Middle School Mathematics | Don't know how to do the finale question, don't have ideas, learn these 5 methods, and make a breakthrough at once

For more information about junior high school and high school, you can get it on the Physics Master app and the Master 100 official account!

Junior High School Mathematics "Finale"

Ideas for solving the problem

Many parents and students often say to the editor, "I have a lot of headaches for the math test, and I can barely finish the multiple-choice questions and fill-in-the-blank questions, but I am a little helpless for the big questions, especially the final finale questions, which I haven't touched at all!"

Indeed, for junior high school mathematics, the finale question is often the most feared by candidates, and many candidates think that it must be difficult and dare not touch it. In fact, if you analyze the finale questions of the high school entrance examination over the years, you will find that it is actually not very difficult.

Generally speaking, there is also an agreement on the difficulty of the finale questions: in the past years, the finale questions are generally composed of 3 questions.

Question 1 is easy to learn and has a score rate of 0.8 or more

Question 2 is a little more difficult, and it is generally a regular question type, with a score rate between 0.6 and 0.7

Question 3 is more difficult and requires higher ability, but the scoring rate is mostly between 0.3 and 0.4

Judging from the finale questions of the high school entrance examination in recent years, most of them are not biased, and the scoring rate is stable between 0.5 and 0.6, that is, the average score of candidates is 7 or 8 points. It can be seen that the finale question is not terrible.

The type of finale question of the high school entrance examination mathematics common test

1. Calculation and proof of line segments and angles

The answers to the questions in the high school entrance examination are generally divided into two to three parts. The first part is basically a series of simple or intermediate questions, which are designed to examine the basics. The second part is often the middle problem of starting to pull points. The significance of easily mastering these questions is not only to get scores, but more importantly, to affect the morale and morale of the army throughout the process of doing the questions.

2. Unary quadratic equations and functions

Among these problems, the dynamic geometry problems involved are the most difficult. The difficulty of geometric problems lies in imagination and construction, and sometimes an auxiliary line is not thought of, and the whole problem is stuck.

Compared with the geometry comprehensive questions, the algebra comprehensive questions do not require too many ingenious methods, but they have relatively high requirements for the candidates' calculation ability and algebra skills.

In the mathematics of the high school entrance examination, algebra problems are often based on unary quadratic equations and quadratic functions, and a variety of other knowledge points are assisted. In the problem of unary quadratic equations and quadratic functions, the pure unary quadratic equation solution method is usually investigated in the form of simple solution. However, in the later difficult questions, it is usually combined with knowledge points such as discriminant roots, integer roots and parabolas.

3. Cross-synthesis of multiple functions

The functions involved in junior high school mathematics are primary functions, inverse proportional functions, and quadratic functions. This kind of question itself is not too difficult, and rarely appears as a finale question, and is generally used as a mid-level question to test the candidate's mastery of the primary function and the inverse proportional function. Therefore, in the face of such problems in the high school entrance examination, we must avoid losing points.

4. Column equation (group) solution application problem

In the high school entrance examination, there is a type of question that is not difficult to say, not difficult and difficult, sometimes there are ideas in three or two, and sometimes there are no ideas after thinking and meditating for a long time, which is the solution of column equations or systems of equations.

Equations can be said to be the most important part of junior high school mathematics, so they are also a compulsory content in the high school entrance examination. Judging from the high school entrance examination in recent years, there are more exams combined with current affairs, so candidates also need to have some life experience. In the actual exam, this kind of question almost always gets a full score or no score, but there are only a few types of questions, so candidates only need to practice more and master each question category and summarize some formulas, and they can deal with it calmly.

5. Dynamic geometry and function problems

On the whole, there are probably two emphases of algebraic comprehensive questions, the first is to focus on geometry, using the properties of geometric figures combined with algebraic knowledge to investigate. The other focuses on the algebraic aspect, and the geometric properties are only an introduction point, which examines the candidate's computational skills. However, there is no strict distinction between the two types of emphasis, and many of the question types are very similar. Among them, the construction function of the geometric figure has been given in the figure is the key object of investigation. When doing this kind of question, we must have the main idea of "reducing complexity" and "increasing flexibility".

