Knowledge point induction in the second volume of mathematics in the second day of junior high school
Chapter 1 One-dimensional linear inequalities and one-dimensional linear inequalities.
1. Generally speaking, formulas connected by symbols (or) and (or) are called inequalities.
The value of the unknown quantity that can make the inequality hold is called the solution of the inequality. The solution of inequality is not to liberate all the inequalities to form the solution set of inequality. The process of finding the solution set of inequality is called solving inequality.
An inequality group consisting of several linear inequality groups is called a linear inequality group.
Solution set of inequality group: the common part of each inequality solution set in the unary linear inequality group.
The basic property of equation 1: Add (or subtract) the same number or algebraic expression on both sides of the equation, and the result is still an equation. Basic property 2: the result of multiplying or dividing the same number on both sides of an equation (the divisor is not 0) is still an equation.
Second, the basic properties of inequality 1: Add (or subtract) the same algebraic expression on both sides of the inequality, and the direction of the inequality remains unchanged. (Note: The shift term needs to be signed, but the inequality remains the same. ) property 2: both sides of the inequality are multiplied (or divided) by the same positive number, and the direction of the inequality remains unchanged. Property 3: Both sides of the inequality are multiplied (or divided) by the same. 2. If ab and c0 represent acbc, if c0, other properties of ac inequality: reflectivity: if ab and bb, and bc and ac.
Third, the steps of solving inequality: 1, denominator; 2. Remove the brackets; 3. Transfer projects and merge similar projects; 4. Convert the coefficient to 1. 4. Steps to solve the inequality group: 1. Solve the solution set of inequality. 2. Represent the solution set of inequality on the same number axis. 5. Enumerate the general steps of solving practical problems with a set of linear inequalities: (1) examining questions; (2) Set an unknown number and find an (unequal) relationship; (3) setting independent variables, setting inequalities (groups) (according to inequalities) (4) solving inequality groups; Test and answer.
6. Frequently asked questions: 1, find the nonnegative solution of 4x-67x- 12. 2. It is known that the solution of 3(x-a)=x-a+ 1r is suitable for 2(x-5)8a, and the range of a is found.
The solution of 3.3x+m-2(m+2)=3m+x is between -5 and 5.
Chapter II Factorization
1. formula: 1, ma+mb+mc=m(a+b+c)2, A2-B2 = (A+B) 3, A2AB+B2 = (AB) 2. Transforming a polynomial into the product of several algebraic expressions is called this deformation.
3. Let the same factor contained in all terms of a polynomial be called the common factor of all terms of this polynomial. The common factor method is to decompose a polynomial into a monomial and then multiply it with the polynomial. The general steps to find the common factor are: (1) If all the coefficients are integer coefficients, take the common factor of the coefficients; (2) Taking the same letter, the index of the letter is lower; (3) Take the same polynomial with lower exponent. (4) The product of all these factors is the common factor.
4. The general steps of factorization are as follows: (1) If there is-first extract-,if each polynomial has a common factor, then extract the common factor. (2) If each polynomial has no common factor, choose the square difference formula or the complete square formula according to the characteristics of the polynomial. (3) Every polynomial must be decomposed until it can no longer be decomposed.
5. The formula in the form of A2+2ab+B2 or a2-2ab+b2 is called the complete flattening method. The methods of factorization are: 1, and the method of extracting common factors.
Chapter III Scores
Note: 1 For any fraction, the denominator cannot be zero.
The difference between fractions and algebraic expressions is that the denominator of fractions contains letters, while the denominator of algebraic expressions does not contain letters.
3 the value of the score is zero, which has two meanings: the denominator is not equal to zero; Molecule equals zero. (If B0 is middle, the score is meaningful; In the score, when B=0, the score is meaningless; When A=0 and B0, the value of the score is zero. )
Common knowledge points: 1, meaning and simplification of score; 2. Addition, subtraction, multiplication and division of scores; 3. The solution of fractional equation and its application.
