Chapter 1 Rational Numbers
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 called complementary angles, that is, each angle is the complementary angle of the other 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 IV Data Collection and Arrangement
Collecting, sorting, describing and analyzing data is the basic process of data processing.
Review the general information seven times.
Chapter 1 One-variable linear equation
1. Definition of linear equation with one variable (including only one unknown, the exponent of the simplified unknown is 1, and the coefficient of the unknown cannot be zero)
2. Add and subtract a number or the same algebraic expression on both sides of the equation at the same time, and the solution of the equation remains unchanged.
3. Both sides of the equation are multiplied or divided by a non-zero number, and the solution of the equation remains unchanged.
4. Steps to solve a linear equation with one variable: remove the denominator; Remove the brackets; Transposition; Merge similar projects; The coefficient of the unknown is 1.
5. Pay attention to the relationship among reciprocal, reciprocal and similar items. There are also problems with this chapter.
Chapter II Binary Linear Equations
1. Definition of binary linear equation (including two unknowns, the number of which is 1)
2. Solution of binary linear equation: substitution elimination method, addition and subtraction elimination method.
Chapter III Polygons
1. the relationship between the inner angles of the triangle
The sum of the internal angles of the (1) triangle is equal to 180.
(2) Any external angle of a triangle is equal to the sum of its two non-adjacent internal angles.
(3) The outer angle of a triangle is larger than any inner angle that is not adjacent to it.
(4) The sum of the external angles of the triangle is 360.
2. Classification of angles
(1) classified by angle
Acute triangle: all three angles are acute.
Right triangle: It has a right angle and two acute angles.
Obtuse triangle: It has an obtuse angle and two acute angles.
Classification of equilateral triangles isosceles triangles (including equilateral triangles)
3. Trilateral relationship of triangle
The sum of any two sides of a (1) triangle is greater than the third side.
(2) The difference between any two sides of a triangle is less than the third side.
4. Related attributes of polygons
The sum of the internal angles of (1)n polygons is (n-2) * 180.
(2) The sum of the external angles of any polygon is 360.
(3) The outer angle of a regular N-polygon is 360 /n n n.
(4)n polygons are unstable (n >；; 3)
(5) Triangle is stable.
5. Lay the floor with regular polygons
(1) The floor can cover the same regular polygon: regular triangle, square and regular hexagon.
(2) Use all kinds of regular polygons to lay the floor for the same reason as written in the textbook.
Chapter IV Axisymmetry
1. Axisymmetric: Fold the graph along a straight line. If it can overlap with another graph, then the two graphs are symmetrical about this straight line.
2. The corresponding points in two graphs are called symmetry points about this line and symmetry axes, and the symmetry of two graphs about this line is also called symmetry axes.
3. Axisymmetric figure: If a figure is folded in half along a straight line and the parts on both sides of the straight line can overlap each other, then this figure is called an axisymmetric figure, and this straight line is its axis of symmetry.
4. The distance between the point on the vertical line of the line segment and the two endpoints of the line segment is equal.
5. If a graph is symmetrical about a straight line, then the perpendicular line connecting the symmetrical points is not the symmetry axis of the graph.
6. If the straight line connecting the corresponding points of two graphs is vertically bisected by the same straight line, then the two graphs are symmetrical about this straight line.
7. Two figures are symmetrical about a straight line. If their corresponding line segments or extension lines intersect, then the intersection point is on the axis of symmetry.
8. Axisymmetric is two figures, and axisymmetric figure is one figure.
9. Axisymmetric and axisymmetric figures have axes of symmetry. If an axisymmetric figure is regarded as a whole, it is an axisymmetric figure. If an axisymmetric figure is divided into two parts along the axis of symmetry, then the two figures are symmetrical about this line.
Chapter five. A rudimentary knowledge of statistics
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