First, master the basic problem-solving ideas of mathematics
In the college entrance examination, many senior three students often can't finish their math papers because of lack of time, and their scores are not high. Mastering the problem-solving ideas can help students find the problem-solving ideas quickly and save thinking time.
Master the ideas of functions and equations. This paper analyzes and studies the quantitative relationship in mathematics from the point of view of movement change, and analyzes, transforms and solves problems by establishing the function relationship and using the image and nature of the function. Starting with the quantitative relationship of the problem, the problem is transformed into an equation or inequality model by using mathematical language to solve it. When solving problems, we can use the idea of transformation to transform functions and equations.
Number-shape combination or shape-number combination. It is not only a "magic weapon" to find the breakthrough point of solving problems, but also a "good prescription" to optimize the way of solving problems. When solving a math problem, you can draw as many pictures as possible to help yourself understand the meaning of the problem correctly and solve the problem quickly.
Special and general ideas. This way of thinking is sometimes particularly effective in solving multiple-choice questions, because when a proposition is established in a general sense, it is bound to be established in its special circumstances. Accordingly, students can directly determine the correct choice in multiple-choice questions. Not only that, it is also useful to explore the problem-solving strategies of subjective questions with this way of thinking.
Discuss ideas by category. When solving a problem, after the solution reaches a certain step, it is impossible to continue with a unified method and formula. This is because the research object contains a variety of situations, which requires classifying all situations, solving them one by one, and then summarizing them to get a solution. This is a confidential discussion.
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. As long as senior three students follow these problem-solving ideas and steps, it is often easy to find the answers to the exercises.
Second, we must carefully examine the questions.
Senior three students need to tell themselves that the most important part of solving problems is to examine the questions. The first step in examining questions is reading questions, which is an important process of obtaining information and thinking. Read the questions slowly, while thinking, pay special attention to the inner meaning of each sentence and find out the implied conditions. If you don't carefully examine the questions, it means that you are in a hurry and need to concentrate on solving them. Once distracted, it is easy to make mistakes. The stem contains problem-solving information, questions and tips. Only by finding out what information is given in the question can we apply the formula to solve the problem. The topic contains literal meaning and implied meaning. Repeated reading and careful examination of the topic can more accurately understand the dry meaning of solving the problem, thus helping to find out the correct method of solving the problem.
Some senior three students have not developed the habit of reading and thinking, and they are 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.
Third, be familiar with the knowledge points involved in the exercises
Solving and doing problems is only a link in the learning process, not the whole learning. Senior three students can't solve problems simply for the sake of solving them. When solving problems, the clearer the mathematical concept, the more familiar with formulas, theorems and laws, and the faster the problem solving speed.
Senior three students need to memorize some mathematical laws and conclusions, so that their usual operation skills can reach the proficiency of automation or semi-automation. Senior three students need to sort out the knowledge structure frequently, form a plate structure and implement "full container" to make the knowledge structure clear at a glance. Senior three students often need to classify exercises, from one case to one category, from one category to multiple categories, from multiple categories to unity, so that several types of problems can be summarized by the same knowledge method.
Fourth, learn to draw pictures to solve problems.
Senior three students turn abstract thinking into image thinking by drawing, which reduces 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. It is very important for senior three students to keep in mind the basic drawing methods of various questions, the images and meanings of various functions, and the evolution process and conditions, so as to improve the speed of solving problems.
Fifth, to solve problems, it is necessary to remember that it is easy before it is difficult.
Senior three students need to know that there are more simple problems to be solved, so that the concept is clear and they are familiar with formulas, theorems and problem-solving steps. Jumping thinking will be formed when solving problems, and the speed of solving problems will be greatly improved. Senior three students need to solve those seemingly simple but important exercises according to their own abilities, and constantly improve their speed and ability to solve problems. With the improvement of speed and ability, and gradually increase the difficulty, you will get twice the result with half the effort.
Senior three students need to train the order of answering questions, the time of answering questions in each part and the examination skills of each course to the degree of unthinking and conditioned reflex through mock exams and time-limited exercises. When you get to the college entrance examination, you can successfully complete the task and achieve the goal of the college entrance examination.