The induction of junior high school mathematics problems
First, the calculation questions:
Scientific counting method, absolute value of reciprocal, simple probability operation, three views to find the original image area, triangle (similarity, congruence, internal angle diplomatic relationship), statistics (mode, median, average), quadratic function (vertex, symmetry axis, expression), function image relationship.
Second, fill in the blanks:
Factorization, quadratic resolution function solution, triangle (similarity, perimeter area calculation), coordinate (motion law of coordinate points), straight line and inverse proportional function image problems.
Third, answer questions:
Power, root, trigonometric function and power (0,-1) calculation;
Solve the inequality group;
Fraction and polynomial simplification (overall replacement evaluation);
Solve the equation;
Prove that the sides of a triangle are geometrically equal;
Linear function and quadratic function;
Fourth, answer questions.
Solution of quadrilateral side length, perimeter and area;
Problems related to circles (secant, angle of circumference, angle of center);
Statistical chart;
Find the triangle area on the axis;
V. Answering questions
Quadratic function (analytical formula, linear equation);
The relationship between circle and straight line;
Triangle angle correlation calculation;
Generally speaking, there are many questions in the senior high school entrance examination, so you need to master the relevant knowledge points skillfully and do the questions quickly. In recent years, the math problems of senior high school entrance examination in Beijing are relatively fixed and difficult, so it is necessary to pay attention to the correct rate and the knowledge plate of triangle and quadrilateral area calculation.
Junior high school mathematics problem-solving skills
1. Have a clear understanding of the signs of success in the math exam.
Junior high school students have passed countless math exams, and there are successes and failures, as well as times and uncomfortable days. So what is the sign of success in the math exam? Some people say it's a score, some people say it's a ranking, and some people say that only when you surpass someone can you really calculate the math test scores as absolute values and relative values. The absolute value is the result of comparing your own math test scores with the passing line and full marks. Relative value is the result of measuring one's math test scores in personal, class, grade, city and other reference systems. It is precisely because of the different frame of reference that some students are more confident, motivated and optimistic. On the other hand, some students are less confident, more suspicious and less enthusiastic than themselves. In my opinion, there are two signs of success in the math exam: First, as long as one's level is normal, it is a successful math exam. Second, don't compare with other students horizontally, but compare with yourself vertically. As long as the first question is eliminated to the set goal, it is a successful math exam.
2. Determine the goal of the math exam
According to statistics, about 25% of candidates fail in the senior high school entrance examination every year. Therefore, when you set a goal before the math exam, although you have the above two signs of success in the math exam in your mind, you must never think that the first one will be able to play my 100% level, which is called normal play, let alone fantasize about extraordinary play. Instead, you should achieve your goal in a three-tier progressive mode. The three-tier progressive model is: first, we must ensure that we do not fail the math exam. The second is to play normally. Normal play is to play your 80% level. It is not easy to play 80%. Playing 80% is undoubtedly a failure. Third, to move towards a higher standard is to strive to play 100% after ensuring 80% performance, and then move towards extraordinary performance. Although it looks like a simple three-story building, what I put forward is: don't smash it? 80%? 100%? Extraordinary. If you want to play 100% as soon as you start the math exam, you may lose all your money if you play beyond the norm. Then one of the best ways to ensure the implementation of the three-level progressive model is the three-round problem-solving method.
3. Dare to give up in the first round of answering questions
The first round of the three-round problem-solving method is that you answer the questions from beginning to end and answer them as soon as you see them. If you can't answer this question, don't answer it. I got stuck in the middle of the answer when I read this question, so I let it go. This is a very crucial point. Why? ? Answer if you can, and answer if you can't. What if I can't do it in the math examination room? The key is between meeting and not meeting, and the difficulty lies in the judgment of meeting and not meeting. You think it's obvious that you will. No, the question is clear. But it's just that some problems get stuck at first sight, or I can't draw a conclusion at once. I need to have a look. I really want to do it, but I can't bear to stop. Every time I lost my precious time unconsciously, I felt that I didn't have enough time in every math exam, and I was defeated in a muddle. ? Answer if you can, and answer if you can't. As a principle, this is an irrefutable truth. However, if we regard it as a mathematics examination method at the same time, because it only points out the direction qualitatively, the quantitative analysis is unclear and lacks maneuverability, some people use it, and some people use it ineffectively; Sometimes it works, sometimes it doesn't. Especially in the important math exam, you have to fight for every question and win every point. When you don't want to give up any problem easily, you want to attack any problem, and you don't want to lose any point, you often fail. And then what? Three rounds of problem solving? It is a quantitative method with clear quantification and strong operability.
