The standard equation can be easily converted into a parametric equation, as shown below:

x= 1，y=t.z=t。

Let the coordinate of a point on the surface of revolution be M(x, y, z).

Because it rotates around the Z axis, when it rotates in a straight line, the Z coordinate of the point above it is unchanged, and the distance from the point to the Z axis is also unchanged.

The distance from the point M(x, y, z) to the Z axis is: root sign (x 2+y 2).

On a straight line, the distance from the point with parameter t to the z axis is:

Root number (1+t 2)

Therefore, the parametric equation of the surface is obtained:

z=t，

x^2+y^2= 1+t^2

Elimination parameter: x 2+y 2 = 1+z 2.

Or write: x 2+y 2-z 2 =1.

It is known as a hyperboloid.

Mathematics problem-solving for postgraduate entrance examination mainly examines the comprehensive application ability, logical reasoning ability, spatial imagination ability and the ability to analyze and solve practical problems, including calculation problems, proof problems and application problems. The content is comprehensive, but some questions can be answered by elementary solution.

Teacher Li, the teaching and research section of cross-examination education mathematics, said that the thinking of solving problems is flexible and diverse, and sometimes the answer is not unique, which requires students not only to do the questions, but also to find out the test intention of the proposer and choose the most appropriate method to answer them.

1, take the postgraduate entrance examination in the basic stage of mathematics, thoroughly understand the textbook and master the outline.

Combine the undergraduate teaching materials with the previous year's syllabus, and thoroughly understand the basic concepts, methods and theorems. Mathematics is a highly logical science. Only by deeply understanding the basic concepts and firmly remembering the basic theorems and formulas can we find the breakthrough and breakthrough point of solving problems.

The analysis of mathematics answer sheets in recent years shows that one of the important reasons why candidates lose marks is that they have incomplete memory of basic concepts and theorems, poor memory, inaccurate understanding and poor grasp of basic problem-solving methods.

The initial review of postgraduate entrance examination should lay a solid foundation in an all-round way and focus on making up for the weak links. Mathematics review for postgraduate entrance examination is basic and long-term, and it should be put in the first place in the initial stage of postgraduate entrance examination.

This is the way to review the basics of mathematics. Reading, doing problems and thinking are indispensable. Reading is the premise and foundation, and it is possible to do the right topic through reading. Doing the problem is the key and the purpose. Only by knowing how to do the questions, doing the right questions and doing the questions quickly can we cope with the exams and achieve our goals. Thinking is to read and do problems more effectively.

2. Different types of math problem-solving in postgraduate entrance examination have different coping strategies.

Coping strategies for solving calculation problems: the focus of calculation problems lies not in the amount of calculation and complexity, but in ideas and methods.

For example, the calculation of multiple integrals, curve and surface integrals, sum function of series, etc. In addition to ensuring the accuracy of operation, it is more important to systematically summarize the problem-solving ideas and skills of various calculation problems, so as to choose the simplest and most effective problem-solving ideas when encountering problems and get the correct results quickly.

There is still more than a month before the exam, and it is very important to sprint before the exam. It is the most immediate effect to choose a simulation problem with appropriate difficulty and a proposition that meets the requirements of the outline.

Coping strategies to solve the problem of proof: first, sensitive to the conditions given by the problem. On the basis of being familiar with the basic theorems, formulas and conclusions, the starting point and ideas of proof are preliminarily determined from the subject conditions; Second, be good at exploring the relationship between conclusions and topic conditions.

For example, the differential mean value theorem is used to prove equality or inequality, and the auxiliary function can be determined from the conclusion, thus solving the key problem of proof.

Coping strategies to solve practical problems: focus on the ability to analyze and solve problems.

First of all, starting from the conditions of the topic, make clear the goal to be solved.

Second, establish the relationship between the conditions given in the topic and the goal to be solved, and integrate this relationship into the mathematical model (pay special attention to the choice of origin and coordinate system for graphic problems), which is also the most important link in solving problems.

