Junior high school math problem-solving skills are a very important part. I have very practical junior high school math problem-solving skills to teach you, I hope it will help you!

The first part is the answering skills of junior high school mathematics exam.

First, the principle of answering questions

After you get the test paper, first check whether it is an undergraduate test paper, then check whether the page number of the test paper is complete, and check whether the test paper is damaged or omitted, reprinted or illegible. If problems are found, they should be reported to the invigilator in time for handling.

When answering questions, generally follow the following principles:

1. From front to back, it's easy before it's difficult. Usually, the difficulty distribution of test questions is from front to back according to each question type, from easy to difficult. So the order of solving problems should also be from small to large, from front to back. Sometimes, of course, but not mechanically step by step. When there is a problem in the middle, you can jump over first, and then attack or give up. Get the easy score first, don't you? A hutong darkens? The general principle is easy first, then difficult, choose to fill in the blanks and then solve the problem.

2. Standardize the answers and divide the questions. Mathematics is divided into volumes I and II, and the objective questions in volume I should be read by computer. One is to label the cards strictly according to the regulations, and the other is to choose the answers carefully. Volume two is the subjective question. Generally speaking, except for the fill-in-the-blank questions, most of the answers are given a few small questions, which are generally scored independently. When you answer, you should answer step by step (level) and try to score step by step. When you encounter difficulties in solving problems, you can do a few steps and strive for it point by point, or you can skip a small question and do the next one directly.

3. Score first and improvise. What are the basic principles to master when answering questions? Do the familiar questions carefully, and do the unfamiliar questions slowly? Make sure that you will never lose points where you can score, and strive for places that are not easy to score, but you should prevent the total score from being affected because the problem takes too long.

4. Fill in the fields, don't leave them blank. Examination marking is a continuous flow operation. If you leave too many blanks on the test paper, you will leave a bad impression on the marking teacher and think that you really can't. In addition, each question has a number of scoring points, which can be given if the scoring points are touched, and points will be deducted if the scoring points are not touched. Therefore, as long as time permits, try to write the corresponding formulas or theorems and other related conclusions in the blank space below the topic.

5. Correct views and rational answers. Answering questions should not be too innovative, leading to wrong views and imprecise logic; Or improvise on the test paper and scribble calligraphy and painting irrelevant to the content of the test paper, which may bring unexpected losses to yourself. Graffiti can be considered as marking the test paper and being convicted of cheating. So answer the question rationally.

6. Clear handwriting and reasonable planning. This is very important for any exam, especially for? Accuracy? In advanced mathematics and physics, if the handwriting is scribbled, it will easily lead to the misjudgment of the marking teacher, such as filling in the circled serial numbers and numbers in the fill-in-the-blank questions. If the handwriting is scribbled, the original correct marks may be lost. In addition, the position and size of the paper should also be planned, and the paper should be arranged as much as possible? Tight front and loose back? Instead of. Loose front and tight back? . Pay special attention to answering questions only in the specified position, and turning over questions will not be scored.

Second, the examination points

Examination includes browsing the whole volume and careful examination.

First, browse before the exam. The examination papers will be distributed 5 minutes before the exam. We will use the limited time from the distribution of the test paper to the beginning of answering questions, and have a general understanding of the whole test paper by browsing before answering questions, and initially estimate the difficulty and time allocation of the test paper, so as to arrange the order of answering questions as a whole and be aware of it. What should candidates do at this time? No shame? In other words, when you see a familiar topic, don't feel glad in your heart, but remind yourself. Don't underestimate your enemy when doing this problem. Be careful of any traps, or the questions you do are just the same, and a subtle change will lead to different answers. . Don't be disturbed when you encounter a problem you have never seen before and suddenly have no idea. On the contrary, you should be happy at this time. I haven't done it, and neither has anyone else. This is my chance. ? Always remind yourself: I am easy to change, I don't care; I'm difficult. I'm not afraid of difficulties.

The second is to carefully examine the questions in the process of answering questions. This is a key step, which requires not missing the question, seeing the question clearly, understanding the meaning of the question, understanding the conditions given by the question and the questions to be answered. Different types of questions, different abilities, different problem-solving methods and strategies, and different scoring methods. For different types of questions, the emphasis is different.

1. Multiple-choice questions account for a large proportion of objective questions (40%), with specific contents and many knowledge points. Double base? Pay equal attention to ability. In the examination of multiple-choice questions, it is necessary to find out whether you have chosen the right sentence or the wrong sentence, and what special methods are used to solve it.

2. Fill in the blanks is an objective question. Generally, it is an intermediate problem, but because there is no intermediate problem-solving process, there is no process score. A little mistake means nothing at all. Serious consequences? . When reviewing questions, we should pay attention to the knowledge points, methods and error-prone points of such questions.

