Let you read a book, not word by word, but carefully read the important things in it, such as formulas, which will certainly pass (of course, more than one factor). Like when I was in high school, I always focused on textbooks, so I was the first in hundreds of exams in the whole high school, more than 90% of the time. Now, I am a tutor, and my students can do anything.
Usually, you should do the questions in moderation, not too much, and certainly not too little. If you do less, you may not be familiar with doing the questions during the exam!
Let's talk about the exam. First of all, it is a matter of time. For most people, it is normal not to have enough time to do math, so there are many times when you don't always think about how to finish the test paper. My math teacher said that it is wise to give up some topics and try to ensure the correctness of them, but this does not mean that you deliberately give up some topics and check them. It depends on the specific situation. For example, if you feel that you really can't work out a single question, and there are many uncertain questions (not very difficult) before, then you can go to the front and check. Don't take chances, always thinking, "Maybe what I did before may be right." The previous one was more than five points. It's a pity to lose! Or you think you did well in the front, and there are still a certain number of questions (which you think you can do) that you haven't done, so do the latter, after all, there are so many points left behind!
In addition, when making a fuss, try to pay attention to skills. Don't always be honest. 120 minutes. How could you do that? You should try some simple methods, which I think are very clear in many books. As long as you seriously understand and appreciate beauty, it is no problem to master those methods!
To talk about some other problems is to try not to think about other things when doing the problem. How many points do I have to get in this exam? If I don't do well in the exam, there will be any bad results. Anyway, in a word, concentrate when you do it! Pay close attention!
One more thing I want to say, don't care too much about your usual grades. If you care too much, you may spend most of your energy. If you have such energy, you might as well spend it on your study, so the effect may be better.
Believe in yourself, there is no need to worry, as long as you don't lose heart, you should be fine.
I always think that there is no fixed method for learning, it depends on the specific situation, so I can't think of any good methods for others. It is very likely that you have a good method, but you didn't show it!
Senior one is a critical period for mathematics learning. Many excellent students in primary and junior high schools have stumbled in mathematics since they entered high school. For many students who have successfully studied mathematics in junior high school, their mathematics scores are not ideal after entering senior high school, and their mathematics learning is frustrated. I think the main reason for this result is that these students don't understand the characteristics of high school mathematics, and they can't learn regularly, which leads to a decline in their grades.
1. Changes in the characteristics of high school mathematics and junior high school mathematics.
1, the mathematical language has a sudden change in abstraction.
Many students reflect that the concepts of set and mapping are difficult to understand, and they feel far away from life and seem to be "mysterious". Indeed, there is a significant difference between junior high school and senior high school. Junior high school mathematics is mainly expressed in vivid and popular language, while senior high school mathematics touches on abstract set language, logic operation language and function language, space solid geometry and so on.
2. Transition of thinking mode to rational level.
Another reason why senior one students have difficulty in mathematics learning is that the thinking method of mathematics in senior high school is very different from that in junior high school. In junior high school, many teachers have established a unified thinking mode for students to solve various problems, such as how to divide the fractional equation into several steps and what to look at first and then what to look at in factorization. Even for plane geometry problems with very flexible thinking, they have determined their own thinking routines for line segments and angles,,,, and. Therefore, junior high school students are used to the stereotype that machinery is easy to operate, while senior high school mathematics has undergone great changes in its thinking form. As mentioned in the last section, the abstraction of mathematical language puts forward high requirements for thinking ability. Of course, the cultivation of ability is gradual, not overnight. This sudden change in ability requirements has made many freshmen feel uncomfortable, leading to a decline in their grades. Freshmen in senior high school must be able to transition from empirical abstract thinking to theoretical abstract thinking.
3. The total amount of knowledge content has increased dramatically.
Another obvious difference between high school mathematics and junior high school mathematics is that the "quantity" of knowledge content has increased sharply. Compared with junior high school, the amount of knowledge and information received per unit time has increased a lot, and the class hours for assisting exercises and digestion have decreased accordingly. This requires, first, to review after class and remember a lot of knowledge; Second, we should understand and master the internal relationship between old and new knowledge, so that the new knowledge can be assimilated into the original knowledge structure smoothly; Thirdly, because knowledge teaching is mostly carried out in a piecemeal way, when the amount of knowledge information is too large, its memory effect will not be very good. Therefore, we should learn to sort out the knowledge structure, form a plate structure, and implement "overall assembly", such as tabulation, so that the knowledge structure can be seen at a glance; Classification, from one case to one class, from one class to many classes, from many classes to unity; Make several kinds of problems isomorphic to the same knowledge method; Fourth, it is necessary to summarize and classify more and establish a knowledge structure network of disciplines.
Second, the learning state is poor.
1, learning habits are backward because of dependence.