Third, according to the category of the mathematical model established in the second step, find the corresponding problem-solving method, and the problem can be solved easily.

3, the postgraduate sprint, correct mentality, and meet the postgraduate entrance examination with high efficiency and quality.

The review of postgraduate entrance examination lasts for such a long time, especially in the final stage of the sprint of postgraduate entrance examination, there will always be times of depression and fatigue. The exam is getting closer and closer. Some students are not ideal in doing simulation problems, and their confidence in mathematics is getting worse and worse. Seeing that the exam is getting closer, their hearts are getting worse and worse.

In the final sprint stage, by doing high-quality simulation questions, candidates have the feeling of doing actual combat and find a better "test" feeling. As long as you find this feeling, you can stabilize your mood and meet the exam with confidence.

However, the types and quantities of simulation questions are numerous and complicated, which is different from the real questions after all. Therefore, Teacher Li, the teaching and research section of cross-examination education mathematics, reminds candidates to have a rational attitude towards each set of simulation questions.

Don't be too hard on yourself. Get high marks for each set of simulation questions. You should also have a different attitude towards the different difficult problems of a set of questions. On the one hand, don't despise most problems just because they are not difficult, and there is no need to be afraid of individual problems.

A set of test questions must consist of the most basic questions and individual problems. We must ensure that we can grasp the basic questions (avoid primary mistakes), effectively complete all the test questions, and try our best to win the difficult problems. With such a gain and loss mentality, we can better stabilize our emotions.

4, the final sprint of postgraduate mathematics, to avoid mistakes in preparing for the exam.

Weak foundation and difficult problems: most of the postgraduate mathematics are medium-sized and easy problems, and the more difficult problems only account for about 20%. The difficult problems are only the further synthesis of simple problems. If you are stuck on a certain question, it must be because you don't understand a certain knowledge point enough, or you are vague about a simple question.

Ignoring the foundation leads candidates to lose a lot of points on many simple questions. It is really not cost-effective to give up the 70% that can be determined for the sake of the 30% that is uncertain. Therefore, we must proceed from reality, go to the foundation, and have a deep understanding, so that even if we encounter some problems, we will break them down smoothly. This is the fundamental solution.

Simple imitation, not understanding: this is a manifestation of speculative psychology. Learning is a very hard work. Many students unilaterally pursue other people's ready-made methods and skills, but they don't know that methods and skills are based on their own in-depth understanding of basic concepts and knowledge, and each method and skill has its specific scope of application and premise of use.

Simple imitation is absolutely impossible, which requires us to give up speculative psychology and thoroughly understand the ins and outs of each method, which will really help us do the problem.

Understanding the problem is equivalent to doing it: mathematics is a rigorous subject, and there is no room for any mistakes. Before we have established a complete knowledge structure, it is difficult to grasp the key points of the problem and ignore the nuances.

Moreover, through hands-on practice, we can standardize the answering mode and improve the proficiency of problem solving and operation. You know, a question as big as three hours is a test of calculation ability and proficiency, and marking is graded step by step. How to answer effectively must be achieved through our own continuous exploration.

Mathematics review in the final stage was ignored: many candidates before the final stage spent a lot of time and energy reviewing mathematics in the early stage of review, and the effect was very good, thinking that they could sit back and relax. In the final stage, they gave up math review and rushed to other subjects. Only when they reviewed math a few days before the exam did they find that they were already very strange and forgot a lot of things, and they felt very bad in doing the problem.

In order to avoid this situation, Mr. Li from the teaching and research section of cross-examination education mathematics reminds students that they should spend at least one hour reviewing mathematics every day, and they should not interrupt or even give up all their previous efforts.

In addition, the problem-solving training at this stage must not be carried out in isolation, and the knowledge system must be systematically sorted out again. It is necessary to combine the weaknesses reflected in solving problems, reorganize the mathematical theoretical framework in a targeted manner, and at the same time conscientiously sum up the problem-solving methods and skills of some specific questions, so we must pay attention to thinking more, summarizing more and summarizing more.