Sharing of problem-solving skills in mathematics fill-in-the-blank questions in senior high school entrance examination
I. Direct method
This is the basic method to solve the fill-in-the-blank problem, starting directly from the problem setting conditions, using the knowledge of definition, theorem, nature, formula, etc., and directly obtaining the result through the processes of deformation, reasoning and operation. 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.
Second, professional methods.
When the conclusion of the fill-in-the-blank question is unique or the information provided in the question setting conditions implies that the answer is a fixed value, and the known conditions contain some uncertain quantities, we can select some appropriate special values (or special functions, or special angles, special positions, 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.
Third, the combination of numbers and shapes.
"It is not intuitive to count the missing shapes, and it is difficult to be nuanced when counting the missing shapes." The problem of large numbers in mathematics implies the information of shapes, and the characteristics of figures also reflect the relationship between numbers. It is necessary to reveal the abstract and complex quantitative relationship through the intuitive image of form, so as to achieve the purpose of "form helps number"; At the same time, we should use the law of numbers and numerical calculation to find ways to deal with shapes and achieve the goal of "promoting shapes by numbers" For some fill-in-the-blank questions with geometric background, if we can think of the shape in the number and help the number with the shape, we can often solve the problem simply and get the correct result.
Fourthly, 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.
Great idea sharing of solving the final math questions in the senior high school entrance examination
1, taking the coordinate system as a bridge, using the idea of combining numbers and shapes.
Throughout recent years, most of the final exam questions in various places are related to the 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. Take the knowledge of straight line or parabola as the carrier, and use the idea of function and equation.
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. Use the variability of conditions or conclusions and 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.