Positive and negative numbers 1. Positive number: a number greater than 0.
2. Negative number: a number less than 0.
3.0 neither positive nor negative.
4. Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than negative numbers.
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"
Number axis 1. Number axis: Numbers are represented by points on a straight line, which is called number axis. Draw a straight line and take any point on the straight line to represent the number 0. This zero point is called the origin, which specifies that the right or upward direction of the straight line is positive; Select the appropriate length as the unit length, so as to take points on the number axis. )
2. Three elements of the number axis: origin, positive direction and unit length.
3. Antiquities: Only two numbers with different symbols are called reciprocal. The antonym of 0 is still 0.
4. Absolute value: 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.
One-dimensional linear equation 1 Equation: Equations connected by "=" are called equations.
2. The nature of the equation:
Properties of equation 1: Add (or subtract) the same number or the same algebraic expression on both sides of the equation, and the result is still an equation;
Property 2 of the equation: both sides of the equation are multiplied (or divided) by the same non-zero number, and the result is still an equation.
3. Equation: An equation with an unknown number is called an equation.
4. Solution of the equation: the value of the unknown quantity that makes the left and right sides of the equation equal is called the solution of the equation;
Note: "The solution of the equation can be substituted".
5. Moving term: after changing the sign, moving the term of the equation from one side to the other is called moving term. The shift term is based on the equality attribute 1.
6. One-dimensional linear equation: An integral equation with only one unknown number, degree 1 and non-zero coefficient is a one-dimensional linear equation.
7. The standard form of one-dimensional linear equation: ax+b=0(x is unknown, a and b are known numbers, a≠0).
8. General steps for solving one-dimensional linear equations:
Simplify the equation-the basic properties of fraction.
Denominator-the simplest common denominator of the same multiplication (multiplication is not omitted).
Remove the brackets and pay attention to the change of symbols.
Move the item-change the flag (keep in front).
Merge similar items-merged symbols.
The coefficient is1-except before.
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.