3. The answer accounts for a large proportion in the test paper (74 points), and it is necessary not only to calculate the results but also to list the problem-solving process. When solving this kind of problems, it is extremely important to examine the questions. Only by understanding the conditions and implied information provided by the topic, associating the general methods of related problems, and finding and determining the specific methods and steps to solve the problem can we solve the problem.

Third, time allocation.

In recent years, with more and more problems in the application of mathematics test questions in college entrance examination, the reading volume is gradually increasing, and scientific use of time is an important content of improvisation. The basic principle of allocating answering time is to ensure that you will never lose points where you can score, and strive for points where it is not easy to score. In the heart

What should be in it? Fractional time ratio? It is undoubtedly more valuable to spend 10 minutes on a big mid-range problem with 12 points than to use 10 minutes to solve a mid-range fill-in-the-blank problem with 1 4 points. Effective use of the best answer time period, usually the answer efficiency of each time period is different. Generally speaking, most candidates will have psychological changes in the last 10 minute, which will affect the normal answer. Especially those candidates who haven't finished the examination paper will be distracted and impatient, and the efficiency of this time period is lower than other time periods.

After the test paper is handed out, you can get a general idea of the type, quantity, score and difficulty of the test paper by browsing the whole volume. Are you familiar with it? Topic? Then determine the answer time corresponding to each question. Generally speaking, the average level candidates can't answer multiple-choice questions (12) for more than 40 minutes, fill in the blanks (4) for less than 15 minutes, and set aside time for solving problems (6) and checking. Of course, this schedule will vary from person to person.

In the process of solving, we should pay attention to the original time arrangement. For example, the question 1 is planned to take 3 minutes, but there are no eyebrows at all after 3 minutes, so you can skip this question for the time being; But if you are close to success, you have to extend the time. It should be noted that the allocation of time should be subject to the purpose of success in the exam, and the time should be grasped flexibly, not rigidly adhering to the original arrangement. The time schedule is only a rough overall arrangement, and it is not necessary to make the time accurate to every 1 minute or every 1 minute. Needless to say, because the time schedule is too tight, it will cause too much psychological pressure and affect the normal answer.

Generally speaking, you need to set aside 5? 10 minutes of investigation time, but if the number of questions is large, you are more sure of the accuracy of your answers, and the investigation time can be shortened or removed. However, it should be noted that only a few excellent candidates can usually complete the design of math test papers within the specified time.

Four. Main problems and problems

A test paper must have big questions and difficult problems to distinguish the knowledge and ability level of candidates, so as to open the grade. Generally, the scores of big questions and difficult questions are relatively high. When you encounter a difficult problem, you should try your best to overcome it at the end. If all the other topics have been finished and checked correctly, and there is still a certain amount of time, you should work hard to overcome this problem. Not everyone can get 150. If you finish the meeting first, you can also give yourself a psychological advantage.

Five, the answering skills of various questions

1. Answer skills for multiple-choice questions

(1) The basic way to master multiple-choice questions is to grasp the characteristics of multiple-choice questions, make full use of the information provided by multiple-choice questions, and never treat all multiple-choice questions as solutions. First of all, read the description of the test questions clearly and confirm the types and requirements. The second is to review the analytical stem, determine the scope and object of choice, and pay attention to the connotation and extension of analytical stem. The third is to discriminate the options, eliminate the mistakes and choose the right one. The fourth is to mark it correctly and check it carefully.

(2) Special value method. It is especially effective for solving equations or inequalities and determining the scope of verification or exclusion of parameters with special values.

(3) Counterexample method. Exclude the wrong answers in the multiple-choice questions, and the rest are correct answers.

(4) guessing method. Because there is no provision for deducting points for wrong choices in math multiple-choice questions, it can't be solved, and guessing can give you more chances to score. Generally, don't guess A except for the questions that need to be calculated.

2. Fill in the blanks and answer questions

(1) It is required to memorize basic concepts, basic facts, data formulas and principles, and be particularly careful when reviewing, paying attention to rote memorization, so as to recall accurately and clearly before the exam. Pay special attention to those concepts, symbols or figures that play a key role or are most likely to be confused and misremembered, because they are often examined. For example, whether the endpoint of the interval is open or closed, the domain of definition and value should be expressed by interval or set, the monotonous interval is wrongly written as inequality, or two monotonous intervals are union, and so on.

(2) Generally, the fourth fill-in-the-blank question may be relatively new in meaning or type, so it is more difficult and can be put back as appropriate.

3. Problem-solving skills

(1) Examine the questions carefully. Pay attention to the key words in the topic and accurately understand the requirements of the examination questions.

(2) specification. To distinguish levels, we should pay attention to the accuracy and simplicity of calculation, the order and coherence of logic.

(3) Give the conclusion. Pay attention to the problems discussed by classification, and finally summarize the conclusions.