Eight-grade mathematics knowledge points
1. Two straight lines that do not intersect in the same plane are called parallel lines, which can also be said to be parallel to each other. For example, 1, 1, the positional relationship between two straight lines in the same plane is (intersecting) and (parallel). When two straight lines intersect at right angles, they are said to be perpendicular to each other.
Parallelogram Rectangular rhombic square trapezoid isosceles trapezoid figure Two groups of quadrangles with parallel opposite sides. Define the parallelogram represented by "",for example: ABCD, the parallelogram ABCD is recorded as a plane with right angles, a group of parallelograms with equal adjacent sides are diamonds, and a group of parallelograms with equal adjacent sides are …
Chapter 18 Review of parallelogram knowledge points: characteristics of parallelogram and special parallelogram and their relationship 1. A rectangle is a special parallelogram, and its four internal angles are _ _ _ _ _. Diagonal line of the rectangle __2. The diamond is a special parallelogram, its four sides are _ _, and its two diagonals are flat …
Knowledge induction of special parallelogram and unary quadratic equation
diamond
1. Definition of rhombus: A group of parallelograms with equal adjacent sides is called a rhombus.
2. The nature of diamonds:
The properties of (1) rhombus are as follows: ① All properties of parallelogram; (2) all four sides are equal; ③ Diagonal lines are perpendicular to each other, and each diagonal line bisects a set of diagonal lines; (4) the diamond is the figure of symmetry axis, which has two symmetry axes, and these two symmetry axes are the straight lines where its two diagonals are located.
(2) rhombic area = bottom × height = half of diagonal product.
3. Diamond trial:
(1) is determined by definition (that is, a set of parallelograms with equal adjacent sides is a diamond).
(2) Parallelograms with diagonal lines perpendicular to each other are rhombic.
(3) A quadrilateral with four equilateral sides is a diamond.
To sum up, the common ideas for judging diamonds are:
There are four diamonds of equal sides.
Diamond quadrangle
parallel
A quadrilateral has a set of equilateral diamonds.
rectangle
1. Definition of rectangle: A parallelogram with a right angle is called a rectangle.
2. The properties of rectangle: (1) has all the properties of parallelogram; (2) All four corners of a rectangle are right angles;
(3) All four corners of a rectangle are equal.
4. The rectangle determination method:
(1) is determined by the definition (that is, a parallelogram with right angles is a rectangle);
(2) A quadrilateral with three right angles is a rectangle;
(3) Parallelograms with equal diagonals are rectangles.
To sum up, the common ideas for judging rectangles are:
square
1. Definition of a square: A group of parallelograms with equal adjacent sides and a right angle is called a square.
2. Properties of Square: Square has all the properties of parallelogram, rectangle and diamond.
(1) sides: four sides are equal, adjacent sides are vertical and opposite sides are parallel and equal.
1(2) Angle: All four angles are right angles.
(3) Diagonal lines: Diagonal lines are equal and bisected vertically, and each diagonal line bisects a set of diagonal lines.
Math learning method in grade two of junior high school
Remember what you should remember, remember what you should recite, and don't think you understand.
Some students think that mathematics is not like English, history and geography. Words, dates, and place names are required. Mathematics depends on wisdom, skill and reasoning. I said you were only half right. Mathematics is also inseparable from memory.
Therefore, mathematical definitions, rules, formulas, theorems, etc. Must recite, some can recite, catchy. For example, the familiar "Three Formulas of Algebraic Multiplication", I think some of you here can recite it, while others can't. Here, I want to remind the students who can't recite these three formulas. If they can't recite it, it will cause great trouble for future study, because these three formulas will be widely used in future study, especially the factorization of senior two, in which three very important factorization formulas are all derived from these three multiplication formulas, and they are deformations in opposite directions.
Remember the definitions, rules, formulas and theorems of mathematics, and remember those that you don't understand for the time being, and deepen your understanding on the basis of memory and application to solve problems. For example, mathematical definitions, rules, formulas and theorems are just like axes, saws, Mo Dou and planers in the hands of carpenters. Without these tools, carpenters can't make furniture. With these tools, coupled with skilled craftsmanship and wisdom, you can make all kinds of exquisite furniture. Similarly, if you can't remember the definition, rules, formulas and theorems of mathematics, it is difficult to solve mathematical problems. And remember these, plus certain methods, skills and agile thinking, you can be handy in solving mathematical problems, even solving mathematical problems.
