Six solutions to break through multiple-choice questions
First, the direct method
This is the most common and basic method to solve multiple-choice questions. We can directly proceed from the conditions, use related concepts, properties, theorems and other knowledge points, and draw conclusions through reasoning.
The advantage of this method is that solving problems is naturally not affected by options; The disadvantage is that some calculations and reasoning will waste a lot of time and energy, and some problems cannot be solved directly. Let's look at the example 1:
Second, the special case method
What is the special case method? It is a method of replacing general conditions with special cases that meet known conditions, drawing special conclusions, then verifying each option and making correct judgments. The commonly used special case methods include special values, special points, special graphs and so on. Let's take an example and look at the following example 2:
Third, the exclusion method.
This is also the most commonly used method when we do multiple-choice questions. We usually start with the conditions given by the topic, use theorems, properties and formulas to estimate or estimate, eliminate interference items and get the correct answer.
The advantage of this method is that we can make simple reasoning and calculation through observation, comparative analysis and judgment, so as to get the correct answer; The disadvantage is that if you don't dig deep into the hidden conditions or grasp the essential characteristics of the problem, it is easy to make omissions and make wrong judgments in the process of elimination. See example 3:
Fourth, the verification method
The so-called verification method refers to the method of substituting conditions into options one by one, or substituting each option into a topic for testing, so as to judge the options. Let's look at the explanation of the following question:
Fifth, the graphic method.
When answering multiple-choice questions related to graphics and images, we often use the thinking method of combining numbers and shapes to draw a schematic diagram, find the characteristics of graphics and images through observation and comparison, and make a quick choice.
The advantage of this method is that the graph is intuitive, and it can make complex calculation and reasoning simpler. The disadvantage is that students need to have strong basic knowledge of mathematics and spatial imagination. For example:
In short, multiple-choice questions are ever-changing, and sometimes multiple methods need to be used alternately, and even individual questions may have other better methods. Therefore, when solving multiple-choice questions, students should pay attention to the structural characteristics of the questions, make full use of the information provided by the questions themselves and alternative answers, master the basic methods of solving problems, and at the same time, open their minds and pay attention to skills, so as to solve these problems accurately and quickly and achieve good results in the senior high school entrance examination.
Basic principles of review
Based on the curriculum standards and mathematics textbooks, on the basis of mastering and consolidating the basic knowledge and skills, we should strengthen the main knowledge, pay attention to the key and difficult points of the textbooks, strengthen the review of weak links, timely check for missing parts, pay attention to the application ability of knowledge, and cultivate flexible and comprehensive problem-solving ability.
Some suggestions in the comments
1. Pay attention to the textbook knowledge, check for leaks and fill gaps. We have completed the first stage of reviewing basic knowledge and strengthening basic skills training. In the second stage of review, we will reflect and summarize the omissions and deficiencies in the last round of review, and we will find that some knowledge has not been mastered well and there is no idea when solving problems, so we should further classify the knowledge and deepen our memory while reviewing. We should further understand the concept and extension, firmly grasp the derivation or proof of laws, formulas and theorems, and further strengthen the ideas and methods of solving problems; At the same time, we should also find some similar questions for intensive training, fill in the blanks in a timely and targeted manner, and never give up easily until we truly understand and do it.
At this stage, it is particularly important to review textbooks, because the examples and exercises in textbooks are important components of textbooks and the main carriers of mathematical knowledge. Only by thoroughly understanding the examples and exercises in the textbook can we master the basic knowledge of mathematics and master the basic methods of mathematics comprehensively and systematically, so as to keep constant and change. Therefore, when reviewing, we should learn to examine these examples from multiple directions and angles, from which we can further clearly grasp the basic knowledge, review the thinking process, consolidate various solutions and understand the mathematical thinking method. There are various forms of review, especially to improve review efficiency.
In addition, at present, the proposition of the senior high school entrance examination is still based on basic questions, some of which are original or modified questions in the textbook, and some big questions are "higher than the textbook", but the prototype is generally an example or exercise in the textbook, which is an extension, deformation or combination of the questions in the textbook. Examples, exercises and homework in textbooks should not only be understood, but also done. At the same time, we should also pay attention to reading textbooks, researching topics, doing some things and thinking about things in textbooks.
