Integers can be divided into positive integers, 0 and negative integers.
Scores can be divided into positive scores and negative scores.
2) It can be divided into positive numbers, 0 and negative numbers.
Positive numbers can be divided into positive integers and positive fractions.
Negative numbers can be divided into negative integers and negative fractions.
The classification of real numbers in the senior high school entrance examination 3 has the following classification methods:
If classified by rational numbers and irrational numbers, there are: real rational numbers, positive rational numbers, zero negative rational numbers, finite decimals, irrational numbers, positive irrational numbers, negative irrational numbers and infinite acyclic decimals.
Since rational numbers and irrational numbers are both positive and negative, real numbers can be divided into: real numbers are positive, real numbers are positive, rational numbers are positive, irrational numbers are zero, negative, real numbers are negative, rational numbers are negative and irrational numbers are negative.
It should be pointed out here that:
(1) rational numbers can be converted into decimals, where integers can be regarded as decimals followed by zero, for example, 5 = 5.0; Fractions can be converted into finite decimals or infinite cyclic decimals, such as 12=0.5 (finite decimal) and 13=0.3 (infinite cyclic decimal).
(2) Irrational numbers are infinitely circulating decimals, including numbers that cannot be opened by the root sign, such as 2, 33, π, etc.
(3) Both finite decimals and infinite cyclic decimals can be converted into fractions, that is, all rational numbers can be expressed by fractions; Infinitely cyclic decimals cannot be converted into fractions, but they are irrational numbers.
Classification of real numbers of knowledge points in senior high school entrance examination Article 4 Irrational numbers:
The decimal of infinite cycle is called irrational number.
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.
If the square of a number x is equal to a, then this number x is called the square root of a.
(3) Positive numbers have two square roots /0 square roots are 0/ negative numbers have no square roots.
(4) Find the square root of a number, which is called the square root, where a is called the square root.
Cubic root:
If the cube of a number x is equal to a, then this number x is called the cube root of a.
② The cube root of positive number is positive number, the cube root of 0 is 0, and the cube root of negative number is negative number.
The operation of finding the cube root of a number is called square root, where a is called square root.
Real number:
① Real numbers are divided into rational numbers and irrational numbers.
② In the real number range, the meanings of reciprocal, reciprocal and absolute value are exactly the same as those of reciprocal, reciprocal and absolute value in the rational number range.
③ Every real number can be represented by a point on the number axis.
I believe that the above explanation of real number knowledge can help students consolidate their study of this knowledge. I hope the students can do well in the exam.
Mathematical knowledge points of senior high school entrance examination: algebraic expressions
For the study of algebra in junior high school mathematics, we have made the following induction and explanation, hoping that students will study the knowledge explained below.
Algebraic formula:
A single number or letter is also algebraic.
Merge similar projects:
Items with the same letter and the same letter index are called similar items.
(2) Merging similar items into one item is called merging similar items.
(3) When merging similar items, we add up the coefficients of similar items, and the indexes of letters and letters remain unchanged.
The above explanation and study of algebra knowledge in mathematics can be well mastered by students, and we will do more explanation and study of mathematics knowledge points later.
Expounding the knowledge points of rational numbers in senior high school entrance examination.
Students are familiar with the knowledge of rational numbers in mathematics, right? The following is the teacher's detailed explanation of knowledge, hoping to help students learn.
Rational number:
① Integer → Positive integer /0/ negative integer
② Score → Positive/Negative Score
Number axis:
① Draw a horizontal straight line, take a point on the straight line to represent 0 (origin), choose a certain length as the unit length, and specify the right direction on the straight line as the positive direction, and you will get the number axis.
② Any rational number can be represented by a point on the number axis.
(3) If two numbers differ only in sign, then we call one of them the inverse of the other number, and we also call these two numbers the inverse of each other. On the number axis, two points representing the opposite number are located on both sides of the origin, and the distance from the origin is equal.
The number represented by two points on the number axis is always larger on the right than on the left. Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than negative numbers.
Absolute value:
On the number axis, the distance between the point corresponding to a number and the origin is called the absolute value of the number.
(2) The absolute value of a positive number is itself, the absolute value of a negative number is its reciprocal, and the absolute value of 0 is 0. Comparing the sizes of two negative numbers, the absolute value is larger but smaller.
Operation of rational number:
add
: ① Add the same sign, take the same sign and add the absolute value.
② When the absolute values are equal, the sum of different symbols is 0; When the absolute values are not equal, take the sign of the number with the larger absolute value and subtract the smaller absolute value from the larger absolute value.
(3) A number and 0 add up unchanged.
Subtraction: Subtracting a number equals adding the reciprocal of this number.
Multiplication:
① Multiply two numbers, the same sign is positive, the different sign is negative, and the absolute value is multiplied.
② Multiply any number by 0 to get 0.
③ Two rational numbers whose product is 1 are reciprocal.
Department:
(1) divided by a number and multiplied by the reciprocal of a number.
②0 is not divisible.
Power: the operation of finding the product of n identical factors A is called power, the result of power is called power, A is called base, and N is called degree.
Mixing order: multiply first, then multiply and divide, and finally add and subtract. If there are brackets, calculate first.
By explaining the knowledge points about rational numbers in mathematics, I believe it can help students learn mathematics well. Students study hard!
