Knowledge points of real number 1 add
Add two numbers with the same sign, take the same sign, and add the absolute values; Add different symbols with different absolute values of two numbers, take the symbol with the larger absolute value, and subtract the symbol with the smaller absolute value from the larger absolute value; Two opposite numbers add up to 0; Add a number to 0 and you still get the number.
2. subtraction: subtracting a number is equal to adding the reciprocal of this number.
multiply
Multiply several non-zero real numbers, and the sign of the product is determined by the number of negative factors. When there are even negative factors, the product is positive. When there are odd negative factors, the product is negative. Multiply several numbers, one factor is 0 and the product is 0.
break up
Dividing by a number is equal to multiplying the reciprocal of this number. Divide two numbers, the same sign is positive, the different sign is negative, and the absolute value is divided by 0. Divide by any number that is not equal to 0 to get 0.
5. Multipliers and prescriptions
The meaning of (1)an is the product a of n, any power of positive number is positive, even power of negative number is positive, and odd power of negative number is negative.
(2) Positive numbers and 0 can be squared, but negative numbers cannot be squared; Positive numbers, negative numbers and 0 can all be turned on.
(3) Zero exponent and negative exponent.
Point-line-polygon knowledge point 1. Composition of geometric figures
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. Point to line, line to surface, surface to body.
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.
note:
(1) indicates points, lines, rays and line segments, and the points, lines, rays and line segments should be marked before the letters.
(2) Lines and rays have no length, but line segments have length.
(3) A straight line has no endpoint, a ray has one endpoint, and a line segment has two endpoints.
(4) The positional relationship between points and straight lines can be divided into two types:
The point is on a straight line, or a straight line passes through the point.
② The point is outside the straight line, or the straight line does not pass through this point.
Plane Cartesian coordinate system 1. Definition: Draw two mutually perpendicular number axes on a plane, and their origins coincide to form a plane Cartesian coordinate system. The horizontal axis is called the X axis or the horizontal axis, and it is customary to take the right as the positive direction; The vertical axis is called Y axis or vertical axis, and the orientation direction is positive. The intersection of the two coordinate axes is the origin of the plane rectangular coordinate system.
2. Any point on the plane can be represented by an ordered number pair, which is denoted as (a, b), where a is the abscissa and b is the ordinate.
3. The coordinate of the origin is (0,0);
The connection line with the ordinate point is parallel to the X axis;
The connecting line of the points with the same abscissa is parallel to the Y axis;
The ordinate of this point on the X axis is 0, which is expressed as (x, 0);
The abscissa of the point on the Y axis is 0, which is expressed as (0, y).
4. After the plane rectangular coordinate system is established, the coordinate plane is divided into four parts, I, II, III and IV, which are called the first quadrant, the second quadrant, the third quadrant and the fourth quadrant respectively. The points on the coordinate axis do not belong to any quadrant.
5. The characteristics of points in several quadrants:
The first quadrant (+,+); The second quadrant (-,+);
The third quadrant (-,-); The fourth quadrant (+,-).
6.(x, y) The point symmetrical about the origin is (-x,-y);
(x, y) The point of symmetry about x is (x,-y);
The point where (x, y) is symmetrical about y is (-x, y).
7. Distance from point to two axes: the distance from point P(x, y) to X axis is ︱ y ︳;
The distance from the point P(x, y) to the y axis is ︱x︳.
8. The coordinates of the points on the bisector of the first and third quadrants are (m, m);
The coordinates of the points on the bisectors of the second and fourth quadrants are (m, -m).
One-dimensional linear equation One-dimensional linear equation refers to an equation with only one unknown number, its highest degree is 1, and both sides are algebraic expressions, which is called one-dimensional linear equation. Finding the value of the unknown quantity in the equation is called the solution of the equation. One-dimensional linear equations are linear equations with only one root.
Criteria for linear equations with one variable
(1) must be an equation first.
(2) Secondly, it must contain an unknown number.
(3) There are no unknowns in the denominator.