There is not much math content in the last semester of senior one, but the difficulty is not low. The difficulty lies not in the depth and comprehensive ability of knowledge points, but in the fact that many students have shown great inadaptability from relatively specific mathematics learning in junior high school to abstract learning in senior high school, which seems to have little to do with life. Therefore, if you think senior one mathematics is "difficult", the focus of review should be to analyze why you think the knowledge points you have learned are "difficult".

Difficulty 1: Abstract function

Although the meaning of the F rule seems simple, if it is not deeply understood, it will have a great influence on the later problem solving. There are two main ways to solve the difficulties of abstract functions:

(1) combines the contents of abstract functions with the properties of concrete functions. Abstract function, as the upper requirement of understanding function, has guiding significance for all concrete functions. The concrete properties of exponential, logarithmic and power functions learned in senior one are the manifestations of abstract function properties in concrete functions. Function's domain, range, monotonicity and parity are the core content of abstract function, and also the expression of concrete properties of concrete function. Combined memory, better effect.

(2) For all synthesis problems related to abstract functions, we should first try to transform the conditions of abstract functions into concrete conditions, and the method of transformation is to use the properties of abstract functions. The conditions of abstract functions will appear in many comprehensive problems. For this kind of problem, the first thing to be solved is to remove F from these conditions. For example, if f (a) < F(b), keep F, even simple A and B, and do not remove F through monotonicity, the problem will not be solved.

Difficulty 2: trigonometric function

The focus of this part is to jump out from the definition of acute trigonometric function in junior high school. In teaching, I noticed that some students still draw right triangles to help them understand trigonometric functions, which is very dangerous and we don't advocate it. The definition of trigonometric function has undergone revolutionary changes after the introduction of real angle and radian system. A in Sina is not necessarily acute or obtuse, but a real angle-radian system. With such a leap in thinking, trigonometric functions are no longer the subsidiary products of triangles (junior high school trigonometric functions are often attached to similar triangles), but function expressions with independent significance.

Since trigonometric function is understood as a functional meaning, its knowledge structure can be completely related to the chapters of the function. The essence of function lies in image. With an image, it has all the attributes. For trigonometric functions, in addition to images, the unit circle is also very effective as an auxiliary means-just as formulas are widely used in quadratic functions.

There are not many patterns in the constant deformation part of the triangle. It can be seen from the teaching that it is not difficult for students to understand the formula, and those who are more skilled in application are those who do more problems. To a certain extent, in fact, it is easy for us to find that there are only a few types of trigonometric identities investigated in Grade One. In the course and review, we will also pay attention to summarizing the "unified theory" of trigonometric identity deformation for students, and master the key methods such as order reduction, auxiliary angle and universal formula, so that the general trigonometric identity can be solved easily. The key is to do more questions.

Difficulty 3: Vector part

This part is actually the easiest part of this semester. The reason is simple. I haven't studied it before, and the first exam won't be too difficult. This part of the review is also the easiest-to understand the various algorithms of vectors around geometric representation, algebraic representation and coordinate representation.

Difficulty 4: Comprehensive questions

The finale questions are basically based on the chapter of function, with vector and triangle operations in the middle. To solve this problem, the method is almost fixed, that is, the condition with F is transformed into the condition without F by using the properties of abstract functions, and then it is simplified or proved by using trigonometric sum vector operation. The method of non-finale problem may be more free, but the comprehensiveness is often not too strong, and it still belongs to the comprehensiveness of each plate.