What are the key points and difficulties in high school mathematics?

Summarize the key and difficult points of high school mathematics and analyze geometry.

Question background? I am a math teacher in senior high school, and my average grade in the math class of the college entrance examination on 20 19 is 126, of which 12 was admitted to a double-class school in 985,21,with a success rate of 100%.

Mathematics in senior high school is as difficult as the function problem mentioned in the topic. Function problem runs through the whole high school mathematics content, and its solving methods and ideas are integrated with various types of questions. Here is an example.

One: Basic elementary functions Common basic elementary functions: exponential function, logarithmic function, power function and trigonometric function. A little more subdivision, that is, inverse proportional function, linear function, quadratic function, transcendental function (this must be noted)

In fact, the functions here have been exposed to several as early as junior high school, but they are often tested in high school textbooks. When solving function problems, you must be very familiar with the properties of basic elementary functions before you can use them flexibly.

To explore the essence of basic elementary function, we must first understand it with its images.

Seeing this, you might as well take 8 minutes to test yourself. Can you list all the properties of three trigonometric functions in 8 minutes?

Its properties are as follows: image, definition domain, value domain, monotone interval (monotone increasing and decreasing interval), symmetry (symmetry center and symmetry axis), periodicity (period and minimum positive period), X corresponding to the solution set of maximum and minimum values of Y.

If you can list all these unintentional omissions within 8 minutes, it means that you have a very clear grasp of the content of this piece, so that when you reach the third year of high school, you won't draw some pictures, you can build images to solve problems without thinking, and you are extremely skilled and won't make mistakes in doing problems.

Learning is learning this realm.

Two: high school math? Difficult point? Derivative Many people say that derivative is difficult. Indeed, derivative is associated with an advanced mathematics, which is a transitional period. In fact, it is what we often call transcendental function, which is to solve problems by combining basic elementary functions.

Here I give you some advice, that is, when learning derivatives, you must master two propositional directions.

The first is the existence theorem of zero (extremely important)

That is to say, when we often derive, we will take the second derivative after catching the ball, but have you ever wondered why we should take the second derivative? What is the meaning of the second derivative?

This piece actually involves the application of a zero-point existence theorem, because each derivative function is recursive, and it is impossible to infer any of its properties across stages!

The second point is one of the derivatives? Hidden zero? problem

This kind of problem is often an extreme point of transcendental function. You can't work it out directly by addition, subtraction, multiplication and division, but we can know that there must be a zero point. At this time, we can use the whole substitution to set this zero point.

Because the extreme points satisfy the function and the whole is zero, then you can find the relationship between them.

Three: Function Ideas Some common function ideas are necessary for high school mathematics, such as the combination of numbers and shapes.

In the daily teaching work, the most important point I have emphasized to students is to draw more pictures! Draw more pictures! ! Draw more pictures! ! !

There are many students who are not good at drawing in the process of solving problems, which must be paid attention to.

So what's the use of drawing? Why does the teacher repeatedly emphasize the idea of combining numbers with shapes to solve problems?

Because we can deepen our understanding of the original intention of the topic through the correct image, so as to achieve no increase or decrease, just right.

And there are many abstract function problems that you can't solve directly. We must help solve them through its image geometric meaning or some properties.

Just like there are several zeros in the function of 12 in these genealogy volumes, we all use the combination of numbers and shapes to transform the original abstract function into the problem of fixing the intersection point of moving images.

Then, it can be easily solved by judging which interval the parameter range changes to meet the meaning of the question.

Thank you. You can follow me privately if you have any questions. There are also many students who often ask me questions in private, and I will answer them one by one. Thanks for your support.