(4) stress efficiency. Write test papers and use draft paper reasonably and orderly to save inspection time.

Six, how to check

In the exam, actively arranging time to check the answer sheet is an important link to ensure the success of the exam. It is a process of filling in the gaps, eliminating the false and retaining the true, especially if the candidates adopt a flexible answering order, they should be combined with the final examination. Because you are likely to miss questions in the process of jumping back and forth, checking can make up for the loopholes in this answering strategy.

The first step in the inspection process is to see if there are any missing or unfinished problems. After finding them, you should quickly complete or rethink the solution. If you have time, combined with the problem-solving process of draft paper, comprehensively review the answering process and results of various types of questions. If you don't have enough time, focus on inspection.

The examination of multiple-choice questions is mainly to check whether there are omissions and review the questions that you have doubts about. But if there is no good reason, generally don't change your judgment according to your first feeling.

When checking the solutions, we should pay attention to the calculation process of reading the draft paper and correct the mistakes in calculation and reasoning. In addition, it is necessary to supplement the reasons and steps of omission, and delete or modify the wrong or inaccurate opinions.

Calculation questions and proof questions are the focus of the inspection, and it is necessary to carefully check whether all the requirements of the questions have been completed; If the time is too hasty to check, there are some simple verification methods: first, check whether the unit is wrong; The second is to see if there is any error in the reference of the calculation formula; The third is to see if the results are compared. Like what? Speaking of which? Like what? It depends on experience to judge, for example, whether the answer to the application question conforms to the practical significance; Whether the numerical conclusion is integer, natural number or regular expression, if the conclusion is decimal or irregular number, it must be recalculated, and it is better to try again in other ways.

Seven, emphasize the draft paper, as important as the test paper.

After the students get the draft paper, please give it a 30% discount first. Then use it in sequence. Leave a blank space between each question on the draft paper and clearly mark the question number. Handwriting should be recognized accurately and must not be scribbled. The advantages of this are:

1. Draft paper shows your thinking of answering questions. When the draft paper is clear, the thinking of answering questions will be clear. At least you know what you've done. If the draft is confusing, introducing this step will often forget how the previous step was obtained.

2. For the problem mentioned above that you can't do for the time being, you had a certain thinking process when you did it for the first time. It's a waste of time to think again. Using draft paper, you can quickly find the last thought breakpoint. Thereby continuing to break the position. Key conclusions should be specially marked.

3. Draft paper is the best helper in the inspection process. If even the calculation process can be clearly found on the draft paper, it will undoubtedly save a lot of time.

The second part is eight steps to improve the speed of solving problems.

During the exam, we often feel that time is tight and the paper should be rolled up before it is finished, although some questions can be worked out as long as we work hard. One of the reasons is that the speed of solving problems is too slow.

Almost every student knows that if you want to get good grades, you must study hard. Only by strengthening practice and doing more exercises can practice make perfect. However, some students lie there doing problems every day, but the amount of solving problems is not much, and they spend a lot of time, but they have not solved many exercises. Shouldn't we find out why? Besides, we have no more time than others. Imagine what it would be like if your problem-solving speed was increased by 10 times. Speed up problem solving 10 times? Is it possible? The answer is yes, it is entirely possible. The key is whether you want to or not.

So, how can we improve the speed of solving problems?

First of all, you should be very familiar with the contents involved in the exercises, so that the concepts are clear and you are very familiar with definitions, formulas, theorems and rules. You should know that solving and doing problems is only a part of the learning process, not the whole learning. You can't solve a problem for the sake of solving it. Solving problems is for reading. Is to check whether you have read the textbook, whether you have a deep understanding of the concepts, theorems, formulas and rules, and whether you can use these concepts, theorems, formulas and rules to solve practical problems. When solving problems, the clearer our concepts are, the more familiar we are with formulas, theorems and laws, and the faster we will solve problems. Therefore, before solving problems, we should familiarize ourselves with, remember and distinguish these basic contents by reading textbooks and doing simple exercises, correctly understand the essence of their meanings, and then do the following exercises all the time. I instruct students to learn in this way, and almost all students have greatly improved the speed of solving problems, with good results.

Second, we should be familiar with the knowledge we have learned before and the knowledge related to other disciplines involved in the exercises. For example, sometimes, we encounter an exercise that we can't do, not because we haven't learned what we want to learn now, but because we want to use a formula we learned in the past, but we can't remember it clearly; Or a physical concept to be used in math problems, we are not very clear; Or we need to use a special theorem, but we have never learned it, which greatly reduces the speed of solving problems. At this time, it is necessary to add some relevant knowledge that must be added first, and explain the concepts, formulas or theorems related to the topic clearly, and then solve the problem, otherwise it is a waste of time. Of course, the speed of solving problems is even more impossible.

