Nine kinds of problems

1. Calculation and Proof of Line Segment and Angle

The answer to the senior high school entrance examination is generally divided into two or three parts.

The first part is basically some simple or intermediate questions, aiming at examining the foundation.

The second part is often the problem of starting to pull points. The significance of mastering these questions easily lies not only in getting scores, but also in the influence on morale and morale in the whole process of doing them.

Generally speaking, it is not difficult to calculate and prove line segments and angles. As long as the key "problem" is found, the following paths will "connect" themselves.

2. Graphic positional relationship

In middle school mathematics, the position relationship of figures mainly includes the relationship between points, lines, triangles, rectangles/squares and circles.

The senior high school entrance examination will be included in the problems of function, coordinate system and geometry, but mainly through the relationship between circle and other figures, among which the most important ones are various problems of circle and triangle.

3. Dynamic geometry

Judging from the senior high school entrance examinations over the years, dynamic questions often appear as finale questions, and the scoring rate is also the lowest.

Dynamic problems are generally divided into two categories, one is algebraic synthesis, and there are moving points and moving straight lines in the coordinate system, which are generally solved by multivariate functions.

The other is the geometric synthesis question, which sets moving points, straight lines and overall translation and flip in trapezoid, rectangle and triangle to examine the comprehensive analysis ability of candidates.

Therefore, the problem of motivation is the top priority of mathematics in senior high school entrance examination. Only by mastering it completely can you get high marks.

4. One-variable quadratic equation and quadratic function

Among these problems, especially the dynamic geometry problem is the most difficult. The difficulty of geometry problem lies in imagination and construction. Sometimes the whole problem gets stuck without auxiliary lines.

Compared with geometry comprehensive questions, algebra comprehensive questions don't need many ingenious methods, but they require candidates' computing ability and algebra skills.

In the mathematics of senior high school entrance examination, algebra problems often appear in the form of quadratic equations and quadratic functions, with monism as the main body and many other knowledge points as the auxiliary. In the quadratic equation and quadratic function problems, the simple solution is usually used to solve the pure quadratic equation.

However, in the later problems, knowledge points such as discriminant of roots, integer roots and parabola are usually combined.

5. Multifunctional cross-synthesis problem

The functions involved in junior high school mathematics include linear function, inverse proportional function and quadratic function. This kind of topic itself is not too difficult, and it rarely appears as the finale. Generally, as a middle-grade topic, it examines the examinee's mastery of linear function and inverse proportional function. Therefore, in the face of such problems, the senior high school entrance examination must avoid losing points.

6. Solve application problems with column equations (groups)

In the senior high school entrance examination, there is a kind of topic that is hard to say, and it is hard to say. Sometimes I have an idea after three or two times, and sometimes I have no idea after thinking hard for a long time. This is to set equations or equations to solve application problems.

Equation can be said to be the most important part of junior high school mathematics, so it is also a compulsory content in the senior high school entrance examination.

Judging from the senior high school entrance examination in recent years, there are many exams combined with current affairs, so candidates need to have certain life experience. In the actual examination, almost all of these questions are full marks or zero marks, but there are few questions, so candidates only need to practice more, master various questions and sum up some formulas, so they can deal with them calmly.

7. Dynamic Geometry and Function Problems

Generally speaking, there are probably two comprehensive problems that focus on several generations. The first one focuses on geometry, which is investigated by combining the properties of geometric figures and algebraic knowledge.

The other focuses on algebra, and the geometric nature is only an introduction point, and more is to examine the calculation ability of candidates.

However, the two key points are not strictly divided, and many problems are similar. Among them, the key object is through the geometric constructor given in the figure. When doing this kind of problems, we must have the theme of "reducing complexity" and "increasing flexibility"

8. Induction and conjecture of geometric figures

The senior high school entrance examination has increased the examination of candidates' ability of induction, summary and guessing, but because the systematic knowledge of series will not be formally investigated until the third year of high school, most of them are placed on the finale of filling in the blanks.

Thinking method is the most important for this kind of inductive summary.

9. Reading comprehension problems

Nowadays, the questions in the senior high school entrance examination are more and more lively, and the emergence of reading comprehension questions in mathematics is the biggest highlight. Reading comprehension is often to give a material, or introduce a priori knowledge, or give an answer to a topic, and then give a question.

For this kind of question, if candidates do it directly in order to quickly and completely ignore the reading materials, they will often waste a lot of time and have no ideas, which is not worth the candle. So how to look at the questions and how to use them becomes the key.

