(1) function synthesis problem: first, given rectangular coordinate system and geometric figure, find the analytical formula of (known) function (that is, the type of known function before solving), then study the figure, find the coordinates of points or study some properties of the figure. The functions known in junior high school are: ① linear function (including proportional function) and constant function, and their corresponding images are straight lines; ② Inverse proportional function, whose corresponding image is hyperbola; ③ Quadratic function, whose corresponding image is parabola. The main method to find the analytic expression of known functions is the undetermined coefficient method, and the key is to find the coordinates of points, while the basic methods to find the coordinates of points are geometric method (graphic method) and algebraic method (analytical method). This kind of questions are basically 24 questions, with a full score of 12, and are basically presented in 2-3 small questions.
(2) Geometric synthesis problem: firstly, the geometric figure is given and calculated according to the known conditions, and then the moving point (or moving line segment) moves, resulting in changes in line segment and area. , and find out the analytical formula of the corresponding (unknown) function (that is, we don't know what the form of the resolution function is before solving it) and the definition domain of the function. Finally, we study it according to the obtained function relationship. Generally, there are: under what conditions is the figure an isosceles triangle, a right triangle, a quadrangle a diamond, a trapezoid, etc. , or explore what conditions two triangles meet to be similar, or explore the positional relationship between line segments, or explore the relationship between areas to find the value of x, and find the value of the independent variable when the straight line (circle) is tangent to the circle. The key to finding the unknown resolution function is to list the equivalent relationship between independent variables and dependent variables (that is, to list the equations containing X and Y) and write it in the form of Y = F (X). Generally, there are direct method (directly listing the equations containing X and Y) and compound method (listing the equations containing X, Y and the third variable, and then finding the functional relationship between the third variable and X, substituting and eliminating the third variable to get the form of Y = F (X)), and of course, parameter method, which has exceeded the requirements of junior high school mathematics teaching. In junior high school, the methods of finding equivalence relations are mainly using Pythagorean theorem, parallel line cutting proportional line segments, triangle similarity and equal area. Finding the domain is mainly to find the special position (limit position) of the graph and solve it according to the analytical formula. The final exploration problem is ever-changing, but it is essential to analyze and study the graph. Find the value of x by geometric and algebraic methods. The geometry synthesis problem basically appears in the 25th question as the finale, with a full score of 14, which is generally presented in three small questions.
When solving mathematical comprehensive problems, we should keep in mind the combination of numbers and shapes, turn big problems into small problems, and don't forget the potential conditions. Classification discussion should be rigorous, equation function should be instrumental, calculation and reasoning should be rigorous, and innovation quality should be improved.
The Secret of Solving the Math Final Question of the Senior High School Entrance Examination (2)
The final exam questions with selection function aim at examining candidates' comprehensive application ability, and have the characteristics of many knowledge points, wide coverage, hidden conditions, complex relationships, difficult thinking and flexible solutions. To solve the mathematical finale problem, we should establish the confidence to win, have solid basic knowledge and skilled basic skills, and master common problem-solving strategies. This paper introduces several commonly used problem-solving strategies for the reference of grade three students.
1, taking the coordinate system as a bridge and 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. With the knowledge of straight line or parabola as the carrier, using 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, using the variability of conditions or conclusions, using 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.
4. 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 final question of the senior high school entrance examination, we should pay more attention to the connection and transformation between different knowledge. A finale of the senior high school entrance examination is generally a comprehensive test that integrates algebra, geometry and trigonometry, so we should make full use of the idea of reduction. The final exam questions are not isolated knowledge points, nor are they personal ways of thinking. It is a comprehensive investigation of candidates' comprehensive ability, involving a wide range of knowledge and using comprehensive mathematical thinking methods. Therefore, some candidates are afraid of the finale, thinking that their level is average, they can't do it, and they give up without even looking at it. Of course, they don't get the points they deserve. In order to improve the scoring rate of the final question, it is necessary to have a scoring strategy of sub-topic and sub-paragraph.
5. Sub-topic score: Generally, there are two or three sub-topics in the final exam. The degree of difficulty is: sub-topic (1) is easy, sub-topic (2) is moderate, and sub-topic (3) is difficult. When you answer, you must get the score of sub-topic (1), and sub-topic (2) should strive to get the score.
6. Grading by section: Just because you can't do the last question in the senior high school entrance examination doesn't mean you don't understand at all, and you can't do it at all. So you should emphasize grading by sections, and the basis of grading by sections is grading by sections. The score of the senior high school entrance examination is graded according to the knowledge points examined in the topic. If you step on knowledge points, you will get points; if you step on more points, you will get more points. Therefore, we should try our best to understand and do the finale of the senior high school entrance examination, give full play to our own level, and turn the finale of the senior high school entrance examination mathematics into the most valuable finale.
Mathematical finale is the most extensive and comprehensive problem in junior high school mathematics. Based on the actual situation of the senior high school entrance examination in recent years, the finale questions mostly appear in the form of function and geometry comprehensive questions. There are many knowledge points in the final exam, and the conditions are quite hidden. Students are required to have strong ability to understand, analyze and solve problems, strong ability to master mathematical knowledge and methods, strong sense of innovation and ability, and of course strong psychological quality.
At the same time, I also collected some problems and solutions of the finale for you, which have been uploaded to the attachment. I hope it will help you, and I wish my classmates excellent results in the exam!
If you agree, please choose a satisfactory answer in time. Your approval is my motivation to help others. Thank you!
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