic expressions, if only multiplication (including power) operations are involved. Or algebraic expressions that contain division but do not contain letters in division are called monomials.
(1) coefficient and number of single items: the numerical factor that is not zero in a single item is called the numerical coefficient of a single item, which is simply referred to as the coefficient of a single item; When the coefficient is not zero, the sum of all the letter indexes in the single item is called the number of times of the single item.
7. Polynomial: The sum of several monomials is called polynomial.
(1) Number and degree of polynomials: the monomial contained in a polynomial is the number of polynomial terms, and each monomial is called a polynomial term; In polynomial, the degree of the term with the highest degree is called the degree of polynomial.
The unary linear equation 1 contains only one unknown, the degree of the unknown is 1, and the coefficient containing the unknown is not zero.
2. The standard form of one-dimensional linear equation: ax+b=0(x is unknown, a and b are known numbers, a≠0).
3. General steps for solving a linear equation with one variable: sorting out the equation ... removing the denominator ... dismantling the bracket ... changing the terminology ... merging similar terminology ... and converting the coefficient into 1 ... (testing the solution of the equation).
Intersecting lines and parallel lines 1, the properties of lines:
Property 1: There is one and only one straight line perpendicular to the known straight line.
Property 2: Of all the line segments connecting a point outside the straight line and a point on the straight line, the vertical line segment is the shortest.
2. Parallelism axiom: At a point outside the straight line, only one straight line is parallel to the known straight line.
Inference of the axiom of parallelism: If two straight lines are parallel to the third straight line, then the two straight lines are also parallel to each other.
3, the nature of parallel lines:
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.
4. Determination of parallel lines:
Judgment 1: congruent angles are equal and two straight lines are parallel.
Decision 2: The internal dislocation angles are equal and the two straight lines are parallel.
Judgment 3: The internal angles on the same side are equal and the two straight lines are parallel.
Inequality 1, the solution of inequality: the value of the unknown that makes inequality valid is called the solution of inequality.
2. Solution set of inequality: All solutions of an unknown inequality constitute the solution set of this inequality.
3. One-dimensional linear inequality: the left and right sides of the inequality are algebraic expressions, and there is only one unknown, and the highest order of the unknown is 1. Inequalities like this are called one-dimensional linear inequalities.
4. One-dimensional linear inequality group: Generally, several one-dimensional linear inequalities about the same unknown quantity are combined to form a one-dimensional linear inequality group.
Congruent triangles 1, when two triangles have the same shape and size, one of them can be moved (or transformed) by translation, rotation, symmetry, etc. to make it coincide with the other. These two triangles are called congruent triangles.
2. The nature of congruent triangles: the corresponding angles and sides of congruent triangles are equal.
3, triangle congruence judgment axiom and inference is:
(1) "corner" is abbreviated as "SAS"
② The abbreviation of "corner" is "ASA"
(3) "Edge" is abbreviated as "SSS"
(4) The abbreviation of "corner edge" is "AAS"
(5) Two right-angled triangles (HL) with equal hypotenuse and right-angled side.
The fraction of 1 is A/B, where a and b are algebraic expressions, and algebraic expressions in which b contains unknowns and b is not equal to 0 are called fractions. Where a is called the numerator of the fraction and b is called the denominator of the fraction.
2. Conditions for meaningful scores: denominator is not equal to 0.
3. Simplification: The common factor of the numerator and denominator of a fraction (not the number of 1) is simplified, and this deformation is called simplification.
4. General scores: scores with different denominators can be converted into scores with the same denominator. This process is called total score.
These are the more important knowledge points I have compiled, and I hope I can help you.