Third, we should be familiar with the basic steps and methods of solving problems. The process of solving problems is a process of thinking. For some basic and common problems, predecessors have summarized some basic problem-solving ideas and common problem-solving procedures. Generally, as long as you follow these ideas and steps, it is often easy to find the answers to the exercises. Otherwise, detours will take more time.

Fourth, learn to sum up. After solving a certain number of exercises, the knowledge involved and the methods of solving problems are summarized, which makes the thinking of solving problems clearer and achieves the effect of giving inferences by analogy. Similar exercises can be seen at a glance, which can save a lot of time in solving problems.

Fifth, we should make practice easy first and then difficult, and gradually increase the difficulty of practice. The process of people's understanding of things is from simple to complex, from the outside to the inside step by step. A person's ability is also gradually increased through exercise. If more simple problems are solved, the concepts are clear and the formulas, theorems and solving steps are familiar, jumping thinking will be formed when solving problems, and the speed of solving problems will be greatly improved. When you get into the habit and encounter general problems, you can also maintain a high speed of solving problems. However, some of our students don't pay much attention to these basic and simple exercises and think it is unnecessary to spend time solving these simple exercises. As a result, the concept is unclear, formulas, theorems and solving steps are unfamiliar, and there is nothing to be done when encountering a slightly difficult problem, let alone the speed of solving problems.

In fact, the labor intensity and efficiency of solving simple exercises are not necessarily lower than solving a complex problem. For example, it is certainly much easier for a person to carry a small bag of rice to the fifth floor than to carry a big bag of rice to the fifth floor. However, if Timmy only goes up and down once, and the person carrying the bag has to go up and down 50 times, or even 100 times, then the person carrying the bag is more labor-intensive than Timmy. So in the same time, solving 50 simple problems and 100 simple problems may take more manpower than solving a difficult problem. For another example, if the weight of this bag of rice is 100 kg, it is too heavy, which exceeds the ability of the rice delivery person, so that the rice delivery person has made great efforts, but failed to carry it to the fifth floor. Although the labor intensity is great, it is in vain. Bag carriers can only carry 100 kg of rice to the fifth floor once, 15 times. The labor intensity may not be great, but the efficiency is self-evident. It can be seen that solving a difficult problem is not as good as solving 30 slightly simple exercises, and the gains may be even greater. Therefore, when studying, we should first solve those seemingly simple but important exercises according to our own ability, so as to continuously improve the speed and ability of solving problems. With the improvement of speed and ability, and gradually increase the difficulty, you will get twice the result with half the effort.

Sixth, carefully examine the questions. For a specific exercise, the most important part of solving the problem is to examine the problem. The first step of examination is examination, which is a process of obtaining information and thinking. Read the questions slowly, think while reading, pay special attention to the inner meaning of each sentence, and find out the implied conditions. What are the known conditions once reading is over? What is the conclusion of the solution? What conditions are still missing? Can you deduce them from the known conditions? In your mind, this information should have formed a network, you have a preliminary idea and solution, and then you can calculate and verify according to your own ideas. Some students have not developed the habit of reading and thinking, and they are very anxious. As soon as they were anxious, they began to solve the problem. As a result, they often miss some information and spend a long time trying to solve it, but still can't find the reason. They think quickly but slowly. Many times, students come to ask questions. I look at the problem with him. Halfway through, he said, teacher, I will. ? Therefore, we should pay special attention to the actual problem-solving and carefully examine the questions.

Seventh, learn to draw. Drawing is a process of translation. When reading a topic, if you can draw an analysis chart of your understanding of mathematics (or other disciplines) according to the meaning of the topic, the topic will become vivid and intuitive. In this way, abstract thinking in solving problems becomes thinking in images, thus reducing the difficulty of solving problems. Some topics, as long as the diagram is analyzed, the relationship will be clear at a glance. Especially for geometry problems, including analytic geometry problems, if you can't draw pictures, sometimes you can't start at all. Therefore, it is very important to keep in mind the basic drawing methods of various questions, the image and significance of various functions, and the evolution process and conditions to improve the speed of solving problems. Pay attention to drawing as accurately as possible when drawing. Accurate drawing sometimes allows you to see the answer at a glance, and then further calculation can confirm it; On the other hand, inaccurate drawing sometimes leads you astray.

Finally, there are commonly used formulas, such as multiplication formula and formulas of trigonometric functions in mathematics, commonly used numbers, such as the square of 1 1 ~ 25, trigonometric function value of special angle, chemical properties, valence and chemical reaction equations of commonly used elements in chemistry, etc. It should be memorized, which is very beneficial to improve the calculation speed.

In short, learning is a deepening cognitive process, and solving problems is only an important part of learning. The more familiar you are with the content of learning, the more familiar you are with the basic ideas and methods of solving problems, the more numbers and formulas you recite, the more you can organically combine the part and the whole to form a jumping thinking, and the speed of solving problems will be greatly accelerated.

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