1, zero is the dividing line between positive and negative numbers.
2. Scores consist of positive scores and negative scores.
3. Positive numbers and fractions are collectively called rational numbers.
Rational number: positive number: positive integer, zero, negative integer
Score: positive score, negative score
4. If we regard positive numbers as fractions with denominator of 1, then in this sense, all rational numbers are fractions.
5. Definition of number axis: The straight line defining origin, positive direction and unit length is called number axis. 6. Any rational number can be represented by a point on the number axis.
7. There are only two numbers with different signs, and we call one of them the inverse of the other.
Also called these two numbers are reciprocal, and the reciprocal of zero is zero.
8. The distance between the point corresponding to a number on the number axis and the origin is called the absolute value of this number. 9. The absolute value of a positive number is itself. 10, the absolute value of the subsidiary is its reciprocal. The absolute value of 1 1 and zero is zero.
12, positive number is greater than zero, zero is greater than negative number, positive number is greater than negative number. 13, two negative numbers, the one with the largest absolute value is smaller. 14、
Rational number addition rule:
Add two numbers with the same sign, take the original sign, and then add the absolute values.
Two numbers with different signs are added, and the sum is zero when the absolute values are equal; When the absolute values are not equal, the absolute value of the sum is the difference between the larger absolute value and the smaller absolute value, and the sign of the sum is the sign of the addend with the larger absolute value. Add a number to zero and you still get the number.
15、
Arithmetic of rational number addition
Commutative law: a+b=b+a associative law: (a+b)+ c=a+(b+c)
16, the subtraction rule of rational numbers
Subtracting a number is equal to adding the reciprocal of this number.
A-b=a+(-b) 17, the symbolic law of multiplication of two numbers.
Positive multiplication is positive, positive multiplication is negative, negative multiplication is positive and negative multiplication is positive. 18, multiplication rule of rational numbers
Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value.
Any number multiplied by zero equals zero. 19. Multiply several numbers that are not equal to zero. The sign of the product is determined by the number of negative factors. When there are strange negative factors,
The product is negative; Even when there are negative factors, the product is positive; Multiply several numbers. If the factor is zero, the product is zero.
In other words, each factor of the product has only one negative sign, and the product is negative;
There are two negative signs and the product is positive; There are three negative signs, and the product is negative; There are four negative signs, and the product is positive; When time is zero, the product is zero.
20, rational number division rule
Divide two numbers, the same sign is positive, the different sign is negative, and divide by the absolute value.
Divide zero by any number that is not zero to get zero. 2 1, the operation of finding the product of n identical factors is called power. The result of multiplication is called power. In, is called.
Do the base number, n is the exponent, an is pronounced as the n power of a, and when an is regarded as the result of the n power of a, it is pronounced as the n power of a.22,
Any power of positive numbers is positive numbers, odd powers of negative numbers are negative numbers, and even powers of negative numbers are positive numbers.
23. The order of rational number mixed operation: multiply first, then multiply and divide, and then add and subtract; Statistical operations from left to right; if
If there are brackets, count the brackets first, then the brackets, and then the braces. 24, write a number as a* 10n (where 1 ≤ A < 10, n is a positive integer), this form of counting method is called.
Scientific symbols (scientific symbols)
Chapter VI Linear Equations (Groups) and Linear Inequalities (Groups)
The meaning of the equation; The meaning of linear equation; Solutions of linear equations; Significance and solution of inequality
1, and the required unknown quantity is represented by letters x, y, etc. These letters are called unknowns. An equation with an unknown number is called an equation. In equations, unknowns are also called elements. In order to find the unknown number, an equivalent relationship is established between the unknown number and the known number, which is the column equation. 2. If a certain value of the unknown quantity can make the left and right sides of the equation equal, then the value of the unknown quantity is called the solution of the equation.