4. Dare to rest for 30 seconds
When you press the method of solving what you can do, releasing what you can't do and releasing what you can't do, you should dare to rest for 30 seconds after finishing the last question before. This kind of rest must be honest rest. For example, you can look at the natural landscape outside the window, trees are swaying, birds are flying and so on. You can also think about your favorite pop songs, TV dramas, etc. Of course, you can't think too far. If you had thought of ten episodes, the exam would have ended long ago. You can also take some deep breathing relaxation methods, self-deep relaxation methods, positive self-suggestion methods and so on. Of course, you can also think nothing and just close your eyes. Pay attention to what kind of rest you choose during the break, but don't think about an unfinished problem.
Why use someone who dares to rest for 30 seconds? Dare you? What about two words? Because most students often feel that time is not enough, how dare they find time to have a rest! In fact, on the contrary, because the math exam is a high-oxygen activity, it consumes a lot of brain and physical strength, and after a while it will produce fatigue. At this time, if you persist with willpower, the efficiency will naturally be low. After rest, brain power will be restored and physical strength will be supplemented. It will be very efficient to put into the problem-solving process after a break, so students who dare to rest will have enough time. This is dialectics. Is this exactly what the saying goes? Sharpen a knife and cut wood by mistake? The truth. Dare to rest for 30 seconds, which is also the embodiment of improving mental state. In the math exam, some students are anxious as soon as they hear the sound of other students turning pages quickly, and they panic when they see other students answer faster from the corner of their eyes. Now you can be unmoved, not quoted, and dare to take the initiative to rest. It goes without saying that there are mistakes in quick answer and success in steady answer. The improvement of mental state needs a tempering process. Dare to rest for 30 seconds is the beginning of a mature mental state, so you must dare to rest. After the break, round two.
5. The second round of vacancies and supplements.
I have done all the questions to be done in the first round. Do I have any questions after the break? The answer is yes. There are two foundations: one is the practical foundation; The first is the theoretical basis.
Almost every candidate has had such an examination experience. During the math exam, I couldn't answer a question, so I had to give up. But when he answers somewhere in the back, he will think of how to deal with the previous question. Or answer the next question, or see a sentence, a symbol, etc. A problem, so as to immediately wake up the memory, have an epiphany, inspire and so on. , in front of the problem is made. This is the basis of practice.
In the math exam, it takes a rising process from the beginning of answering questions to reaching the best thinking state in the math exam, that is, 1 o'clock in the figure. But after reaching the best state of mind, some people can still come down. For example, they think they can make a small problem of about 4 points, but they can't do it after digging for a long time, and their mood is in a mess. This is by no means the best state, their state of mind has declined. Some people have plummeted, and some people can get up after falling and reach their best mentality again. The ideal state we hope is to reach the best state of mind as soon as possible. When we reach the best state of mind, it will last until the end of the exam.
