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.

Do a good summary.

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.

Easy first, then difficult, and gradually increase the difficulty of practice.

The process of people's understanding of things is from simple to complex. There are many simple problems to be solved, so as to have a clear concept and be familiar with formulas, theorems and solving steps. When you solve problems, you will form jumping thinking, 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. Some students don't pay much attention to these simple exercises and think it is unnecessary to spend time solving them. 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.

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.

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.

Examine the questions carefully.

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 when a student asks a question, the teacher reads the question 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.

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.

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.