3. An equation with only one unknown number and one unknown number is called a linear equation. 4. The property of the equation is 1: add (or subtract) the same number or equations with letters on both sides of the equation at the same time, and the result is still an equation. Property 2 of the equation: When both sides of the equation are multiplied by the same number (or divided by the same non-zero number), the result is still an equation. 5. The rule of removing brackets is that there is a "+"sign in front of brackets. After removing brackets, all items in brackets remain unchanged. Parentheses are preceded by a "-"sign. When the brackets are removed, all items in the brackets will change their symbols. 6. The general steps to solve a linear equation are:-denominator; -Remove the brackets;
-transposition;
-in the form of ax=b(a≠0)
-Divide the two sides by the coefficient of the unknown quantity to get the solution of equation x=b/a 7. The general steps to solve the application problem of sequence equation are as follows:-setting unknowns (elements); -column equation; -Solving equations;
-Test and answer.
8. The relationship represented by the inequality symbol "< >" ≤ "and ≥" is called inequality.
9. Inequality 1: Add (or subtract) the same number or the same formula with letters on both sides of the inequality, and the direction of the inequality remains unchanged, that is, if A > B, A+M > B+M.
If a < b, then a+m < b+m.
10, inequality 2: both sides of the inequality are multiplied (or divided) by the same positive number at the same time, and the direction of the inequality remains unchanged, that is:
If a > b and m > 0, then am > BM (or a/m > b/m) If a < b and m > 0, then am < BM (or a/m < b/m).
1 1, inequality 3: both sides of the inequality are multiplied (or divided) by the same negative number at the same time, and the direction of the inequality changes, that is:
If a > b and m < 0, am < BM (or a/m > b/m) If a < b and m < 0, am > BM (or a/m < b/m).
12. In an inequality with unknowns, the value of the unknowns that can accommodate the inequality is called the solution of the inequality. 13. Generally speaking, a linear equation has only one solution, and a linear inequality can have countless solutions. The global solution of inequality is called the solution set of inequality.
14, an inequality that contains only one unknown quantity and the degree of the unknown quantity is once is called a linear inequality of one variable. 15. The general steps to solve a linear inequality with one variable are similar to those to solve a linear equation with one variable, which can be summarized as:-naming; -Remove the brackets;
-transposition;
-the form is ax > b (or ax < b) (where a≠0)- two sides are divided by the coefficient of unknown quantity, and the solution set of inequality is obtained.
16, an inequality group consisting of several linear inequalities with the same unknown number is called a unary linear inequality group. The common part of the solution set of all inequalities in an inequality group is called the solution set of this inequality group. The process of finding the solution set of inequality group is called solving inequality group.
If the solution set of each inequality has no common part, then this inequality group has no solution. 17. The general steps to solve a linear inequality group are:-find the solution set of each inequality in the inequality group;
-representing the solution set of each inequality on the number axis;
-Determine the common part of each inequality solution set, and then get the solution set of this inequality group.
18. A linear equation with two unknowns is called a binary linear equation.
19, 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. 20. There are countless solutions to a binary linear equation, and all the binary linear solutions are called the solution set of this binary linear equation. 2 1, the system of equations composed of several equations is called the system of equations. If there are two unknowns in an equation group and the terms containing the unknowns are both linear terms, then such an equation group is called a binary linear equation group.
22. In a system of binary linear equations, the appropriate solution for each equation is called the solution of binary linear equations.
23. Eliminate an unknown by "substitution" and transform the equation into a linear equation. This solution is called substitution elimination method, or substitution method for short.
24. Eliminate an unknown by adding (or subtracting) two equations, and transform the equation into a one-dimensional linear equation. This solution is called addition, subtraction and elimination.
25. If there are three unknowns in an equation group, and the terms containing these unknowns are all linear terms, such an equation group is called a ternary linear equation group.
26. When solving application problems with column equations, the number of unknowns should be flexibly selected.
For the application problem of two unknowns, it is generally solved by column binary linear equations; Generally, a series of ternary linear equations are used to solve the application problem of three unknowns.
