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The last question about mathematics in college entrance examination
In the national college entrance examination mathematics papers over the years, the score of the final question (the last question to be solved) is 14, which accounts for nearly 10% of the total score of the paper. It is comprehensive and requires high mathematics ability and thinking ability of candidates, and its difficulty and importance are self-evident ... The finale generally involves three major issues: function (the sequence belongs to a special function) and analytic geometry.

Analytic geometry

It is the difficulty of the college entrance examination, and this year is mainly determined by the characteristics of the subject. Analytic geometry is a subject that solves geometric problems by algebraic method. Therefore, there are both tangible and numerical, and there are more investigations on the idea of combining numbers and shapes, and the requirements are higher. Furthermore, in the process of solving geometric problems by algebraic methods, the requirements for algebraic methods, that is, letter operations or equation deformation are also quite high, and these difficulties are concentrated together, making it very difficult to analyze geometric problems.

To solve the problem of analytic geometry, don't be afraid at first. Why? Now the problem of analyzing geometry is not the most difficult problem in the college entrance examination, so students should be confident to solve it well. How to solve it? It is necessary to analyze the difficulties in analytic geometry. When many students do analytic geometry, they may not know where to start. The second pair of equations is there and they don't know how to deal with it. The third operation was not enough, and the first calculation was wrong. In view of these problems, it is suggested that students do not know where to start in the review process, that is, do a good job of mutual transformation between geometric quantities and algebraic quantities, and how to quickly transform geometric quantities into algebraic expressions. Like the definition of conic curve, establish the relationship between numbers and shapes, and transform numbers and shapes appropriately. Another one, many students have written a bunch of formulas, and I don't know what to do. This often lacks goals. Analytic geometry should be a holistic thinking. You should think about what to do before you do it. If it is aimless, such as putting the linear equation and conic equation there, what to do next is unknown, but it is actually a lack of goals. So pay attention to the overall thinking.

Synthesis of inequality between function and sequence of numbers

This is also the focus of the college entrance examination. This part is especially about ability. The questions about this part of the ability test in the college entrance examination are often an organic combination of several key points and hot spots. They all come from simple questions, which are the superposition of simple questions. So if you want to do this kind of problem well, I think it may be much better to master all aspects of knowledge systematically than to dig deep into one aspect. You just learned a lot in one aspect, but you can't integrate it organically, so you can't do this kind of problem well.

In other words, the most important thing is to grasp the basics and learn how to break a seemingly complicated problem into several parts on the premise of fully mastering this basic knowledge point and basic method. Of course, these parts are small. For example, if a comprehensive problem is broken down into these parts, which are function and value domain, and those parts are series, it may be very simple for students to do it.

I just remembered that some time ago, we just started school and had a monthly exam. After the exam, a teacher told me that the two best students in their class didn't do any new questions during the holiday, and they all had a good time with the previous questions. The two best students in the exam are like this. It makes sense if you think about it. On the other hand, let's take a look at the questions done by senior three, which have a lot of content. In fact, I have done it in my first and second year of high school. In the first round of review, many things are reviewed comprehensively, so it is very important for you to go back and summarize what you did wrong, what you missed and what you did. On this basis, if some students turn a blind eye to the previous wrong questions in the second round of review, it is not enough, so do some new questions appropriately.