Number axis 1. The concept of number axis: the straight line defining the origin, positive direction and unit length is called number axis.
Three elements of the number axis: origin, unit length and positive direction.
2. Points on the number axis: All rational numbers can be represented by points on the number axis, but not all points on the number axis represent rational numbers. (Generally, the right direction is the positive direction, and the points on the number axis correspond to any real number, including irrational numbers. )
3. Compare the size with the number axis: Generally speaking, when the number axis faces the right, the number on the right is always greater than the number on the left.
Probability 1. Random events: Events that may or may not occur under certain conditions are called random events.
Mutually exclusive events: Two things that cannot happen at the same time are called mutually exclusive events.
3. Opposing events: that is, there must be a mutually exclusive events called opposing events.
4. Inevitable events: those events that can be determined in advance in each experiment without experiments are called inevitable events.
5. Impossible events: those events that will never happen in every experiment are called impossible events.
Steps to solve a quadratic equation with one variable 1. Steps of the matching method:
First, the constant term is moved to the right of the equation, then the coefficient of the quadratic term is changed to 1, and the square of half the coefficient of 1 is added, and finally the complete square formula is obtained.
2. The steps of factorization method:
Turn the right side of the equation into 0, and then see if you can extract the common factor, formula (here refers to the formula in factorization) or cross multiplication, and if you can, turn it into the form of product.
3. Formula method
Just substitute the coefficients of a quadratic equation with one variable, where the coefficient of the quadratic term is a, the coefficient of the linear term is b, and the coefficient of the constant term is c.
Parallel lines 1. In the same plane, if two straight lines have no intersection point, then the two straight lines are parallel to each other, which is recorded as: a ∨ b.
2. Parallelism axiom: After passing a point outside a straight line, there is one and only one straight line parallel to this straight line.
3. If two straight lines are parallel to the third straight line, then the two straight lines are parallel to each other.
4. The method of judging that two straight lines are parallel:
(1) Two straight lines are cut by the third straight line. If congruent angles are equal, two straight lines are parallel. To put it simply: the same angle is equal and two straight lines are parallel.
(2) Two straight lines are cut by a third straight line. If the internal dislocation angles are equal, two straight lines are parallel. To put it simply: the internal dislocation angles are equal and the two straight lines are parallel.
(3) Two straight lines are cut by a third straight line. If they are complementary to each other, the two straight lines are parallel. To put it simply: the internal angles on the same side are complementary and the two straight lines are parallel.
5. Properties of parallel lines
(1) Two parallel lines are cut by a third straight line and have the same angle. To put it simply: two straight lines are parallel and have the same angle.
(2) Two parallel lines are cut by a third line, and the internal dislocation angles are equal. To put it simply: two straight lines are parallel and their internal angles are equal.
(3) The two parallel lines are cut by the third straight line and complement each other. Simply put, two straight lines are parallel and complementary.
Congruent triangles 1. After flipping and translating, two triangles that can completely overlap are called congruent triangles, and the three sides and three angles of the two triangles are equal.
2. Determination of triangle congruence
(1)SSS (side by side)
A triangle with three equal sides is congruent triangles.
(2)SAS (edge)
A triangle with two equal corners is congruent triangles.
(3)ASA (corner)
Two angles and their sides correspond to congruences of triangles.
(4)AAS (corner)
The opposite sides of two angles and one angle correspond to congruences of equal triangles.
(5)RHS (right angle, hypotenuse, edge)
In a pair of right-angled triangles, the hypotenuse is equal to the other right-angled side.
3. Angle dividing line
(1) Draw a ray from the vertex of an angle and divide it into two identical angles. This ray is called the bisector of this angle.
(2) Nature
The two angles of the bisector of the (1) angle are equal, both equal to half the angle.
② The distance between the point on the bisector of the angle and both sides of the angle is equal.
Rational number 1. Definition: A number consisting of integers and fractions. Include positive integer, 0, negative integer, positive fraction and negative fraction. Can be written as the ratio of two integers.
2. Number axis: In mathematics, numbers can be represented by points on a straight line, which is called number axis.
3. Inverse number: Inverse number is a mathematical term, which means that two numbers with equal absolute values and opposite signs are opposite to each other.
4. Absolute value: absolute value is the distance from a point corresponding to a number on the exponential axis to the origin. The absolute value of a positive number is itself, and the absolute value of a negative number is its inverse; The absolute value of 0 is 0, two negative numbers, the larger absolute value is smaller.
5. Addition and subtraction of rational numbers
Add the same symbol to the same symbol and add the absolute values. For the addition of different symbols, take the sign of the addend with large absolute value, and subtract the sign with small absolute value from the sign with large absolute value.
6. Rational number multiplication
Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value.
Multiply any number by 0, and the product is 0. For example: 0× 1=0.
7. Division of rational numbers
Dividing by a number that is not zero is equal to multiplying the reciprocal of this number.
Divide two numbers, the same sign is positive, the different sign is negative, and divide by the absolute value. Divide by 0
For any number that is not 0, you get 0.
8. Power of rational number
The operation of finding the product of n identical factors is called power, and the result of power is called power. Where a is called the base and n is called the exponent. When a. When it is regarded as the result of the n power of A, it can also be read as "the n power of A" or "the n power of A"