The dependence of junior high school students on learning is obvious. First, in order to improve the score, teachers list various questions in junior high school mathematics teaching, and students rely on teachers to provide "model essays" to apply; Second, parents are eager for their children to succeed, and it is common for them to go home to help their children. After entering senior high school, teachers' teaching methods have changed, the applied "model" has disappeared, and parents' ability to help can't keep up, from "participating in learning" to "urging learning". Many students, like junior high school, are very dependent, follow the teacher's inertia and have no initiative in learning.
2. lax thinking. Some students transplanted the idea of junior high school to senior high school. They thought that they didn't study hard in the first and second days of junior high school, but only tried to get into high school one or two months before the junior high school exam, and some of them may be key classes in key middle schools. Therefore, they think that there is so much study in senior three, and there is no need to work so hard in senior two and senior three, just wait until the senior three exam. Similarly, students who have this idea will also be admitted to an ideal university. This is a big mistake. Because in Guangzhou, it can be said that high school education is universal, so there is no obvious selectivity in the topics of the senior high school entrance examination, and students are easy to get high marks. But the college entrance examination is different. At present, it is impossible to popularize higher education in our country. Higher education can still be said to be elite education, and only some students with good grades can be selected to go to college. Therefore, the topics of the college entrance examination are highly selective. If you are lucky enough to be admitted to the university in senior three, you will regret it in the end. Students may wish to inquire about the current situation of senior three. How many students are anxious to find a tutor because they don't study hard in Grade One and Grade Two? Now they are approaching the college entrance examination and find that they have missed a lot of knowledge.
3. study law. Teachers usually explain the ins and outs of knowledge in class, analyze the connotation of concepts, analyze key and difficult points, and highlight thinking methods. However, some students don't pay attention in class, don't hear or fully hear the main points, and take notes in a big book, which has many problems. After class, I can't consolidate, summarize and find the connection between knowledge in time, but I just do my homework in a hurry and do the problems in disorder, and I am confused about the concepts, laws and questions.
4, do not pay attention to the foundation. Some students who "feel good about themselves" often despise the study and training of basic knowledge, skills and methods. They often forget what to do, but they are very interested in difficult problems. In order to show their "level", they aim too high, value "quantity" over "quality" and fall into the ocean of problems. To regular work or
5. Do not have the conditions for further study. Compared with junior high school mathematics, senior high school mathematics is a leap in depth, breadth and ability requirements. This requires that you must master basic knowledge and skills to prepare for further study. Many aspects of senior high school mathematics are difficult, with new methods and high analytical ability, such as the solution of quadratic function values, the discussion of real root distribution and parameter variables, the deformation and flexible application of trigonometric formulas, and the formation of spatial concepts. Sort out and combine application problems and practical application problems. Some contents are still out of touch in junior high school textbooks. If you don't take remedial measures, you will inevitably fail to keep up with the requirements of high school.
Third, scientific study.
It is not enough for high school students to study, but also to study. Only by paying attention to scientific learning methods and improving learning efficiency can they change passive learning into active learning and improve their academic performance.
1, cultivate good study habits. Repeated use of methods will become people's habit. What are the good study habits? Good study habits include making plans, self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class.
(1) Making a plan makes the learning purpose clear, the time arrangement reasonable, unhurried and steady, which is the internal motivation to promote our active learning and overcome difficulties. However, the plan must be practical, with both long-term plans and short-term arrangements. In the process of implementation, we must be strict with ourselves and temper our will to learn.
(2) Self-study before class is the basis of good new lessons and good learning results. Self-study before class can not only cultivate self-study ability, but also improve interest in learning new lessons and master the initiative in learning. Don't go through the motions in self-study, pay attention to quality, try to understand the teaching materials before class, pay attention to the teacher's ideas as much as possible in class, grasp the key points, break through difficulties and solve problems.
(3) Classroom is the key link to understand and master basic knowledge, skills and methods. "What they have learned is not enough". Students who have taught themselves before class can concentrate more. They know where to be detailed and where to go, and only write down what they should remember, instead of copying everything, paying attention to one thing and losing another. To learn mathematics, we must first cultivate interest, listen carefully in class, ask questions immediately if you can't, and don't wait for class to end.
Mathematics is one of the compulsory subjects, so we should study it seriously from the first day of junior high school. So, how can we learn math well? Introduce several methods for your reference:
First, pay attention to the lecture in class and review it in time after class.
The acceptance of new knowledge and the cultivation of mathematical ability are mainly carried out in the classroom, so it is necessary to pay attention to the learning efficiency in the classroom and seek correct learning methods. In class, we should follow the teacher's ideas, actively explore our thinking, predict the next steps, and compare our own problem-solving ideas with what the teacher said. In particular, we should do a good job in learning basic knowledge and skills, and review them in time after class, leaving no doubt. First, before doing all kinds of exercises, you should recall the knowledge points that the teacher said. Correctly grasp the reasoning process of various formulas, and try to recall the unclear places instead of turning to the book immediately. In a sense, you should not create a learning style of asking questions if you don't understand. For some problems, you should calm down and analyze them carefully and try to solve them yourself. At every learning stage, you should sort out and summarize and combine the points, lines and surfaces of knowledge into knowledge.
