1, classification and concept of numbers: integers and fractions are collectively called rational numbers (finite decimals and infinite cyclic decimals), such as √3, π, 0. 10 100 1 are called irrational numbers; Rational numbers and irrational numbers are collectively called real numbers. Real numbers can also be divided into positive integers, positive fractions, 0, negative integers, negative fractions, positive irrational numbers and negative irrational numbers. Extended data 2. Natural numbers (0 and positive integers); Odd 2n- 1, even 2n, prime number, composite number.

3. The reciprocal product of (1) is1; (2) The sum of opposites is 0 and the quotient is-1; (3) The absolute value is a distance, not a negative number.

4. Number axis: ① definition ("three elements"); ② Points correspond to real numbers one by one.

5. Inverse number

A real number and its inverse are a pair of numbers (only two numbers with different signs are called inverse numbers, and the inverse of zero is zero). Seen from the number axis, the points corresponding to two opposite numbers are symmetrical about the origin. If a and b are opposites, then a+b=0, A =-B, and vice versa.

6. Absolute value

The absolute value of a number is the distance between the point representing the number and the origin, |a|≥0. When the absolute value of zero is itself, it can also be regarded as its inverse. If |a|=a, then a ≥ 0; If |a|=-a, then a≤0. Positive numbers are greater than zero, negative numbers are less than zero, positive numbers are greater than all negative numbers, and the absolute values of the two negative numbers are smaller.

7. Countdown the seconds

If A and B are reciprocal, there is ab= 1, and vice versa. The numbers whose reciprocal equals itself are 1 and-1. Zero has no reciprocal.

real arithmetic

1, additive commutative law: a+b = b+a.

2. Additive associative law: (a+b)+c=a+(b+c)

3. Multiplicative commutative law: ab=ba

4. Multiplicative associative law: (ab)c=a(bc)

5. Distribution law of multiplication to addition: a(b+c)=ab+ac.

6. Operation sequence of real numbers: calculate the power first, then multiply and divide, and finally add and subtract. If there are brackets, count them first.

The concept of one-dimensional linear equation

1. Equation: An equation with an unknown number is called an equation.

2. Solution of the equation: The value of the unknown quantity that can make both sides of the equation equal is called the solution of the equation.

3. Properties of the equation

Adding (or subtracting) the same number or the same algebraic expression on both sides of the (1) equation, the result is still an equation.

(2) Both sides of the equation are multiplied (or divided) by the same number (the divisor cannot be zero), and the result is still an equation.

4. One-dimensional linear equation

An integral equation with only one unknown number and the highest order of the unknown number is 1 is called a linear equation with one variable, where equation) is an unknown number.

Lines, rays and line segments

1. Geometry: Various graphics abstracted from objects, including three-dimensional graphics and plane graphics.

Three-dimensional figures: Some geometric figures are not all on the same plane, but three-dimensional figures.

Plane figure: All parts of some geometric figures are on the same plane. They are plane figures.

2. Points, lines, surfaces and bodies

Synthesis of (1) Geometry

Point: The point where straight lines intersect is the point, which is the most basic figure in geometry.

Line: The intersection line between faces is a line, which can be divided into straight lines and curves.

Face: Surrounding the body is the face, which is divided into plane and curved surface.

Volume: Geometry is also called volume for short.

(2) inching into a line, the line moves into a plane, and the plane moves into an adult.

3. The concept of straight line: A tightly drawn line gives us the image of a straight line, which is straight and extends infinitely in two directions.

4. The concept of ray: A point on a straight line and the part next to it are called rays. This point is called the endpoint of the ray.

5. The concept of line segment: Two points on a straight line and the part between them are called line segments. These two points are called the endpoints of the line segment.

6. Representation of points, lines, rays and line segments: In geometry, we often use letters to represent figures. A dot can be represented by capital letters. Lowercase letters can represent a straight line. A ray can be represented by an endpoint and another point on the ray. The endpoint of a line segment can be represented by two capital letters.