There is no doubt that the speed of solving problems is important to the math exam, so how to improve the speed of solving math problems? Come with me and see how.
First, we should be very familiar with the contents involved in the exercises, make the concepts clear, and be 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, be familiar with the previous knowledge involved in the exercises and related knowledge of other disciplines.
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 clarify the concepts, formulas or theorems related to the topic before solving the problem, otherwise it is a waste of time. Of course, the speed of solving problems is even more impossible.
Third, 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.
Five, should be 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 the person carrying the rice only goes up 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 the person carrying the rice. 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.
Seven, 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 images and meanings 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.
Eight, common knowledge points should be kept in mind.
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, and it is time-consuming and laborious, which is very beneficial to improve the calculation speed.
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