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.

For commonly used formulas

For example, the multiplication formula and trigonometric function formula in mathematics, commonly used numbers, such as the square of 1 1 ~ 25, the trigonometric function value at a special angle, the chemical properties, valences and chemical reaction equations of commonly used elements in chemistry, etc. It should be kept in mind, and it takes time to master it easily, 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.

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.

Examine/consider carefully the questions to be answered or the topics to be written.

Carefully examine the questions. 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, and I watch them with him. Halfway through, he said, "Teacher, I can."

Therefore, we should pay special attention to the actual problem-solving and carefully examine the questions.

The process of people's understanding of things is from simple to complex, from the outside to the inside step by step.

Increase the difficulty of practice

We should make it easy first and then difficult, and gradually increase the difficulty of practice. 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 problem-solving steps are unfamiliar, and there is nothing to be done when encountering a slightly more 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, gradually increasing the difficulty will achieve twice the result with half the effort.

Learn to summarize.

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.