The establishment of the senior high school entrance examination is to provide a basis for a higher school to select outstanding talents, and the design of the final questions of the senior high school entrance examination is also to examine students' ability to comprehensively apply what they have learned;
It has the characteristics of wide knowledge, wide coverage, hidden conditions, complex relationship, difficult thinking and flexible solution, which is also one of the pain points for many students who are about to take the senior high school entrance examination.
There are generally 2-3 small questions in the final exam. Common finale questions: 1, calculation and proof of line segments and angles.
The first question is generally to examine some simple questions or questions with moderate difficulty, such as the knowledge of parabola. The first question is generally to find the analytical formula of parabola, or to prove that parabola intersects with X axis (generally, a conclusion can be drawn through discriminant);
If we examine the knowledge points of the circle, the first question may be to prove that a line is the tangent of the circle;
If we look at the moving point, rotation, etc. The first problem is generally to prove that two triangles are congruent. The purpose of this setting is to check the foundation.
The second part is often a difficult problem to start scoring, and the third part is more difficult. Generally speaking, it is not difficult to calculate and prove line segments and angles. As long as the key "eyes" are found, the logic of the following topics will become clearer and clearer.
2, graphic position relationship. In middle school mathematics, the position relationship of figures mainly includes the relationship between points, lines, triangles, parallelograms, diamonds, rectangular squares and circles.
3. Dynamic geometry. Judging from the senior high school entrance examination in recent years, dynamic questions often appear as finale questions, and the scoring rate is generally low. Of course, I believe many students have no time to do the finale in the end.
Dynamic problems generally fall into two categories. One is algebraic synthesis. There are moving points and moving straight lines in the coordinate system, which requires the area of a certain figure (mostly triangle and quadrilateral). Generally, it is solved by multivariate functions (generally quadratic functions and linear functions).
The other is the geometric synthesis problem, which sets moving points, moving lines and overall translation and flip in trapezoid, rectangle and triangle to test students' comprehensive analysis ability. For students with a good sense of space, doing this branch has certain advantages;
For some students with intensive phobia, for example, when they see a lot of graphics, the line segments will be dizzy and may suffer some losses.
4. One-variable quadratic equation and quadratic function. In the mathematics of senior high school entrance examination, algebra problems often appear in the form of quadratic equations and quadratic functions, with monism as the main body and many other knowledge points as the auxiliary.
In the quadratic equation and quadratic function problems, the simple solution is usually used to solve the pure quadratic equation. However, in the later problems, knowledge points such as discriminant of roots, integer roots and parabola are usually combined.
5. Cross-integration of multiple functions. The functions involved in junior high school mathematics include linear function, inverse proportional function and quadratic function.
This kind of topic is not difficult in itself, and it rarely appears as the finale. Generally, it is a medium-grade topic to examine students' mastery of linear function or inverse proportional function.
6, column equation (group) to solve application problems. Equation can be said to be the most important part of junior high school mathematics, so it is also a compulsory content in the senior high school entrance examination.
Judging from the senior high school entrance examination in recent years, it is necessary for candidates to have certain life experiences because of the combination of current events or life events.
7. Dynamic geometry and function problems. Generally speaking, there are probably two comprehensive problems that focus on several generations. The first one focuses on geometry, which is investigated by combining the properties of geometric figures and algebraic knowledge.
The other focuses on algebra, and the geometric nature is only an introduction point, and more is to examine the calculation ability of candidates. However, the two key points are not strictly divided, and many problems are similar.
Among them, the key object is through the geometric constructor given in the figure. When doing this kind of problems, we must have the theme of "reducing complexity" and "increasing flexibility"