Multiple-choice questions have certain depth and comprehensiveness, which requires students to firmly and comprehensively master the basic knowledge they have learned, and at the same time have the ability to summarize, analyze and evaluate.
1, exclusion method (screening method)
Starting from the known conditions, combined with options, through observation, analysis, speculation and calculation, obviously wrong answers are eliminated one by one, thus narrowing the scope of thinking and improving the speed of solving problems.
For example, multiple-choice questions of quadratic function and linear function images, eliminate the wrong options one by one, so as to determine the correct ones.
2. Verification method
Substitute each option into the original question, verify whether it meets the meaning of the question, and then draw a conclusion. For example, if the image passes this point, you can bring in problems through verification and get the correct options.
3. Special value method
According to the conditions of the question, select appropriate special numerical values to replace the letters and numbers in the question, get the answer through calculation, and then get the correct answer by analogy with the general answer.
For example, some numerical values can be used to verify the results of standard questions and reasoning.
★ Fill in the blanks
Fill-in-the-blank question is a common basic question in junior high school mathematics examination, which highlights students' ability to use knowledge accurately, rigorously, comprehensively and flexibly to operate correctly.
Fill-in-the-blank questions only require answers, and it is difficult to judge whether the results are correct without the target information provided by the options. One mistake, zero for the whole question. If you want to fill in the blanks quickly and accurately, you must work hard on the words "accurate, skillful and fast".
1, direct method
The direct method is the most basic method to solve the fill-in-the-blank problem, which requires students to use the knowledge of definition, theorem, nature and formula directly from the setting conditions. Through the process of reasoning and operation, the result can be obtained directly.
2. Number-shape combination method
The combination of number and shape is an important mathematical method, which requires students to make a figure that conforms to the meaning of the problem according to the specific characteristics of the conditions of the problem when solving the problem, so as to think about the shape by number and help the shape.
Through the observation, analysis and research of images, we can inspire the thinking of solving problems and find out the implicit conditions of problems, thus simplifying the process of solving problems and testing the results of solving problems.
★ Solve the problem
Analytic questions are questions that need to write out the process of solving problems, which occupy a considerable proportion in the mathematics questions of the senior high school entrance examination, and the competition in the examination also focuses on the scoring rate of analytical questions.
Solving problems involves many knowledge points, wide coverage, strong comprehensiveness, large span and flexible problem solving, involving numerical calculation, function images and property calculation applications.
The key to solving the problem is to obtain "symbolic information" from the language narrative of the topic, "image information" from the images and graphs of the topic, and flexibly use definitions, formulas, properties and theorems for calculation and reasoning. Use various mathematical ideas to establish various mathematical models to solve problems.
1, structure graph
Complex geometric problems generally need to add appropriate auxiliary lines to solve smoothly, such as connecting, extending, making parallel, making vertical, etc. , and transform irregular and unusual graphics into regular or special images.
Such as: constructing equal-length line segments, three-line octagons, congruent triangles, similar triangles, right-angled triangles, etc. , so as to use the nature and judgment of special graphics to solve the problem.
2, the combination of dynamic and static
In the process of graphic movement, we should carefully study the changing law of graphics, grasp the dynamic and static combination of active variables and driven variables, explore the relationship between them, and solve them by functional relationship.
Mathematics focuses on practice, and we should pay attention to summing up the skills and methods of solving problems in actual combat.
Sometimes when we write several papers, we are practicing a problem-solving idea and method. At this time, it is necessary to draw inferences and solve many problems.
The most effective way to learn mathematics is to find a breakthrough in solving problems through exploration and experience, so as not to get stuck in the ocean of problems and increase the pressure and burden on yourself.
Think and answer questions.
★ Function and equation thought
Function thought refers to analyzing and studying the quantitative relationship in mathematics from the viewpoint of movement change, and analyzing, transforming and solving problems by establishing the functional relationship and using the image and nature of the function.
The idea of equation is to solve the problem by transforming the problem into an equation or inequality model with mathematical language from the quantitative relationship of the problem.
When solving problems, students can use the idea of transformation to transform functions and equations.
★ Special and general ideas
This way of thinking is sometimes particularly effective in solving multiple-choice questions, because when a proposition is established in a general sense, it is bound to be established in its special circumstances. Accordingly, students can directly determine the correct choice in multiple-choice questions.
Not only that, it is also useful to explore the problem-solving strategies of subjective questions with this way of thinking.
★ Extreme thoughts
The general steps of extreme thinking to solve problems are:
1, try to conceive a variable related to the unknown quantity;
2. Confirm that the result of this variable through the infinite process is an unknown quantity;
3. Construct the function (sequence) and get the result by using the limit calculation method or directly calculate the result by using the limit position of the graph.
★ Discuss ideas by category.
Students often encounter such a situation when solving problems. After solving a certain step, they can't continue with unified methods and formulas.
This is because the research object contains a variety of situations, so it is necessary to classify all the situations, solve them one by one, and then summarize the solutions comprehensively, which is classified discussion.
There are many reasons for the discussion of classification, and there are many situations in the mathematical concept itself, such as the limitations of mathematical operation rules, some theorems and formulas, and the uncertainty and change of graphic position.
It is suggested that students unify standards when discussing and solving problems in different categories.