1, the idea of "equation"
Mathematics studies the spatial form and quantitative relationship of things. The most important quantitative relationship in junior high school is equality, followed by inequality. The most common equivalence relation is "equation". For example, uniform motion, distance, speed and time are equivalent, and a related equation can be established: speed and time = distance. In this equation, there are generally known quantities and unknown quantities. An equation containing unknown quantities like this is an "equation", and the process of finding the unknown quantities through the known quantities in the equation is to solve the equation.
Energy conservation in physics, chemical equilibrium formula in chemistry, and a large number of practical applications in reality all need to establish equations and get results by solving them. Therefore, students must learn how to solve one-dimensional linear equations and two-dimensional linear equations, and then learn other forms of equations.
The so-called "equation" idea means that for mathematical problems, especially the complex relationship between unknown quantities and known quantities encountered in reality, we are good at constructing relevant equations from the viewpoint of "equation" and then solving them.
2. The idea of "combination of numbers and shapes"
In the world, "number" and "shape" are everywhere. Everything, except its qualitative aspect, has only two attributes: shape and size, which are left for mathematics to study. There are two branches of junior high school mathematics-algebra and geometry. Algebra studies "number" and geometry studies "shape". It is a trend to learn algebra by means of "shape" and geometry by means of "number". The more you learn, the more inseparable you are from "number" and "shape". In senior high school, a course called "Analytic Geometry" appeared, which used algebra to study geometric problems.
3. The concept of "correspondence"
The concept of "correspondence" has a long history. For example, we correspond a pencil, a book and a house to an abstract number "1", and two eyes, a pair of earrings and a pair of twins to an abstract number "2". With the deepening of learning, we also extend "correspondence" to a form, a relationship, and so on. For example, when calculating or simplifying, we will correspond the left side of the formula, A, Y and B, and then directly get the result of the original formula with the right side of the formula.
The cultivation of self-study ability is the only way to deepen learning.
When learning new concepts and operations, teachers always make a natural transition from existing knowledge to new knowledge, which is the so-called "reviewing the past and learning the new". Therefore, mathematics is a subject that can be taught by itself, and the most typical example of self-study is mathematician Hua.
We listen to the teacher's explanation in class, not only to learn new knowledge, but more importantly, to subtly influence the teacher's mathematical thinking habits and gradually cultivate our own understanding of mathematics.
The stronger the self-study ability, the higher the understanding. With the growth of age, students' dependence will be weakened, while their self-learning ability will be enhanced. So we should form the habit of previewing.
Therefore, solid mathematics learning in the past laid the foundation for future progress, and it is not difficult to learn new lessons by yourself. At the same time, when preparing a new lesson, it goes without saying that it is great to listen to the teacher explain the new lesson with questions when you encounter any problems that you can't solve.
Learn to learn, knowledge is still someone else's. The test of whether you can learn math well is whether you can solve problems. Understanding the definitions, rules, formulas and theorems related to memory is only a necessary condition for learning mathematics well, and being able to solve problems independently and correctly is the symbol of learning mathematics well.
Related articles in the second volume of eighth grade mathematics knowledge points:
★ The arrangement of mathematics knowledge points in the second volume of the eighth grade
★ Arrangement of knowledge points in the second volume of eighth grade mathematics
★ Knowledge point induction and mathematics learning methods in the second volume of junior two mathematics.
★ Knowledge points in the second volume of eighth grade mathematics
★ Mathematics knowledge points in the second volume of the eighth grade
★ Sort out and summarize the knowledge points of eighth grade mathematics.
★ Summarize the mathematics knowledge points in the second volume of the eighth grade.
★ Knowledge points of the second volume of second grade mathematics published by People's Education Press
★ Mathematics knowledge points in the second volume of the eighth grade
★ Knowledge points in the second volume of Mathematics in the second day of junior high school