① There is only one unknown in an equation, and the exponent of the unknown is 1. Such an equation is called a linear equation.

② Adding or subtracting or multiplying or dividing (non-0) an algebraic expression on both sides of the equation at the same time, the result is still an equation.

Steps to solve a linear equation with one variable:

Denominator is removed, items are shifted, similar items are merged, and the unknown coefficient is changed to 1.

Binary linear equation: An equation that contains two unknowns and all terms are 1 is called binary linear equation.

Binary linear equations: The equations composed of two binary linear equations are called binary linear equations. A set of unknown values suitable for binary linear equation is called the solution of this binary linear equation. The common * * * solution of each equation in a binary linear system of equations is called the solution of this binary linear system of equations.

Methods of solving binary linear equations: substitution elimination method/addition and subtraction elimination method.

2. Inequality and Inequality Group

Inequality:

(1) Formulas connected by "=" symbols are called inequalities.

② Add or subtract the same algebraic expression on both sides of the inequality, and the direction of the inequality remains unchanged.

③ Both sides of inequality are multiplied or divided by a positive number, and the direction of inequality remains unchanged.

④ Both sides of inequality are multiplied or divided by the same negative number, and the unequal numbers are in opposite directions.

Solution set of inequality;

(1) can make the value of an unknown inequality known as the solution of inequality.

(2) All solutions of an inequality with unknowns constitute the solution set of this inequality.

③ The process of finding the solution set of inequality is called solving inequality.

One-dimensional linear inequality: an inequality with algebraic expressions on both sides and only one unknown number of degree 1 is called one-dimensional linear inequality.

One-dimensional linear inequality system;

(1) Several linear inequalities about the same unknown quantity are combined into a linear inequality group.

② The common part of the solution set of each inequality in a linear inequality group is called the solution set of this linear inequality group.

③ The process of finding the solution set of inequality group is called solving inequality group.

3: Function

Variable: dependent variable, independent variable. When using images to represent the relationship between variables, we usually use points on the horizontal axis as independent variables and points on the vertical axis as dependent variables.

Linear function:

(1) If the relationship between two variables X and Y can be expressed as y = kx+b (where B is constant and K is not equal to 0), then Y is said to be a linear function of X..

When B=0, y is said to be a proportional function of X. ..

Linear function image:

① Take the values of the independent variable X and the corresponding dependent variable Y of a function as the abscissa and ordinate of a point respectively, and trace the corresponding point in the rectangular coordinate system. A graph composed of all these points is called an image of a function.

② The image with the proportional function Y=KX is a straight line passing through the origin.

③ In a linear function, when k < 0 and b < 0, it passes through 234 quadrants; When k < 0, b > 0, pass through quadrant124; When k > 0 and b < 0, pass through quadrant134; When k > 0 and b > 0, pass through quadrant 123.

④ When k > 0, y value increases with the increase of x value, and when x < 0, y value decreases with the increase of x value.

Second, space and graphics.

A: Understanding of graphics:

1: point, line and surface

Points, lines and faces:

① Graphics are composed of points, lines and surfaces.

(2) Lines intersecting face to face and points where lines intersect.

(3) Points become lines, lines become surfaces, and surfaces become bodies.

Expand and collapse:

(1) In a prism, the intersection of any two adjacent faces is called an edge, and a side is the intersection of two adjacent edges. All sides of the prism have the same length, the upper and lower bottom surfaces of the prism have the same shape, and the side surfaces are cuboids.

(2) N prism is a prism with N faces on its bottom.

Cutting a geometric figure: cutting a figure with a plane, and the cutting surface is called a section.

Three views: main view, left view and top view.

Polygon: It is a closed figure composed of some line segments that are not on the same straight line.

Arc, sector:

(1) A graph consisting of an arc and two radii passing through the end of the arc is called a sector.

② The circle can be divided into several sectors.

2. Angle

Line:

① A line segment has two endpoints.

(2) The line segment extends infinitely in one direction to form a ray. A ray has only one endpoint.

③ A straight line is formed by the infinite extension of both ends of a line segment. A straight line has no end.

Only one straight line passes through two points.

Comparison length:

① Of all the connecting lines between two points, the line segment is the shortest.

② The length of the line segment between two points is called the distance between these two points.

Measurement and representation of angles;

The (1) angle consists of two rays with a common endpoint, and the common endpoint of the two rays is the vertex of the angle.

② One degree of 1/60 is one minute, and one minute of1/60 is one second.

Angle comparison:

The angle (1) can also be regarded as a light rotating around its endpoint.

(2) The ray rotates around its endpoint. When the ending edge and the starting edge are on a straight line, the angle formed is called a right angle. The starting edge continues to rotate, and when it coincides with the starting edge again, the angle formed is called fillet.

(3) The ray from the vertex of an angle divides the angle into two equal angles, and this ray is called the bisector of the angle.

Parallel:

(1) In the same plane, two disjoint straight lines are called parallel lines.

② One and only one straight line is parallel to this straight line after passing through a point outside the straight line.

If both lines are parallel to the third line, then the two lines are parallel to each other.

Vertical:

Two straight lines are perpendicular to each other if they intersect at right angles.

(2) The intersection of two mutually perpendicular straight lines is called vertical foot.

③ On the plane, there is one and only one straight line perpendicular to the known straight line at one point.

3. Intersecting lines and parallel lines

Angle:

(1) If the sum of two angles is a right angle, then the sum of the two angles is complementary; If the sum of two angles is a right angle, then these two angles are called complementary angles.

② The complementary angle/complementary angle of the same angle or equal angle is equal.

③ The vertex angles are equal.

④ congruent angle/internal dislocation angle are equal/internal angles on the same side are complementary, and two straight lines are parallel, and vice versa.