Chapter VII Drawing of Line Segment and Angle
Drawing of straight lines; Ray drawing; Drawing of line segments; Angle drawing; measurement of angle
1, the length of the line segment connecting two points is called the distance between two points. 2. Two line segments can be added (or subtracted), and their sum (or difference) is also a line segment, and its length is equal to the sum (or difference) of the two line segments.
3. A shop that divides a line segment into two equal line segments is called the midpoint of this line segment.
4. An angle is a graph composed of two rays with a common endpoint. The endpoint of the common * * is called the vertex of the angle, and the two rays are called the edges of the angle.
5. An angle is a graph formed by light rotating around its endpoint to another position. The ray at the initial position is called the starting edge of the angle, and the ray at the end position is called the ending edge of the angle.
6. Two angles can be added (or subtracted), and their sum (or difference) is also an angle, and its degree is equal to the sum (or difference) of the angles of these two angles.
7. Draw a ray from the vertex of an angle and divide the angle into two equal angles. This ray is called the bisector of this angle.
8. If the sum of the degrees of two angles is 90, then these two angles are called complementary angles. One of the angles becomes the complement of the other. If the sum of the degrees of two angles is 180, then these two angles are called complementary angles, which are called complementary angles for short. One of the angles is called the complementary angle of the other. 9. The complementary angles of the same angle (or equal angle) are equal; The complementary angles of the same angle (or equal angle) are equal; 10. An angle is equal to its complementary angle. What is the angle? This is an acute angle. An angle is equal to its complementary angle. What kind of angle is this? Are two complementary right angles acute? Can't they all be right angles? Could it all be blunt instruments? cannot
Chapter 8 Re-understanding of Cuboid
Vertex of a cuboid; The edge of a cuboid; The face of a cuboid; Surface area of cuboid; Volume formula of cuboid;
1. A cuboid has six faces, eight vertices and twelve sides. 2. Every face of a cuboid is a rectangle.
3. The twelve sides of a cuboid can be divided into three groups, and the four sides in each group have the same length.
4. The six faces of a cuboid can be divided into three groups, and the two faces in each group have the same shape and size.
5. Page 1 15: Understanding the relationship between sides in a cuboid;
As shown in the figure, the straight lines of edge EH and edge EF are on the same plane, and they have one thing in common, which is called this.
Two edges intersect.
The straight lines of side EF and side AB are on the same plane, but they have nothing in common, so we call them two.
The edges are parallel.
The straight line between edge EH and edge AB is neither parallel nor intersecting, so we call these two edges different planes. Generally speaking, if the straight line AB and the straight line CD are on the same plane and have only one common point, then these two lines are called.
The positional relationship of straight lines is intersection, which is read as: straight line AB intersects with straight line CD.
7. If the straight line AB and the straight line CD are in the same plane, but there is no common point, then say the position of the two straight lines.
The relationship is parallel, marked as AB∑CD, and read as: straight line AB is parallel to straight line CD. 8. If the straight line AB and the straight line CD are neither parallel nor intersect, then the positional relationship between the two straight lines is called different.
Face, pronunciation: straight line AB is different from straight line CD. 9. The straight line PQ is perpendicular to the plane ABCD. Remember: straight line PQ⊥ plane ABCD is read as: straight line PQ is perpendicular to plane ABCD.
ABCD 10 plane,
How to check that the straight line is perpendicular to the plane? You can use the "plumb line" test.
If the thin rod is perpendicular to the wall, it can be tested with a "triangular ruler". You can also use "hinge origami" to check whether the straight line is perpendicular to the plane.
1 1, the straight line PQ is parallel to the plane ABCD, which is recorded as: straight line PQ∨ plane ABCD, and read as: straight line PQ is flat.
Walking on the plane, ABCD. 12, how to check that the straight line is parallel to the plane? You can use the "plumb line" test. You can also use "rectangular paper" to test.