Second, do more questions appropriately and develop good problem-solving habits.
If you want to learn math well, it is inevitable to do more problems, and you should be familiar with the problem-solving ideas of various questions. First of all, you should start with the basic problems, follow the exercises in the textbook, and lay a good foundation repeatedly. Then find some extracurricular exercises to help you broaden your thinking, improve your ability to analyze and solve problems, and master the general law of solving problems. For some error-prone problems, you can prepare a set of wrong questions, write your own solution ideas, and find out your own mistakes by comparing the correct solution process. In order to correct it in time. We should develop good problem-solving habits at ordinary times. Let your energy be highly concentrated, make your brain excited, think quickly, enter the best state, and be able to use it freely in the exam. Practice has proved that at the critical moment, your problem-solving habit is no different from your usual practice. If you are careless and careless when solving problems, it will often be exposed in the big exam, so it is very important to develop good problem-solving habits at ordinary times.
Third, adjust the mentality and treat the exam correctly.
First of all, we should focus on basic knowledge, basic skills and basic methods, because most exams are basic topics. For those difficult and comprehensive topics, we should think hard and try our best to sort them out. After finishing the problem, it is necessary to sum up. We should adjust our mentality, calm ourselves down at any time, think in an orderly way and overcome impetuous emotions. Especially always have confidence in yourself.
Be prepared before the exam, practice routine questions, spread your own ideas, and avoid improving the speed of solving problems on the premise of ensuring the correct rate before the exam. For some easy basic questions, you should be sure of 12 and get full marks; For some difficult questions, you should also try to score, learn to score hard in the exam, and make your level normal or even extraordinary.
Therefore, if you want to learn mathematics well, you must find a suitable learning method, understand the characteristics of mathematics, and let yourself enter the vast world of mathematics.
How to learn math well II
To learn mathematics well, senior high school students must solve two problems: one is to understand the problem; The second is the method.
Some students think that learning to teach well is to cope with the senior high school entrance examination, because mathematics accounts for a large proportion; Some students think that learning mathematics well is to lay a good foundation for further study of related majors. These understandings are reasonable, but not comprehensive enough. In fact, the more important purpose of learning and teaching is to accept the influence of mathematical thought and spirit and improve their thinking quality and scientific literacy. If so, they will benefit for life. A leader once told me that the work report drafted by his secretary from the liberal arts major could not satisfy him because it was flashy and lacked logic. So, I have to write my own manuscript. It can be seen that even if you are engaged in secretarial work in the future, you must have strong scientific thinking ability, and learning mathematics is the best thinking gymnastics. Some senior one students feel that they have just graduated from junior high school, and there are still three years before their next graduation. They can breathe a sigh of relief first, and it is not too late to wait until they are in senior two and senior three. They even regard elementary school and junior high school as "successful" experiences. Second, the most important and difficult content of high school mathematics (such as function and algebra) is in Grade One. Once these contents are not learned well, it will be difficult for the whole high school mathematics to learn well. Therefore, we must pay close attention to it at the beginning, even if we are slightly relaxed subconsciously, it will weaken our learning perseverance and affect the learning effect.
As for the emphasis on learning methods, each student can choose a suitable learning method according to his own foundation, study habits and intellectual characteristics. Here, I mainly put forward some points according to the characteristics of the textbook for your reference.
L, pay attention to the understanding of mathematical concepts. The biggest difference between senior high school mathematics and junior high school mathematics is that there are many concepts and they are abstract. Learning "taste" is very different from the past, and the solution to the problem usually comes from the concept itself. When learning a concept, it is not enough to know its literal meaning, but also to understand its hidden deep meaning and master various equivalent expressions. For example, why are the functions y=f(x) and y=f? Another example is why when f (x-l) = f (1-x), the image of function y=f(x) is symmetrical about y axis, while the images of y = f (x-l) and y = f (1-x) are symmetrical about the straight line x = 1.
2' Learning solid geometry requires good spatial imagination, and there are two ways to cultivate spatial imagination: one is to draw pictures frequently; Second, the self-made model is helpful to imagination. For example, the model with four right-angled triangular pyramids looks more and thinks more than the exercises, but it will eventually reach the realm of imagination without relying on the model.
3. When learning analytic geometry, don't treat it as algebra, just don't draw it. The correct way is to calculate while drawing, and try to calculate in drawing.
On the basis of personal study, it is also a good learning method to invite several students of the same level to discuss together, which can often solve problems more thoroughly and benefit everyone.