6. Induction and conjecture of geometric figures

The high school entrance examination has increased the examination of candidates' ability to induct, summarize and guess, but because the systematic knowledge of the number series will not be formally examined until high school, most of them are placed in the fill-in-the-blank finale questions. For this kind of inductive problem, the method of thinking is the most important.

Ideas for solving the finale questions of mathematics in the high school entrance examination

1. Learn to use the combination of numbers and shapes

Throughout the recent years, the finale questions of the high school entrance examination across the country, most of them are related to the plane Cartesian coordinate system, which is characterized by the establishment of the correspondence between points and numbers, that is, coordinates, on the one hand, the algebraic method can be used to study the properties of geometric figures, and the properties of geometric figures are used to study the quantitative relations and seek algebraic problems. On the other hand, with the help of geometric intuition, some algebraic problems can be answered.

2. Learn to use the ideas of functions and equations

The key to solving problems with equation ideas is to construct equations (groups) using known conditions or known conclusions in formulas and theorems. This idea has a wide range of applications in algebra, geometry, and real life.

Straight lines and parabolas are two important types of functions in junior high school mathematics, that is, the primary function and the quadratic function. Therefore, whether it is to find its analytic formula or study its properties, it is inseparable from the idea of functions and equations. For example, the determination of the analytic formula of a function often requires the solution of a series of equations or systems of equations according to known conditions.

3. Learn to use the idea of categorical discussion

Classification discussion ideas can be used to test the accuracy and rigor of students' thinking, often through the variability of conditions or the uncertainty of the conclusion to investigate, some problems, if you do not pay attention to the classification and discussion of various situations, it may cause misunderstanding or omission, throughout the recent years of the high school entrance examination finale classification discussion of ideological solutions has become a new hot spot.

When solving some mathematical problems, sometimes there are multiple situations, and it is necessary to classify various situations, solve them one by one, and then synthesize the solution, which is the classification discussion method. Classification discussion is a logical method, an important mathematical idea, and an important problem-solving strategy, which embodies the idea of dividing the whole into zeros and the product into whole and the method of categorization and sorting.

Principles of classification:

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

(2) classify according to one standard at a time;

(3) The classification discussion should be carried out step by step, and the correct classification must be thorough, neither repeated nor omitted.

4. Learn to use the idea of equivalence transformation

Transformational thinking is one of the most basic mathematical ideas for solving mathematical problems. When studying mathematical problems, we usually transform 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, and between the known and the unknown, between quantity and graph, and between graph and graph, all of them can be transformed to obtain a turning point to solve the problem.

The finale question of the high school entrance examination is not an isolated knowledge point, nor is it an individual method of thinking, it is a comprehensive examination of the candidate's comprehensive ability, involving a wide range of knowledge, and the mathematical thinking methods used are also more comprehensive. Therefore, some candidates have a sense of fear of the finale, thinking that their level is average, they can't do it, and they give up without even looking at it, and of course they can't get the score they deserve.

5. Learn to grab points

If you can't solve a math finale question in the high school entrance examination, it doesn't mean that you don't understand it at all, you can't know it at all, and you should transform the whole problem solution idea into a score point.

For example, the finale of mathematics in the high school entrance examination generally has two to three sub-questions under the big questions, and the difficulty level is that the first sub-question is easier, and most students can get scores; the second sub-question is medium, which plays the role of connecting the previous and the next; and the third question is difficult, but it is often built on the basis of the two sub-questions of 1 and 2.

Therefore, when we solve the problem, we must get the score of the first question, the score of the second question, and the score of the third question, so as to greatly improve the possibility of getting a high score in mathematics in the high school entrance examination.

The scoring standard of the high school entrance examination is to score according to the knowledge points tested in the question, and the score will be scored if you solve the knowledge points correctly and grasp the score points.

Therefore, for the finale questions of the mathematics high school entrance examination, answer the score point as close as possible, maximize your level, and turn the mathematics finale question of the high school entrance examination into a stepping stone for high scores.

To solve the finale of mathematics in the high school entrance examination, first, we must establish the confidence to win, second, we must have solid basic knowledge and proficient basic skills, and third, we must master the commonly used problem-solving strategies.

Wait for a one-click triple

Your support is the driving force for Xiaobian's continuous update!