Mathematics is a science, and understanding ability is very important. Without understanding ability, your math and even all science studies will be very difficult. However, the cultivation of understanding ability is very difficult. You must try to understand some philosophical theories and relatively abstract mathematical models that are difficult for you. The simplest training is also very difficult, so for a moderately difficult question, it is necessary to see that the auxiliary line can reflect its practice within 1 minute. Secondly, we should not only understand what the teacher said, but also try to figure out the specific mental process when the teacher did the problem. This is the basic ability of many people to learn mathematics well.

Third, diligence.

I met many students who worked hard but still couldn't learn science well. The dumb thing about the math exam is that it is easy to pass as long as you study hard according to the teacher's requirements, but it is far from enough to get 145 by the teacher's practice. Even poor students still have simple and easy learning methods. Only by mastering the correct methods can we gain something through diligence.

Fourth, the method

(1) geometry

Geometry learning is the most skillful for students at this stage. Let me introduce the trick of learning (solving) geometry problems.

1, remarks

In geometry class, students should not only learn to take notes and extract blackboard books, but also sort out the basic graphics involved in the teacher's lecture after class. What is a basic graphic? The basic figure is similar to the method of adding common auxiliary lines when we do geometry, except that the basic figure is a complete figure after adding common auxiliary lines. How to filter basic graphics? In fact, it's very simple. Combine the homework of the day, sort out and screen, find out similar auxiliary line addition or similar problem-solving methods, and sort them into the attributes of basic graphics, that is, all the conditions and proof methods that basic graphics can prove. This is a long-term process, but it will make you think hard when solving geometry problems after memorizing basic figures and their attributes, with high accuracy and efficiency.

2, the steps to solve the problem

First read the topic and express the known conditions on the geometric diagram (preferably on draft paper). Secondly, when doing the proof, show the known conditions and verification conditions on another diagram. At this point, when the topic is relatively simple, you can solve the problem directly, saving time. However, if the topic is complicated and you can't figure it out in 10 minutes, try to combine the two pictures and try to connect the conditions between the two pictures through auxiliary lines until you draw an auxiliary line to prove it.

Choose the right method to do evaluation questions. To solve the area problem, we should skillfully use the properties of basic graphics or directly combine them with known data through graphics similarity, congruence, translation and rotation, and calculate all conditions that can be proved directly or indirectly as much as possible, plus appropriate auxiliary lines. The cultivation of this ability needs a large number of proof questions as the basis for solving problems easily.

(2) Algebra and rational number and irrational number operations

1, summary formula

In class notes and homework, sort out the equivalence relations with high occurrence rate and deduce them by yourself.

2. Memory formulas and typical examples

Similar to the endorsement of liberal arts, the effect of understanding memory is better

3. Solutions to problems

First, simplify the known relationships and find out all the equivalent relationships that can be found.

Secondly, the connection is sought or proved to be deformed and the equivalence relation is found out.

Using appropriate formulas, backward derivation or ingenious methods to solve or verify, the basic idea is the same as geometry, and it also needs usual accumulation.

(3) Other types of problems

The basic ideas of other questions are basically the same as those of geometry and algebra mentioned above. I believe that after skillfully using the learning method of geometric algebra, students will certainly be able to sum up their own set of thinking modes and achieve good results in the basic learning of mathematics.

Verb (abbreviation of verb) popularization (please implement it on the premise that the bank has spare capacity)

1, special exercise for senior high school entrance examination

Practice the mid-term exam questions related to the questions you have learned properly, don't rush to achieve success, and read all the lines: the information recommends the Orsay deep-water bomb. Don't think too difficult a problem, just do an example.

2. Synchronous learning of Olympic mathematics

Buy one or two synchronized Olympic math books for self-study, and ask teachers or classmates questions if you don't understand. For most students, you can't study in advance, and you can't ignore the importance of normal homework.

3. Students who have too much spare time can take part in Olympic math classes or competitions as appropriate. Don't ask for awards, but focus on participation.

PS: I am a top student in Class 6, Grade 20 10 of Chengdu No.7 Yucai School.