1. 1 positive and negative numbers

A number with a negative sign "-"in front of a number that is not 0 is called a negative number.

It has the opposite meaning to negative number, that is, I learned that numbers other than 0 are called positive numbers (sometimes "+"is added before positive numbers as needed).

1.2 rational number

Positive integers, 0 and negative integers are collectively called integers, and positive and negative fractions are collectively called fractions.

Integers and fractions are collectively called rational numbers.

Numbers are usually represented by points on a straight line, which is called the number axis.

Three elements of number axis: origin, positive direction and unit length.

Take any point on a straight line to represent the number 0, and this point is called the origin.

Numbers with only two different signs are called opposites. (Example: the reciprocal of 2 is-2; The reciprocal of 0 is 0)

The distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A, and it is recorded as |a|.

The absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0. Two negative numbers, the larger one has the smaller absolute value.

Addition and subtraction of rational number 1.3

Rational number addition rule:

1. Add two numbers with the same sign, take the same sign, and then add the absolute values.

2. Add two different symbols with different absolute values, take the symbol of the addend with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value. Two opposite numbers add up to 0.

When a number is added with 0, it still gets this number.

Rule of rational number subtraction: subtracting a number is equal to adding the reciprocal of this number.

Multiplication and division of rational number 1.4

Rational number multiplication rule: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by 0 is 0.

Two numbers whose product is 1 are reciprocal.

Rational number division rule: dividing by a number that is not equal to 0 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 0 by any number that is not equal to 0 to get 0. mì

The operation of finding the product of n identical factors is called power, and the result of power is called power. In the n power of a, a is the base and n is the exponent.

The odd power of a negative number is negative and the even power of a negative number is positive. Any power of a positive number is a positive number, and any power of 0 is 0.

Scientific counting method is used to express numbers greater than 10 as the n power of a× 10.

From the first non-zero digit to the last digit on the left of a number, all digits are valid digits of this number.

Chapter II One-variable Linear Equation

2. 1 From Formula to Equation

An equation is an equation with unknowns.

All equations contain only one unknown (element) X, and the exponent of the unknown X is 1 (degree). Such an equation is called a linear equation with one variable.

Solving the equation is to find the value of the unknown quantity that makes the left and right sides of the equation equal, and this value is the solution of the equation.

Properties of the equation:

1. Add (or subtract) the same number (or formula) on both sides of the equation, and the result is still the same.

2. Both sides of the equation are multiplied by the same number, or divided by the same number that is not 0, and the results are still equal.

2.2 Starting from the Ancient Algebra Books-Discussion on the Linear Equation of One Variable (1)

Moving the sign of the term on one side of the equation to the other side is called moving the term.

The third chapter is the preliminary understanding of graphics.

3. 1 color graphics

Geometry is also called solid for short. What surrounds the body is the surface.

3.2 Lines, rays and line segments

Axiom of line segment: Of all the connecting lines between two points, the line segment is the shortest (the line segment between two points is the shortest).

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

3.3 Angle measurement

1 degree =60 minutes 1 minute =60 seconds 1 fillet =360 degrees 1 flat angle = 180 degrees.

3.4 Angle comparison and operation

If the sum of two angles is equal to 90 degrees (right angle), they are said to be complementary angles, that is, each angle is the complementary angle of another angle.

If the sum of two angles is equal to 180 degrees (flat angle), it is said that the two angles are complementary, that is, each angle is the complement of the other angle.

The complementary angles of equal angles (same angles) are equal.

The complementary angles of equal angles (same angles) are equal.

Chapter V Intersecting Lines and Parallel Lines

5. 1 intersection line

The vertical angles are equal.

One and only one straight line is perpendicular to the known straight line.

Of all the line segments connecting a point outside the straight line with a point on the straight line, the vertical line segment is the shortest (in short, the vertical line segment is the shortest).

5.2 parallel lines

After a point outside the straight line, there is one and only one straight line parallel to this straight line.

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

Conditions of parallel lines:

Two straight lines are cut by a third straight line. If congruent angles are equal, two straight lines are parallel.

Two straight lines are cut by a third straight line. If the internal angles are equal, two straight lines are parallel.

Two straight lines are cut by a third straight line. If they are complementary, then these two straight lines are parallel.

5.3 Properties of parallel lines

Two parallel lines are cut by a third straight line and have the same angle.

Two parallel lines are cut by a third line, and their inner angles are equal.

Two parallel lines intersect with the third straight line, which complement each other.

A statement that judges a thing is called a proposition.

Chapter VI Plane Cartesian Coordinate System

6. 1 plane rectangular coordinate system

A word containing two numbers represents a definite position, where the two numbers represent different meanings. We call this number pair consisting of two numbers A and B in sequence an ordered pair.

Chapter VII Triangle

7. 1 Line segment related to triangle

Triangles are stable.

7.2 Angle related to triangle

The sum of the internal angles of a triangle is equal to 180 degrees.

The outer angle of a triangle is equal to the sum of two non-adjacent inner angles.

The outer angle of a triangle is greater than any inner angle that is not adjacent to it.

7.3 sum of polygons and their internal angles

Is the sum of the internal angles of the N-polygon equal to: (n-2)? 180 degrees

The sum of the outer angles of a polygon is equal to 360 degrees.

Chapter VIII Binary Linear Equations

8. 1 binary linear equations

An equation contains two unknowns (X and Y) whose exponents are 1. Equations like this are called binary linear equations.

Two binary linear equations are combined to form a system of linear equations with two unknowns.

The values of two unknowns that make the values on both sides of the binary linear equation equal are called the solutions of the binary linear equation.

The common * * * solution of two equations of binary linear equations is called the solution of binary linear equations.

8.2 elimination

The idea of solving the unknowns one by one from more to less is called elimination thought.

Chapter 9 Inequality and Unequal Groups

9. 1 inequality

Formulas that indicate the size relationship with less than sign or greater than sign are called inequalities.

The value of the unknown quantity that makes the inequality valid is called the solution of the inequality.

The value range of x that can make inequality hold is called the solution set of inequality, which is called the solution set for short.

An inequality whose unknown number is 1 is called a linear inequality of one variable.

The essence of inequality:

Add (or subtract) the same number (or formula) on both sides of the inequality, and the direction of the inequality remains unchanged.

Both sides of inequality multiply (or divide) the same positive number, and the direction of inequality remains unchanged.

When both sides of the inequality are multiplied (or divided) by the same negative number, the direction of the inequality changes.

The difference between any two sides in a triangle is less than the third side.

The sum of any two sides in a triangle is greater than the third side.

9.3 One-dimensional linear inequality system

When two linear inequalities are combined, a unitary linear inequality is formed.

Chapter 10 Real Numbers

10. 1 square root

If the square of a positive number x is equal to a, then this positive number x is called the arithmetic square root of a, and 2 is the root index.

The arithmetic square root of A is pronounced as "root number A", and A is called radix.

The arithmetic square root of 0 is 0.

If the square of a number is equal to a, then this number is called the square root or quadratic root of a.

The operation of finding the square root of a number is called square root.

10.2 cube root

If the cube of a number is equal to A, then this number is called the cube root or cube root of A. ..

The operation of finding the cube root of a number is called finding the cube root.

10.3 real number

Infinitely cyclic decimals are also called irrational numbers.

Rational numbers and irrational numbers are collectively called real numbers.

I'm in grade seven. Sorry, that's all I can do. . . . . . .