Math 1 common problem-solving methods, collocation method
The so-called formula is to change some items of an analytical formula into the sum of positive integer powers of one or more polynomials by using the method of constant deformation. The method of solving mathematical problems with formulas is called matching method. Among them, the most common method is to make it completely flat. Matching method is an important method of constant deformation in mathematics. It is widely used in factorization, simplifying roots, solving equations, proving equality and inequality, finding extreme values of functions and analytical expressions.
2, factorization method
Factorization is to transform a polynomial into the product of several algebraic expressions. Factorization is the basis of identity deformation. As a powerful mathematical tool and method, it plays an important role in solving algebra, geometry and trigonometry problems. There are many methods of factorization, such as extracting common factors, formulas, grouping decomposition, cross multiplication and so on. Middle school textbooks also introduce the use of decomposition and addition, root decomposition, exchange elements, undetermined coefficients and so on.
3. Alternative methods
Method of substitution is a very important and widely used method to solve problems in mathematics. We usually refer to unknowns or variables as elements. The so-called method of substitution is to replace a part of the original formula with new variables in a complicated mathematical formula, thus simplifying it and making the problem easy to solve.
4. Discriminant method and Vieta theorem.
The unary quadratic equation ax2+bx+c=0(a, B, C belong to R, A? 0) Discrimination of roots, △=b2-4ac is not only used to judge the properties of roots, but also widely used as a problem-solving method in algebraic deformation, solving equations (groups), solving inequalities, studying functions and even geometric and trigonometric operations.
Vieta's theorem not only knows one root of a quadratic equation, but also finds another root. Knowing the sum and product of two numbers, we can find the symmetric function of the root, calculate the sign of the root of quadratic equation, solve the symmetric equation and solve some problems about quadratic curve. , has a very wide range of applications.
5, undetermined coefficient method
When solving mathematical problems, it is first judged that the obtained results have a certain form, which contains some undetermined coefficients, then the equations about undetermined coefficients are listed according to the problem setting conditions, and finally the values of these undetermined coefficients or some relationship between these undetermined coefficients are found. This method is called undetermined coefficient method to solve mathematical problems. It is one of the commonly used methods in middle school mathematics.
6. Construction method
When solving problems, we often use this method to construct auxiliary elements by analyzing conditions and conclusions, which can be a figure, an equation (group), an equation, a function, an equivalent proposition and so on. And establish a bridge connecting conditions and conclusions, so that the problem can be solved. This mathematical method of solving problems is called construction method. Using construction method to solve problems can make algebra, trigonometry, geometry and other mathematical knowledge permeate each other, which is beneficial to solving problems.
Learning methods of junior high school mathematics 1. Preview before class
Pre-class preparation is neglected by many students and parents, who prefer to spend a lot of time in remedial classes. In fact, prepare well before class on time, so that you can focus on the class. Focus on what you don't understand in class and take notes. Review in time after class. Learning is a step-by-step process, and you won't eat a fat man in one bite; Instead of biting off more than one can chew, it is better to follow the normal learning rules, which will neither delay learning nor play.
Second, lay a good foundation in mathematics.
In mathematics learning, mathematical concepts, definitions of basic theorems and formulas are the basis. Students must first understand, learn to verify when they need to verify, and deduce whatever they can; Only in this way can we understand memory; Really learn. If you don't understand the basic concepts, theorem definitions and formulas, you can't remember them; How do you do this problem? Therefore, laying a good foundation is the key.
Third, be familiar with the examples and thoroughly understand the textbooks.
Mathematics examination and senior high school entrance examination are based on textbooks. So the examples in the book must be thoroughly understood. Go through all the knowledge points in the textbook; Key memory.
Fourth, do the questions in time after class.
Practice after class, and do it in time after learning a lesson. Consolidate what you have learned; Ask the teacher or classmates in time if you don't understand.
Fifth, do synchronous training questions.
The application of mathematical formulas and theorems also needs to do some synchronous training questions in peacetime. But not greedy. You must learn and understand what you do. Summarize other people's methods, find out the gaps and make up for the shortcomings.
Sixth, summarize more comparative memories.
There are many similar or similar theorem definitions and formulas in mathematics. We should be good at summing up their differences and connections. For quick memory. Doing problems is also to sum up good problem-solving methods and skills; It will take a step forward.
Learning methods vary from person to person, so students should sum up more and find their own methods in combination with themselves. Junior high school mathematics is not difficult, I believe everyone can learn it well.
Suggestions on improving junior high school math scores 1. Have a correct attitude towards homework.
We should take it seriously ideologically. If we form the habit of laziness, there will be more problems in the future. If you don't work hard today, you will lose more tomorrow and it will be more difficult to improve. Because the formation of a good habit is to make up your mind to stick to it. Although it is easy to resist because of too many bad habits or problems left over in the process of persistence, and sometimes it is easy to give up, you should know that once a good habit is formed, you will often encounter fewer and fewer problems and your grades will naturally improve.
Second, we must concentrate.
When you are doing your homework, don't do anything else or think about anything else. You can't do two things at once. Finish your homework as soon as possible before you can do anything else.
Third, learn to sum up.
If you can quickly reflect the knowledge points needed for this topic after seeing it, then the speed of doing the topic will be improved, and you should also sum up your own ideas after doing it. To sum up more, you will find that many topics are regular and can get twice the result with half the effort. It can be very easy to encounter similar problems in the future.
Fourth, create a good writing environment.
Try to keep quiet when the children are doing their homework. Don't put anything on the desk except books and school supplies to avoid distracting them. Parents should not nag and reprimand too much, but encourage their children more.
3 Strengthen the computing power
Calculation has always been a core content of mathematics, and almost every mathematical problem needs calculation. Then, the accuracy of calculation is particularly important. In order to improve math scores, the accuracy of calculation must be improved. So how to improve the accuracy of calculation? I also gave some suggestions here.
First, strengthen students' intentional attention and good calculation habits.
(1) The habit of carefully examining questions. After getting the topic, carefully examine the topic, see the requirements of the topic clearly, and want to understand what problems should be paid attention to in the process.
(2) the habit of careful inspection. Check the train of thought first to see if there are any omissions, and then replace the answer with the original question. If it is a calculation problem, check every step carefully.
(3) the habit of writing carefully. Writing should be clean and tidy, so that you can see the topic clearly and avoid it.
The occurrence of mistakes.
Second, strengthen the ability of oral calculation.
Any calculation is based on oral calculation, and the ability of oral calculation directly affects the improvement of students' other calculation abilities. To improve the ability of oral calculation, we must first do the basic training of oral calculation, so we should practice some oral calculation frequently.
Third, quick calculation and clever calculation.
When doing calculation at ordinary times, we should pay attention to the clever use of operation and speed up the operation, especially the fraction calculation part. Sometimes there are many people, and it will be difficult to divide them. At this time, it may be a better choice to write the denominator as a product.
Fourth, strengthen the estimation ability.
Many problems, especially application problems, can be roughly estimated after seeing the problems. With this estimation ability, sometimes the calculation error can be seen at once. So we can also estimate the scope of the answer before doing the problem. If the calculated answer is not within this range, we need to check it.
V. The nature of rational use of some figures