6. The third rotating thinking to solve problems
After the break, check the questions you have done before and after. After passing the inspection, theoretically you played your own 100% level, but in fact it was 80%. Because although you passed the inspection, there is still a possibility that you didn't check it out or checked it wrong, so it is 80%. Although it is 80%, it is not easy. A math exam, playing your 80% level is a successful math exam. You watch sports competitions and you watch the Olympic Games. How many athletes and sports teams have accumulated the essence of years of training and buried their wishes for four years, just to fight on the field. This kind of fighting is often played at 80% of the usual training level to win and get the card. To play 80%, you must realize that my level has been played, and that is my level. I am worthy of myself and my parents, but if the math exam is not over yet, there is still time, there is no need to check it again. At this time, you must not reach 80%. You must try to go beyond the normal state and do those questions that you have not done. But I can't. I've done it twice and I haven't done it yet. That means it's difficult, right? Hard bones? . For difficulties and? Hard bones? It is no longer possible to adopt traditional practices. At this time, we must attack, to difficulties and? Hard bones? Launch a general attack. So how to attack? We can attack by changing our thinking and solving problems.
The method of empathy is based on this kind of thinking. When you solve a problem, it is not enough to do it right. Only when you know how many solutions there are to this problem and which one is the best can you be considered excellent. Many people have had this experience. When solving problems, they remembered which chapter and section the question came from, how the teacher emphasized it when he spoke, what knowledge points the question was tested and what the teacher wanted to test. At this time, I felt confident in answering this question and solved the problem smoothly. This is inspiration. Actually, there is nothing mysterious about inspiration. Everyone has got a little inspiration from generate in the math exam. Of course, if you can see through the trap and confusion of a question, then you are a top expert. In a word, at this time, attack when you should attack, attack when you should attack, inch by inch, 1 minute. But we should change our thinking and see which questions can be attacked and which points can be remembered. Think about which chapter and section it comes from. Which knowledge point does the teacher want to test? What is the relationship between integrals? At this time, you should let go of your memory ability, comprehension ability, multi-directional association ability, reverse thinking ability, divergent thinking ability and innovation ability, and think in multiple directions, angles and levels. At this time, new ideas may be opened, excitement may be activated, and sparks of inspiration may bloom in the air like fireworks on New Year's Eve. Students, try it boldly! The inspiration you once had will reappear again and again.
7. Change the three-round problem-solving method into self-theorem.
Three-round problem-solving method is a brand-new method for answering mathematics exams, and it is a scientific, reasonable and effective method for answering mathematics exams that has been verified by practice. Students who know, master and use the three-round problem-solving method have made progress to varying degrees. However, the application of three-round problem-solving method varies from person to person and from subject to subject. In order to flexibly use the three-wheel problem-solving method, we must first understand its scientificity, rationality and effectiveness; The second is to practice, and it is impossible to master such a brand-new method without repeated practice; Third, we should sum up and see if we are good at three rounds, two rounds or four rounds. How long is the interval between two breaks? In short, it is by no means a round to the end. Whether it will or not, we should spell out the answering methods of the three or five rounds of mathematics exams that have been used since elementary school. This is a brand-new method of solving problems by turns. For different subjects, the application of three-round problem-solving method should also be different. For example, mathematics, physics and chemistry are such three rounds. Chinese should be a round before reading the topic, and the end should be checked after reading it. Then the reading problem is a round, and the last round is to write a composition wholeheartedly. The ideal state is that the composition is finished and the remaining time is no more than 5 minutes. If there is too much left, it means that the current time allocation is unreasonable and needs to be improved. English, history. The three rounds of political geography also vary from subject to subject.
Junior high school mathematics learning methods
In fact, it is not difficult to learn mathematics well. It is much easier to master the knowledge in junior high school than in senior high school. You must listen in class, no matter how hard it is, you can't listen in class, because teachers sometimes talk about knowledge that is not in books or their own experience and skills.
Do your homework after class, and don't ask yourself to buy questions. You just need to finish the homework assigned by the teacher carefully. You need to listen to the teacher's comments on your homework. Whether you are right or wrong, you should listen. This is the time for teachers to talk about methods, so it is most important to concentrate in class.
The same is true of the test paper. Don't stop listening to the lecture just because you are right. Sometimes the teacher speaks more than that question.
The most important thing is the above, as long as you do it, your grades will never be bad! Finally, communicate with classmates more and verify each other's answering skills. I don't know how to ask questions.
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