2. Pay attention to classroom learning and improve efficiency. Under the guidance of teachers, through classroom teaching, students are required to master the internal relationship between knowledge points, clarify the knowledge structure and form an overall understanding. Through the systematic induction of basic knowledge and the classification of problem-solving methods, they can deepen their memory on the basis of forming knowledge structure. At the very least, they should accurately grasp the meaning of each concept, sort out the vague concepts in their usual study, master the knowledge more firmly, and let themselves know the position of each knowledge point in the whole junior high school mathematics. If you want to attend classes and take notes, you should grasp the key points of knowledge in each class, solve problems, improve learning efficiency, and timely check for leaks and fill gaps according to your own specific situation.
3. Consolidate basic knowledge and learn to think. In mathematics examination questions over the years, basic scores account for the most, plus basic scores in some intermediate and difficult questions, so scores account for a larger proportion. We must lay a good foundation, and through systematic review, we can meet the requirements of "understanding" and "mastering" junior high school mathematics knowledge, and we can skillfully, correctly and quickly apply basic knowledge.
Some questions will create new question situations for the knowledge and methods to be examined, especially for some questions that need to be highly discriminated; Each math test with medium or above difficulty usually involves multiple knowledge points and multiple mathematical thinking methods, or skillfully designs the test questions at the intersection of knowledge. Therefore, each of our classmates should learn to think. What the teacher teaches us in class is the angle, method and strategy of thinking. We should use the learned methods and strategies to understand how to think correctly in the process of solving problems with new situations.
4. Pay attention to the transfer of knowledge and learn to achieve mastery through a comprehensive study. Some examples and exercises in the textbook are not isolated, but closely related. The knowledge of other disciplines is also inextricably linked with mathematics. We should learn to discover, study and show the inner connection of these knowledge from the closest point of thinking development. This not only helps us to understand the textbook knowledge deeply, but also helps us to strengthen the knowledge focus. More importantly, it can effectively promote the construction of our own mathematical knowledge network and method system. Knowledge and ability can be transferred in a benign way, so as to achieve the effect of drawing inferences from others. By exploring the internal relationship between typical examples and exercises in textbooks, we can form a knowledge network and method system more effectively while deeply understanding the knowledge in textbooks. For example, the discriminant of the root of a quadratic equation can not only solve the problems of determining the root and finding the letter coefficient when the root is known, but also solve the factorization of the quadratic trinomial, the determination of the root of the equation group and the coordinates of the intersection of the quadratic function image and the horizontal axis.
5. Review the gradient and choose typical exercises. If the first stage is the basis of the senior high school entrance examination review, focusing on double-base training, then the second stage review is the extension and improvement of the first stage review. At this stage, the exercises should be selected with certain difficulty, but the harder the better, the harder the topic, the better. Questions should be typical and representative, and the selected questions can be completed step by step. Only in this way can we stimulate our desire to learn from ourselves and make it more difficult for us to solve it.
6. Pay attention to basic knowledge and problem-solving methods. Basic knowledge is the concepts, formulas, axioms and theorems involved in junior high school mathematics curriculum. Students are required to master the internal relationship between knowledge points, clarify the knowledge structure, form an overall understanding and comprehensively apply it. Every year, there will be one or two difficult comprehensive math problems in the senior high school entrance examination. The knowledge used to solve these problems is the basic knowledge that students learn and does not depend on those special and non-universal problem-solving skills.
In addition to the basic knowledge, the mathematical proposition of the senior high school entrance examination also attaches great importance to the examination of mathematical methods, such as collocation method, undetermined coefficient method, discriminant method and other operational mathematical methods. When reviewing, you should master each method, the types of questions it adapts to, including the steps of solving problems.
7. Form mathematical ideas and learn to use them. The further formation and continuous cultivation of mathematical thought is very important, because it is widely used. For example, equation thought, special and general thought, combination of numbers and shapes, function thought, classified discussion thought, transformation and transformation thought, etc. To deepen our understanding of these ideas, we should do more related topics at present; Judging from the senior high school entrance examination in recent years, the final "finale question" is often related to this kind of question type. Many students only pay attention to algebraic knowledge or geometric knowledge when solving this kind of problems, and they will not skillfully convert algebraic knowledge and geometric knowledge.