When we see a question, we need to know what it is testing, and we need to know clearly which part of knowledge each knowledge point comes from.

Keeping in mind the key points, difficulties and error-prone points of each part of knowledge can greatly reduce our error rate. Just like when you see a fractional equation, you will definitely think of checking the root, when you see a quadratic equation, you will definitely think of calculating delta, and when you see an isosceles triangle, you will definitely pay attention to classification and discussion, and you will definitely think of the integration of three lines.

All the knowledge learned in junior high school has its most basic part and the most difficult part, which corresponds to the three different requirements of ABC in our senior high school entrance examination requirements. We should be aware of every part of knowledge, especially the geometric model.

For example, we should know the models of single tangent, double tangent, triple tangent, non-vertical similarity, double vertical similarity and triple vertical similarity between circles and tangents. Only in this way can our thinking of doing problems come faster and clearer.

Furthermore, for constructing isosceles triangles and right-angled triangles, it is often necessary to discuss who is the waist, who is the bottom, which is the right-angled side and which is the hypotenuse, so the systematic method here becomes particularly important.

In order to ensure that the discussion is not lost, it must be divided according to certain principles, otherwise it may be lost and repeated. Therefore, we must learn to summarize the basic questions and basic knowledge points, so as to ensure smooth and rigorous problem solving.

Second, the basic knowledge is comprehensive.

Why is this important? Because comprehensive knowledge can provide us with more ideas and broader problem-solving space. For example, many students will say that the bisector, median line and height are important segments in the triangle, so there is actually a very important segment-the median line.

Although this line segment is not discussed with the first three, it is often used in solving triangle problems, so if you don't realize the problem of triangle center line when solving problems, you may not be able to make auxiliary lines.

Therefore, it is very beneficial for us to associate and apply knowledge points as a whole. For another example, what method can be used to solve the length of a line segment? Most students can name many kinds, such as Pythagorean Theorem, similar triangles, congruent triangles, trigonometric functions, and the properties of special triangles. However, methods such as area method and constructing parallelogram are often forgotten.

This is the incompleteness of induction, which is often a possible method to solve comprehensive problems, so it is very important to summarize thoroughly.

Another example is the problem of derivation angle in the proof question. Except for the three-line octagon, which everyone has always been sensitive to, after we learn similarity and congruence, we are often used to using these methods to solve the relationship between angles. In fact, there are two very important methods that are most easily overlooked.

One is "the sum of the internal angles of a triangle = 180"

2. "One outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it",

Staring at the blank is that there are many students in the outer corner.

Therefore, after the knowledge we have learned is gradually enriched, we should be good at sorting it out, putting together every knowledge point we have learned, stringing it into a line and hanging it into a series of circles, so as to know how many theorems there are in a * * * and how many questions remind us of common problems;

When giving a string of right angles, we should think about where we can see right angles and what are the properties and functions of right triangles.

Therefore, we should comprehensively summarize the knowledge involved in each part of the test center and the problem-solving methods involved in each kind of knowledge. Only in this way can we ensure that our thinking is broad and our methods are flexible, so that we won't say that we can't think of a way to look at a problem and we can't think of the way to use it.

Third, deepen the basic knowledge.

This part is related to the comprehensive problem behind us. Depth is the application and migration of basic knowledge. There is no problem in the senior high school entrance examination. The problem we are talking about is just to organically combine many simple knowledge points, or slightly deform them or hide them.

Then this part needs everyone to use our basic knowledge flexibly and skillfully to answer. The premise of flexible application is a deep understanding of knowledge points. For example, the sum of two sides is greater than the third side, and the difference between the two sides is less than the third side.

Many students can only think of using it to solve the range problem, but in fact, in the comprehensive problem, this part of knowledge is more used to solve the line segment relationship and the maximum problem.

If we can have this understanding, we can naturally think of translating line segments to construct triangles or parallelograms in comprehensive problems. For another example, an image of a quadratic function intersects with any straight line, which not only shows that the two images intersect, but also shows that the binary linear equation they form has real roots.

For right triangle, it is not only the object we solve, but also we should realize that it is a very good tool for angle transformation. When a special angle appears, we should be able to think of constructing a right triangle and transforming the conditions.

These are all ways to deepen the understanding of basic knowledge after doing a certain amount of questions.

To sum up, why always emphasize the importance of basic knowledge?

Because the whole junior high school mathematics, there will be no problems beyond the outline or let everyone have no knowledge to solve problems.

Most of the topics are presented by our basic knowledge alone or in groups. Therefore, if you master the basic knowledge, you can do the easy problems well, solve the difficult problems quickly and make the big problems stable.