In the high school mathematics test paper, the fill-in-the-blank questions rank second, after the multiple-choice questions, including 4 questions, with ***20 points. Fill-in-the-blank problem is an objective test that only requires writing the results and does not require the calculation process.
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There are many similarities between fill-in-the-blank questions and multiple-choice questions: small and flexible, simple in structure, small in calculation, and wide in knowledge to be investigated. According to the content form filled in when filling in the blanks, the blanks can be divided into the following types:
(1) quantitative type:
Candidates are required to fill in numerical values, numerical sets or quantitative relationships.
For example, the solution of equations, the solution set of inequalities,
The domain, range, value or minimum value of a function,
Line segment length, angle size, etc.
(2) qualitative type:
What is required to be filled in is an object with a certain nature.
Or to fill in some attributes of a given mathematical object,
For example, fill in the focal coordinates and eccentricity of a given conic.
When solving the fill-in-the-blank problem,
Because it does not reflect the process, only the result is required.
Therefore, the requirement for correctness is higher and stricter than solving problems.
Therefore, when reviewing for the exam, we should understand the knowledge points contained in each question. Only by mastering all the mathematical knowledge points can we be familiar with the problem-solving skills. To have reasonable analysis and judgment, every step of reasoning and operation requires less calculation and more thinking, which will be the basic premise for solving the fill-in-the-blank problem quickly and accurately.
The basic strategy to solve the fill-in-the-blank problem is accurate, fast and neat. This is similar to doing multiple-choice questions, except that we still have options to refer to in multiple-choice questions. Filling in the blanks requires us to use our knowledge flexibly! Therefore, we should study the problem-solving skills of fill-in-the-blank questions.
Accuracy is the premise of solving fill-in-the-blank problems. There is no middle score in the fill-in-the-blank question, one step error and no score in the whole question. Therefore, we should carefully examine the questions, make in-depth analysis, correctly deduce them, beware of omissions, and ensure accuracy.
Speed is a necessary condition to win time and get high marks. The time to answer the fill-in-the-blank questions should be controlled at about 20 minutes, and the sooner the better, to avoid the phenomenon of "losing points over time";
Cleanliness is a sufficient condition for maintaining scores. Only by writing the correct answers neatly on the answer sheet can the marking teacher ensure the correct marking, which is particularly important when marking online.
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Fill-in-the-blank questions in college entrance examination mathematics are generally basic or intermediate questions, and most of them are computational (especially inferential calculation) and conceptual (qualitative) judgment questions. When you answer, you must actually calculate or make logical deduction and judgment according to the rules. I'm here to give you a few examples to talk about problem-solving skills. I wish you a helping hand on the way to the college entrance examination!
Direct teaching method
Just like multiple-choice questions, some questions in fill-in-the-blank questions can be solved directly by applying the properties of formula theorems. After you get the topic, you can get the result directly through deformation, reasoning, operation and other processes according to the information provided by the topic. It is the most basic and commonly used method to solve fill-in-the-blank problems. To solve the fill-in-the-blank problem by direct method, we should be good at seeing the essence through phenomena, skillfully use the methods of solving equations and inequalities, and consciously adopt flexible and simple solutions.
Specialized method
When the information provided in the conclusion or condition of the fill-in-the-blank question implies that the answer is a fixed value, and the known condition contains some uncertain quantities, we can select some suitable special values (or special functions, or special angles, special positions of graphs, special points, special equations, special models, etc.). ) that is, meet the conditions to deal with the uncertainty in the problem, so as to draw the conclusion of exploration. This can greatly simplify the process of reasoning and argumentation.
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Equivalent transformation method
By "simplifying complexity and turning strangeness into familiarity", the problem is equivalently transformed into an easy-to-solve problem and the correct result is obtained.
A combination of numbers and shapes
After mastering these problem-solving skills, there are several classic problem-solving methods of high school mathematics to introduce to you!
Several classical problem-solving methods commonly used in high school mathematics;
1, matching method
The so-called formula is to change some items of an analytical formula into the sum of positive integer powers of one or more polynomials by using the method of constant deformation. The method of solving mathematical problems with formulas is called matching method. Among them, the most common method is to make it completely flat. Matching method is an important method of constant deformation in mathematics. It is widely used in factorization, simplifying roots, solving equations, proving equality and inequality, finding extreme values of functions and analytical expressions.
2, factorization method
Factorization is to transform a polynomial into the product of several algebraic expressions. Factorization is the basis of identity deformation. As a powerful mathematical tool and method, it plays an important role in solving algebra, geometry and trigonometry problems. There are many methods of factorization, such as extracting common factors, formulas, grouping decomposition, cross multiplication and so on. Middle school textbooks also introduce the use of decomposition and addition, root decomposition, exchange elements, undetermined coefficients and so on.
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3. Alternative methods
Method of substitution is a very important and widely used method to solve problems in mathematics. We usually refer to unknowns or variables as elements. The so-called method of substitution is to replace a part of the original formula with new variables in a complicated mathematical formula, thus simplifying it and making the problem easy to solve.
4. Discriminant method and Vieta theorem.
The root discrimination of unary quadratic equation ax2+bx+c=0(a, B, C belongs to R, a≠0) and△ = B2-4ac is not only used to judge the properties of roots, but also widely used in algebraic deformation, solving equations (groups), solving inequalities, studying functions and even geometric and trigonometric operations as a problem-solving method.
Vieta's theorem not only knows one root of a quadratic equation, but also finds another root. Knowing the sum and product of two numbers, we can find the symmetric function of the root, calculate the sign of the root of quadratic equation, solve the symmetric equation and solve some problems about quadratic curve. , has a very wide range of applications.
5, undetermined coefficient method
When solving mathematical problems, it is first judged that the obtained results have a certain form, which contains some undetermined coefficients, then the equations about undetermined coefficients are listed according to the problem setting conditions, and finally the values of these undetermined coefficients or some relationship between these undetermined coefficients are found. This method is called undetermined coefficient method to solve mathematical problems. It is one of the commonly used methods in middle school mathematics.
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6. Construction method
When solving problems, we often use this method to construct auxiliary elements by analyzing conditions and conclusions, which can be a figure, an equation (group), an equation, a function, an equivalent proposition and so on. And establish a bridge connecting conditions and conclusions, so that the problem can be solved. This mathematical method of solving problems is called construction method. Using construction method to solve problems can make algebra, trigonometry, geometry and other mathematical knowledge permeate each other, which is beneficial to solving problems.