Summary of compulsory knowledge points in junior high school mathematics: a quadratic equation.
Students have mastered the method of solving practical problems with linear equations of one variable. When solving some practical problems, we will encounter a new equation-a quadratic equation. The purpose of this chapter is to understand this equation, discuss its solution and use this equation to solve some practical problems.
In this chapter, firstly, the concept of quadratic equation is introduced through the problems of statue design, making square boxes and volleyball competition, and the general form of quadratic equation is given. Then let the students find some simple solutions of the quadratic equation of one yuan through numerical substitution, experience the solutions of the quadratic equation of one yuan, and give the concept of the root of the quadratic equation of one yuan.
The section "Decreasing Order-Solving the Quadratic Equation of One Variable" introduces three methods for solving the quadratic equation of one variable: collocation method, formula method and factorization method. The following are explained separately.
(1) When introducing collocation method, the formal equation is first derived through practical problems. Such an equation can be transformed into a simpler equation, and the solution of this equation can be obtained from the concept of square root. Then an example is given to illustrate how to solve the equation in the form of. Then an example is given to show that the quadratic equation of one variable can be transformed into a formal equation, and the matching method is derived. Finally, an example of solving a quadratic equation with one variable by collocation method is given. The example involves a quadratic equation whose quadratic coefficient is not 1, and also involves a quadratic equation without real number roots. For the quadratic equation with one variable without real number roots, students will have a further understanding of this content after learning the formula method.
(2) When introducing the formula method, we first discuss the solution of the equation with the help of collocation method, and get the root formula of the quadratic equation with one variable. Then arrange an example of solving a quadratic equation with one variable by formula method. In the example, it involves a quadratic equation with two equal real roots and a quadratic equation without real roots. This leads to three situations of the solution of the quadratic equation with one variable.
(3) When factorization is introduced, firstly, the quadratic equation of one variable which is easy to use factorization is deduced through practical problems, and the factorization method is deduced. Then arrange an example of factorization to solve a quadratic equation with one variable. Finally, three methods for solving the quadratic equation of one variable are summarized, namely collocation method, formula method and factorization method.
In the section of "Practical Problems and Quadratic Equation of One Yuan", four inquiry columns are arranged to explore issues such as communication, cost reduction rate, area, uniform and variable motion. Make students further understand that equation is an effective mathematical model to describe the real world.
Radial
Students have learned about translation and axis symmetry, explored their properties and applied them to pattern design. The graphic transformation in this book adds a new member-rotation. The chapter "Rotation" is to understand this change and explore its essence. On this basis, we know the centrosymmetric and centrosymmetric graphs.
The "rotation" section first introduces the concept of rotation through examples. Then let the students explore the essence of rotation. On this basis, an example is given to illustrate the method of making the rotation diagram. Finally, an example shows that rotation can be used for pattern design.
The "central symmetry" section first introduces the concept of central symmetry through examples. Then let the students explore the essence of central symmetry. On this basis, an example is given to illustrate the method of constructing a centrally symmetric graph with a graph. After these contents, the concept of central symmetric figure is introduced through line segments and parallelograms. Finally, the relationship between the coordinates of points with symmetrical origin and the method of forming a graph with central symmetry by using this relationship with a graph are introduced.
Expand reading: memorize the methods to improve math scores. Don't think understanding is enough.
Therefore, mathematical definitions, rules, formulas and theorems must be memorized, and some of them are best memorized and catchy. For example, the familiar "Three Formulas of Algebraic Multiplication", if you can't recite these three formulas, will cause great trouble for future study, because these three formulas will be widely used in future study, especially the factorization to be learned in senior two, in which three very important factorization formulas are all derived from these three multiplication formulas and deformed in the opposite direction.
Remember definitions, rules, formulas, theorems, etc. Remember what you know about mathematics, temporarily remember what you don't know, and deepen your understanding on the basis of memory and when you apply them to solve problems. If you can't remember the definition, rules, formulas and theorems of mathematics, it will be 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.
The cultivation of learning 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.
Confidence can make you stronger.
In the exam, I always see that some students have a lot of blanks in their papers, but they haven't done a few questions at all. Of course, as the saying goes, art is bold, art is not timid. However, it is one thing to fail, and it is another thing to fail. The solution and result of a slightly more difficult math problem are not obvious at a glance. It is necessary to analyze, explore, draw, write and calculate. After tortuous reasoning or calculation, some connection between conditions and conclusions will be revealed and the whole idea will be clear.