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 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 IV Data Collection and Arrangement
Collecting, sorting, describing and analyzing data is the basic process of data processing.