Classification of real numbers in senior high school entrance examination Part V: Concept and classification of real numbers.
1, classification of real numbers, positive rational numbers, rational numbers, zero finite decimals and infinite cyclic decimals.
Negative rational number
Positive irrational number
Irrational number infinite acyclic decimal
Negative irrational number
Integers include positive integers, zero and negative integers.
Positive integers are also called natural numbers.
Positive integer, zero, negative integer, positive fraction and negative fraction are collectively called rational numbers.
2. Irrational number
When understanding irrational numbers, we should grasp the moment of "infinite non-circulation", which can be summarized into four categories:
(1) An inexhaustible number, such as 7, 2, etc. ;
π(2) a number with a specific meaning, such as pi, or a simplified number containing pi, such as+8; three
(3) Numbers with specific structures, such as 0,101001001… etc.
Second, the reciprocal, reciprocal and absolute value of real numbers.
1, reciprocal
A real number and its inverse are a pair of numbers (only two numbers with different signs are called inverse numbers, and the inverse of zero is zero). Seen from the number axis, the points corresponding to two opposite numbers are symmetrical about the origin. If a and b are opposites, then a+b=0, A =-B, and vice versa.
2. Absolute value
The absolute value of a number is the distance between the point representing the number and the origin, |a|≥0. When the absolute value of zero is itself, it can also be regarded as its inverse. If |a|=a, then a ≥ 0; If |a|=-a, then a≤0. Positive numbers are greater than zero and negative numbers are less than.
Zero, positive number is greater than all negative numbers, two negative numbers, the larger absolute value is smaller.
Step 3 count down the seconds
If A and B are reciprocal, there is ab= 1, and vice versa. The numbers whose reciprocal equals itself are 1 and-1. Zero has no reciprocal.
4, the relationship between real numbers and points on the number axis:
Every irrational number can be represented by a point on the number axis.
Some points on the number axis represent rational numbers and some represent irrational numbers.
Real numbers correspond to points on the number axis one by one, that is, each real number can be represented by a point on the number axis; On the contrary, every point on the number axis represents a real number.
The nature of junior high school mathematics line segment
(1) Axiom of Line Segment: Of all the straight lines connecting two points, the line segment is the shortest. It can also be simply said that the line segment between two points is the shortest.
(2) The length of the line segment connecting two points is called the distance between these two points.
(3) The midpoint of the line segment is equal to the distance between the two endpoints.
(4) The relationship between the size of a line segment and its length is consistent.
The fastest way to learn mathematics in senior one.
Preview reading before class
When previewing the text, you should prepare a piece of paper and a pen, and write down the key words, questions and problems that need to be considered in the textbook. You can simply repeat and reason about definitions, axioms, formulas and rules on paper. Key knowledge can be approved, marked, circled and marked in textbooks. Doing so not only helps us to understand the text, but also helps us to concentrate on listening in class.
Consolidation after class
It is also important to consolidate knowledge after class. After-class consolidation can make your knowledge points have a memorable effect and deepen the effect of memorizing mathematics knowledge points.
Will compare
When learning basic knowledge (such as concepts, definitions, laws, theorems, etc.). ), we should use comparison, analogy, counterexample and other ways of thinking to understand its connotation and extension, and distinguish between similar and confusing basic knowledge. For example, when learning prism, we can compare it with the cylinder that we are already familiar with, sum up their similarities and differences, and achieve the purpose of deepening memory and understanding.
Write a summary of mathematics learning
Writing a summary of mathematics learning once a week is also a good way to improve junior high school mathematics learning performance. When writing a summary of junior high school mathematics learning, you can review the general situation of mathematics learning this week, and also write down some plans for your mathematics learning next week and next month, so that you can not only summarize your past learning, but also plan your future mathematics learning. Together, our mathematics learning ideas and goals will be clearer.
Knowledge points of real number classification in senior high school entrance examination 6 1. Digital classification and concept number system table;
Note: Classification principle: 1) Proportionality (no weight, no leakage) 2) Standard.
2. Non-negative number: the collective name of positive real number and zero. (Form: x0)
Property: If the sum of several non-negative numbers is 0, then each non-negative number is 0.
3. Countdown:
① Definition and representation
② attribute: a.a1/a (a1); 1/a，aC.0
4. The opposite number:
① Definition and representation
② Property: the position of aB.a and -a on the number axis when A.a0; The sum of c is 0 and the quotient is-1.
5. Number axis:
① Definition (three elements)
② Function: a. Visually compare real numbers; B. clearly reflect the absolute value; C. establish a one-to-one correspondence between points and real numbers.
6. Odd numbers, even numbers, prime numbers and composite numbers (positive integer natural numbers)
Definition and expression:
Odd number: 2n- 1
Even number: 2n(n is a natural number)
7. Absolute value:
(1) definition (2):
Algebraic definition:
Geometric definition: the geometric meaning of the absolute value top of the number A is the distance from the point corresponding to the real number A on the number axis to the origin.
②│a│0, and the symbol │ │ is a sign of non-negative numbers;
③ There is only one absolute value of number A;
(4) To deal with any kind of topic, as long as there is a │ │ in it, the key step is to remove this │ │ symbol.