The last question in the high school math exam is generally difficult, which is called the finale of the high school math exam.
The purpose of the final math test of the senior high school entrance examination is generally to open the gap between candidates.
Introduction of several common solutions to the final problem of mathematics in senior high school entrance examination.
First, take the coordinate system as a bridge and use the idea of combining numbers and shapes.
Throughout recent years, most of the mathematical finale questions in senior high school entrance examination are related to coordinate system, which is characterized by establishing the corresponding relationship between points and numbers, that is, coordinates. On the one hand, the properties of geometric figures can be studied by algebraic method, and the position of points can be transformed into coordinate problems. Thirty-six measures: the point is on the image, and the coordinates of the point satisfy the equation; On the other hand, with the help of geometric intuition, some algebraic problems can be solved and the coordinate problem can be transformed into the relationship of line segments. The problem can be solved by the methods of "finding the length of line segment in rectangular coordinate system, considering the similarity of triangle before 80%" and "finding the length of line segment in geometry, constructing right triangle before 80%".
Second, based on the knowledge of straight line or parabola, the equation is solved by function modeling.
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. "The objective function should be established before 100% for scheme selection and maximum problem" and "The extreme value problem of quadratic function should be considered before 100% for vertex drawing".
When solving the comprehensive problem of image problems of univariate linear function and quadratic function, we should combine the characteristics of image and the nature of function, and keep in mind the geometric meaning of parameter a\k, "Thirty-six measures: the role of k in univariate linear function", "the role of a in univariate quadratic function" and "the graphic symmetry of quadratic function".
Thirdly, using the variability of conditions or conclusions and the idea of logical division.
Throughout the logical division in recent years (that is, classified discussion), solving problems has become the focus and must be tested every year. The reason is that the idea of logical division can examine the accuracy and rigor of students' mathematical thinking, often through the variability of conditions or the uncertainty of conclusions. Please keep in mind "Thirty-six measures: no repetition or omission in classified discussion", "no growth or omission" and "special point and special love" to avoid unnecessary loss of points caused by careless classified discussion in various situations.
Fourthly, synthesize multiple knowledge points and apply the idea of equivalent transformation.
Any mathematical problem can't be solved without returning to thought. The transformation in junior middle school mathematics generally includes the transformation from known to unknown and from complex to simple. As the finale of the senior high school entrance examination, we should pay more attention to the connection and transformation between different knowledge. A final question of the senior high school entrance examination is generally a comprehensive test of the integration of algebra and geometry, and we should make full use of the idea of reduction.
Fifth, master the definition method and apply the idea of inductive conjecture.
In the new curriculum standard, there is a new type of question, that is, the open question of material reading comprehension and law inquiry. This kind of questions mainly examines students' ability to acquire new knowledge and apply what they have learned. The image point is "sugar fried chestnuts, now fried and now sold". The key to reading material comprehension questions is to understand the knowledge points that the material itself wants to explain. Such knowledge points are either the expansion of teaching materials or the simple knowledge points of high school mathematics, which is difficult to some extent. To solve this kind of problem, we must first master the definition method, regardless of the willy-nilly, and there are "36 plans: understand the problem and draw a gourd with a gourd" Exploring open questions regularly is a must for senior high school entrance examination, which combines students' divergent thinking ability and mathematical research ability. In view of the fact that this kind of topic is relatively difficult, the proposition principle of "low starting point, high falling point" is adopted in the proposition, which is convenient for students to get started, so the score rate of the items in the middle school exam is still relatively high, but candidates must achieve "36 plans: open-minded, well-founded and well-founded" to avoid unnecessary loss of points.