In the days of young study, many people often chase the teacher for knowledge points. Knowledge point is the basic unit of transmitting information, which plays an important role in improving learning navigation. Want a coherent knowledge point? The following is a summary of the basic knowledge points of junior high school mathematics that I have compiled for you. Welcome to share.
Summary of basic knowledge points of junior high school mathematics 1 1, number and algebra a, number and formula: 1, rational number: ① integer → positive integer /0/ negative integer ② score → positive score/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 numbers: addition;
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 Multiplication of two numbers, positive sign of the same sign, negative sign of different sign, absolute value. ② Multiply any number by 0 to get 0. ③ Two rational numbers whose product is 1 are reciprocal.
Division: ① Dividing by a number equals multiplying 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.
2. Real irrational numbers: Infinitely circulating decimals are called irrational numbers.
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.
3. Algebraic expressions
Algebraic expression: A single number or letter is also an algebraic expression.
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.
4. Algebraic expressions and fractions.
Algebraic expression:
(1) The algebraic expression of the product of numbers and letters is called monomial, the sum of several monomials is called polynomial, and monomials and polynomials are collectively called algebraic expressions.
② In a single item, the index sum of all letters is called the number of times of the item.
③ In a polynomial, the degree of the term with the highest degree is called the degree of this polynomial.
Algebraic expression operation: when adding and subtracting, if you encounter brackets, remove them first, and then merge similar items.
Power operation: AM+AN=A(M+N)
(AM)N=AMN
(A/B)N=AN/BN division.
Multiplication of algebraic expressions:
(1) Multiply the monomial with the monomial, multiply them by their coefficients and the power of the same letter respectively, and the remaining letters, together with their exponents, are the factors of the product.
(2) Multiplying polynomial by monomial means multiplying each term of polynomial by monomial according to the distribution law, and then adding the products.
(3) Polynomial multiplied by polynomial. Multiply each term of one polynomial by each term of another polynomial, and then add the products.
There are two formulas: square difference formula/complete square formula.
Division of algebraic expressions:
(1) Divide the single division, coefficient and the same base power separately, and take it as the quotient factor; For the letter only contained in the division formula, it is used as the factor of quotient together with its index.
(2) Polynomial divided by single item, first divide each item of this polynomial by single item, and then add the obtained quotients.
Factorization: transforming a polynomial into the product of several algebraic expressions. This change is called factorization of this polynomial.
Methods: Common factor method, formula method, grouping decomposition method and cross multiplication were used.
Score:
① Algebraic expression A is divided by algebraic expression B. If there is a denominator in division B, then this is a fraction. For any fraction, the denominator is not 0.
② The numerator and denominator of the fraction are multiplied or divided by the same algebraic expression that is not equal to 0, and the value of the fraction remains unchanged.
Knowledge points of junior high school mathematics: the relationship between the position of straight line and constant
①k & gt； 0, the inclination of the straight line is acute.
②k & lt； 0, the inclination of the straight line is obtuse.
③ The steeper the image, the greater the |k|.
④b & gt； The intersection of line 0 and Y axis is above X axis.
⑤b & lt； The intersection of the 0 straight line and the Y axis is below the X axis.
Junior high school mathematics knowledge points 2 basic knowledge points summary 1. Unary linear equation: an integral equation with only one unknown number, the number of unknowns is 1, and the coefficient of the unknown term is not zero.
2. The standard form of one-dimensional linear equation: ax+b=0(x is unknown, a and b are known numbers, a≠0).
3. General steps for solving a linear equation with one variable: sorting out the equation ... removing the denominator ... dismantling the bracket ... changing the terminology ... merging similar terminology ... and converting the coefficient into 1 ... (testing the solution of the equation).
4. Set up a linear equation of one variable to solve application problems:
(1) reading problem analysis method: it is mostly used for "sum, difference, multiplication and division problems"
Read the stem carefully, find out the key words that represent the equal relationship, such as "big, small, many, few, yes, * * *, combination, for, completion, increase, decrease, match-",list the text equations with these key words, and set the unknown number according to the meaning of the question. Finally, using the relationship between quantity and quantity in the question, fill in the algebraic expression and get the equations.
(2) Drawing analysis method: mostly used for "trip problem"
Analyzing mathematical problems with graphics is the embodiment of the combination of numbers and shapes in mathematics. Read the question carefully, and draw the relevant figures according to the meaning of the question, so that each part of the figure has a specific meaning. Finding the equation relationship through graph is the key to solve the problem, so as to obtain the basis of concise equation. Finally, using the relationship between quantity and quantity (unknown quantity can be regarded as known quantity), filling in the relevant algebraic expression is the basis of getting the equation.
1 1. Common formulas for solving application problems with column equations:
(1) Travel problem: distance = speed time;
(2) Engineering problems: workload = work efficiency and working time;
(3) ratio: part = total ratio;
(4) Downstream problem: Downstream velocity = still water velocity+water velocity, and countercurrent velocity = still water velocity-water velocity;
(5) Commodity price: selling price = pricing discount, profit = selling price-cost;
(6) Perimeter, area and volume: C circle =2πR, S circle =πR2, C rectangle =2(a+b), S rectangle =ab, C square =4a,
S square =a2, S ring = π (R2-R2), V cuboid =abc, V cube =a3, V cylinder =πR2h, V cone =πR2h.
The content of this chapter is the core of algebra and the basis of all algebraic equations. Colorful problem situations and happiness in solving problems can easily arouse students' interest in mathematics, so we should pay attention to the study of problems around us, guide students to carry out effective mathematical activities and cooperative exchanges, and let students acquire knowledge, improve their ability and experience mathematical thinking methods in the process of active learning and inquiry learning.
