1 methods and skills of mathematical sequence in senior high school
I. Formula method
If a series is arithmetic progression or geometric progression, the arithmetic difference, the first n terms of geometric progression and the formula are directly used for summation. Note that the value of the public notice Q of geometric series should be divided into q= 1 and q≠ 1.
2. Reverse addition
If the sum of two terms with the same distance from the beginning to the end of a series is equal, then the sum of the first n terms of this series can be added in reverse order, for example, arithmetic progression's formula for the sum of the first n terms is derived in this way.
Three. Dislocation subtraction
If the sum of a series consists of the product of the corresponding items of a arithmetic progression and a geometric progression, then the sum of the first n items of this series can be found by this method. For example, the sum formula of the first n items of geometric progression is derived by this method.
Four. Split-period offset method
When the general term of a series is decomposed into the difference between two terms, some middle terms can cancel each other out, so that sum can be obtained. It should be noted that after cancellation, not only the first item and the last item are left, but also the first two items and the last two items are left, and the rest items appear symmetrically.
Verb (abbreviation for verb) grouping summation method
If the general formula of a series is composed of several arithmetic progression, geometric progression or summable series, we can sum them separately by grouping summation method, and then add and subtract them.
2 Senior high school mathematics series questions answering skills
The conventional types of high school series are nothing more than two, arithmetic progression and geometric progression. These two topics are relatively simple. Remember the formula, the summation is also relatively simple, and the use of the formula should be familiar.
The topic is often not so simple and easy. The slightly more difficult topic is the combination of arithmetic and some geometric series. Some methods to be adopted here are dislocation elimination.
There are a variety of topics, and the problems that often appear in the end are all common items that have not been touched, and some even don't give connection items. For these two categories, I think we should accumulate the following methods.
For summation and other topics, Cauchy inequality can be transformed into geometric series summation, denominator scaling, mathematical induction and functions.
For the problem of finding the general term, we can find the law by substitution evaluation, and then verify it by mathematical induction, or we can use accumulation or multiplication.
In short, every time you encounter a strange series problem, you should sum it up and get a solution, or learn a scaling method from it, which is very helpful in the future.
3 college entrance examination mathematics problem solving methods
The process of solving problems should be standardized.
Mathematics problems in college entrance examination should be correct, complete and standardized. It should be due to the nonstandard expression and scribbling of the math calculation questions in the college entrance examination, which is also a major aspect that causes non-intellectual factors to lose points in the math examination paper in the college entrance examination.
To solve the math calculation problem of the college entrance examination, we must first comprehensively examine the meaning of the problem and accept the concept quickly, which is "face"; Through lengthy narration, grasp the key words and put forward key data, which is the "point"; It is a "line" to synthesize the connection, refine the relationship and establish the mathematical model by mathematical methods, thus transforming the application problem into a pure mathematical problem. Of course, the process and result of solving math problems in college entrance examination are inseparable from the actual background.
Mature first, then grow.
We can get many positive factors as well as some negative ones after the entrance examination of mathematics. For the latter, there is no need to panic. We should think that the test questions are difficult for all candidates. Through this hint, you can ensure emotional stability. After grasping the whole math book of the college entrance examination as a whole, we can implement the pre-ripe method, that is, first do those mathematical calculations with relatively familiar content, familiar question structure and clear problem-solving ideas. In this way, you can make your thinking fluent and extraordinary while winning familiar math problems, so as to achieve the goal of winning middle and high-level problems.
High school students know how to learn math well.
First, prepare a notebook and a draft book. Notebooks are not for you to remember formulas and concepts. Those things are all in the book. There is no need to copy them into the notebook again. The notebook mainly records the examples given by the teacher. After all, the teacher is very experienced, and the examples given must be very representative. If necessary, you can recite the problem-solving methods of examples and understand the ideas.
The draft is just some unimportant questions. If the teacher asks you to draw inferences, you don't need to write it down in your notes, but you must do it accordingly. It's definitely better to write two strokes on paper and work it out than just think about it.
Secondly, we must concentrate on class and have some interaction with teachers. After a long time, the teacher is watching your lecture 90% of the time. If you don't nod, she won't go on . After all, a class lasts for 40 minutes, and a teacher gives each student less than one minute on average, so being selfish means buying yourself time.
If you have questions after class, you'd better not ask your classmates, especially those who think they are smart, so they are good at math. Don't ask such people. It's not that people don't want to tell you. It's exam-oriented education. Those clever students don't necessarily listen carefully in class. Some people just do the problems according to their own ideas. Those problem-solving methods may be suitable for them but not for you, so you must find a teacher who will give you a set of problem-solving methods that are most suitable for the exam.
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