Problem solving strategy

1. Learn to use the combination of numbers and shapes.

The idea of combining numbers with shapes refers to a mathematical idea that studies the relationship between numbers by using the properties of geometric figures to seek the solution of algebraic problems, or studies the properties of geometric figures by using the relationship between numbers to solve geometric problems.

The idea of combining numbers and shapes skillfully combines quantitative relations with geometric figures and solves the problem.

Throughout the country in recent years, most of the final exam questions are related to the plane rectangular coordinate system, which is characterized by establishing the corresponding relationship between points and numbers, that is, coordinates. On the one hand, we can study the properties of geometric figures by algebraic methods, on the other hand, we can get the answers to some algebraic problems through geometric intuition.

2. Learn to use functions and equations.

Starting with the analysis of the quantitative relationship of the problem, the unknown number is set appropriately, and the quantitative relationship between the known quantity and the unknown quantity in the studied mathematical problem is transformed into a mathematical model of equations or equations, so as to solve the problem. This is the thinking method of the equation.

The key to solving problems with equation thinking is to construct equations (groups) by using known conditions or conclusions in formulas and theorems. This idea is widely used in algebra, geometry and real life.

Straight line and parabola are two important functions in junior middle school mathematics, that is, linear function and quadratic function. Therefore, no matter how to find its analytical formula and study its properties, it is inseparable from the idea of functions and equations. For example, to determine the resolution function, it is often necessary to establish equations or equations and solve them according to known conditions.

3. Learn to use the idea of classified discussion

The idea of classified discussion can be used to test the accuracy and rigor of students' thinking, often through the variability of conditions or the uncertainty of conclusions. If we do not pay attention to the classified discussion of various situations, some problems may have wrong solutions or missing solutions. Throughout recent years, it has become a new hot spot to solve the final exam questions by classified discussion.

When solving some mathematical problems, sometimes there will be many situations, which need to be classified and solved one by one, and then integrated solutions. This is the classified discussion method.

Classified discussion is a logical method, an important mathematical thought and an important problem-solving strategy, which embodies the idea of breaking the whole into parts and the method of sorting out.

Classification principle:

(1) Each part of the classification is independent of each other;

(2) Classification according to standards;

(3) The classification discussion should be gradual, and the correct classification must be comprehensive, without repetition or omission.

4. Learn to use the idea of equivalent transformation.

Transforming thinking is a basic mathematical thought to solve mathematical problems. When learning mathematical problems, we usually turn unknown problems into known problems, complex problems into simple problems, abstract problems into concrete problems and practical problems into mathematical problems.

The connotation of transformation is very rich. Known and unknown, quantity and graph, graph and graph can all be transformed to solve problems.

Any mathematical problem can't be solved without returning to thought. The transformation in junior middle school mathematics generally includes the transformation from known to unknown and from complex to simple. As the final question of the senior high school entrance examination, we should pay more attention to the connection and transformation between different knowledge. A finale of the senior high school entrance examination is generally a comprehensive test that integrates algebra, geometry and trigonometry, so we should make full use of the idea of reduction.

The final exam questions are not isolated knowledge points, nor are they personal ways of thinking. It is a comprehensive investigation of candidates' comprehensive ability, involving a wide range of knowledge and using comprehensive mathematical thinking methods.

Therefore, some candidates are afraid of the finale, thinking that their level is average, they can't do it, and they give up without even looking at it. Of course, they don't get the points they deserve. In order to improve the scoring rate of the final question, it is necessary to have a scoring strategy of sub-topic and sub-paragraph.

5. learn to score points.

The failure to solve a math finale problem in the senior high school entrance examination does not mean "I don't know anything, I don't know anything". We should turn the whole problem-solving idea into a scoring point.

For example, there are generally two or three small questions under the big question of the final exam. The difficulty level is 1. Small questions are relatively easy, and most students can get points. The second problem is moderate and plays a connecting role; The third question is more difficult, but it is often based on two small questions: 1 and 2.

Therefore, when we answer the questions, we must get the score of item 1, the score of item 2 and the score of item 3, which greatly improves the possibility of getting high marks in mathematics in the senior high school entrance examination.

The scoring standard of the senior high school entrance examination is to score according to the knowledge points examined in the topic. If you understand the knowledge points and grasp the scoring points, you will get points. Therefore, for the final math exam, we should try our best to answer "close" scores, give full play to our own level, and turn the final math exam into a stepping stone to high scores.

To solve the math finale of the senior high school entrance examination, we must first establish the confidence to win; Second, we must have solid basic knowledge and skilled basic skills; Third, we should master common problem-solving strategies.