Junior high school mathematics knowledge points 3 summary of basic knowledge points "children's pilot and solution essentials of binary quadratic equation and binary quadratic equation" has been finished for everyone. The next knowledge point is the number axis. I hope students can understand the knowledge essentials of directed straight line and number axis.
number axis
1 1 directed line
In science and technology and daily life, in order to distinguish two different directions of a straight line, one direction can be defined as positive and the other as negative.
The straight line that specifies the positive direction is called a directed straight line, which is pronounced as a directed straight line L.
12 axis
We call the real number corresponding to any point on the number axis the coordinates of that point.
For each coordinate (real number), a unique point can be found in a few weeks, and this point is the coordinate of a straight line.
The number of any directed line segment on the number axis is equal to the difference between its terminal coordinates and its starting coordinates, and the length of any directed line segment is equal to the absolute value of the difference between its two power-off coordinates.
The above content is the number axis of junior high school mathematics knowledge points. I believe that students can master it well after reading it. Want to know more and more comprehensive junior high school mathematics knowledge, pay attention to it.
Summary of junior high school mathematics knowledge points: plane rectangular coordinate system
The following is the study of the content of plane rectangular coordinate system. I hope students can master the following content well.
Cartesian coordinates/Cartesian coordinates
Plane Cartesian coordinate system: Draw two mutually perpendicular number axes with coincident origin on the plane to form a plane Cartesian coordinate system.
The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, and the intersection of the two coordinate axes is the origin of the plane rectangular coordinate system.
Elements of a plane rectangular coordinate system: ① On the same plane; ② Two axes of numbers are perpendicular to each other; ④ The origin coincides.
Three rules:
① The specified positive direction: the horizontal axis is right, and the vertical axis is oriented in the positive direction.
(2) the provisions of the unit length; Generally speaking, the unit length of the horizontal axis and the vertical axis is the same; In fact, sometimes it can be different, but it must be on the same axis.
③ Quadrant definition: the upper right is the first quadrant, the upper left is the second quadrant, the lower left is the third quadrant, and the lower right is the fourth quadrant.
I believe that the students have mastered the knowledge of plane rectangular coordinate system, and I hope they can all be admitted.
Knowledge points of junior high school mathematics: the composition of plane rectangular coordinate system
Let's learn about the composition of the plane rectangular coordinate system.
Composition of plane rectangular coordinate system
Two number axes perpendicular to each other on the same plane and having a common origin form a plane rectangular coordinate system, which is called rectangular coordinate system for short. Usually, the two number axes are placed in the horizontal position and the vertical position respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, and the X axis or Y axis is collectively called coordinate axis, and their common origin O is called the origin of rectangular coordinate system.
Through the explanation and study of the composition knowledge of plane rectangular coordinate system, I hope students can master the above contents well and study hard.
Junior high school mathematics knowledge points: the nature of the coordinates of points
The following is a study on the coordinate properties of points in mathematics. Students should take a closer look.
Properties of point coordinates
After the plane rectangular coordinate system is established, the coordinates of any point on the coordinate system plane can be determined. Conversely, for any coordinate, we can determine a point it represents on the coordinate plane.
For any point C on the plane, the intersection point C is perpendicular to the X-axis and Y-axis respectively, and the corresponding points A and B perpendicular to the X-axis and Y-axis are respectively called the abscissa and ordinate of the point C, and the ordered real number pairs (A, B) are called the coordinates of the point C. ..
A point is in different quadrants or coordinate axes, and its coordinates are different.
I hope that the students can master the knowledge of the above coordinate nature, and I believe that the students will achieve excellent results in the exam.
Knowledge points of junior high school mathematics: general steps of factorization
About the general steps of factorization in mathematics, we will explain the following knowledge.
General steps of factorization
If the polynomial has a common factor, first mention the common factor, and then consider the formula method if there is no common factor. If it is a polynomial with four or more terms,
Usually, the group decomposition method is used, and finally the cross multiplication factor is used to decompose the factors. So it can be summarized as "one mention", "two sets", "three groups" and "forty words".
Note: Factorization must be decomposed until each factor can no longer be decomposed, otherwise it is incomplete factorization. If the topic does not clearly indicate the scope of factorization, it should refer to factorization within rational numbers, so the result of factorization must be the product of several algebraic expressions.
I believe the students have mastered the general steps of factorization, and I hope they will do well in the exam.
Knowledge points of junior high school mathematics: factorization
The following is the knowledge explanation of factorization in mathematics. I hope the students will study hard.
factoring
Definition of factorization:
Transforming a polynomial into the product of several algebraic expressions is called decomposing this polynomial.
Decomposition element:
① The result must be an algebraic expression ② The result must be a product ③ The result is equation ④.
The relationship between factorization and algebraic expression multiplication: m(a+b+c)
Common factors:
The common factor of each term of a polynomial is called the common factor of a polynomial.
Methods for determining common factors:
① When the coefficient is an integer, take the greatest common divisor of each term. The product of the greatest common divisor of the same letter and the lowest power of the same letter is the common factor of this polynomial.
To select a common factor:
① Determine the common factor. ② Determine the quotient formula ③ The common factor formula and the quotient formula are written in the form of product.
Factorizing attention;
(1) Lost letters are not allowed.
(2) It is not allowed to lose the same items. Please check the quantity of items.
③ Change the double brackets into single brackets.
(4) The results are arranged in the order of number, single letter and single polynomial.
⑤ The same factor is written as a power.
⑥ The first minus sign is placed outside the brackets.
⑦ Similar items in brackets are merged.
Through the above explanation and study of factorization content knowledge, I believe that students have mastered it very well, and I hope the above content will be helpful to students' learning.
;