1. The ability of basic examination is mainly reflected in multiple-choice questions and fill-in-the-blank questions.

2. The comprehensive ability of the senior high school entrance examination is mainly reflected in the last three questions.

3. In the application of senior high school entrance examination ability, there will be one or two popular math questions in the choice of fill-in-the-blank questions, and there will be an application question (usually a probability application question) among the big questions.

4. Test the ability in new questions. Especially in the new curriculum reform area, science propositions seem relatively simple on the surface. When you do the questions, you will find that the calculation amount is not as large as the previous ones, but most of them are innovative questions.

The center of this "four-test ability" is to examine mathematical thinking methods.

From the autumn exam of 2009 to the spring exam of 20 10, we can clearly understand the determination of the reform of Shanghai mathematics college entrance examination. Although the reform of the autumn exam in 2009 caused a voice of doubt, the spring exam on 20 10 continued the spirit of reform. Judging from the types of questions in the spring exam, we should pay attention to the following points:

1, item structure reform: In the item structure, the spring exam of 20 10 is consistent with the autumn exam of 2009, that is, 14 fills in the blank, 4 multiple-choice questions, 5 answers, ***23 questions, which is higher than the previous 1 1 or 6544. The change of item structure has a great influence on the candidates in the autumn exam in 2009, mainly because the candidates are not used to this change and have great psychological pressure, which affects the performance of the exam. However, after half a year's adaptation, I believe that the change of item structure will not have much influence on the spring exam of 20 10, even if the autumn exam structure of 20 10 changes back to its original appearance, I believe the influence will not be too great.

2. Pay attention to the examination of new content: in the autumn exam of 2009, all new knowledge points in the new textbook were basically tested, such as determinant, algorithm, polyhedron and rotator (sphere), probability statistics, vector and so on. 20 10 spring exam, these new contents have increased the intensity of the exam, especially the revolving body, and tested a fill-in-the-blank question about the cylinder and a solution question about the ball; In addition, the test difficulty of the algorithm has also increased. For vectors, the 22 nd question (penultimate question) in the 20 10 spring exam is based on vectors and combined with the related contents of analytic geometry. It can be seen that the new content is the focus of the examination and must be taken seriously.

3. Strengthen the examination of inquiry questions: Inquiry questions are also one of the hot spots in the reform of college entrance examination, focusing on examining students' inquiry learning ability. Question 23 (the last question) of the 20 10 spring exam examines the inquiry question, asking for a true proposition through the inquiry of the question, and giving extra points according to the quality of the proposition. There are many types of inquiry questions, and this is one of them. In 2006, I took the generalized conclusion, and in 2007, I took the existential conclusion. This is the first time that this type has been graded according to the quality of propositions, and the research on this kind of problems should be strengthened.

4. Pay attention to the training of the series comprehensive questions: 20 10 spring exam, the series is the last question, which is very difficult. The last answer of the college entrance examination in 2008 and 2009 is to examine the series, which shows the importance of the series. Throughout the recent 10 college entrance examination, the last solution usually examines functions, series and analytic geometry, and the probability of the occurrence of series is relatively high, mainly because the series talks about the law of numbers, and the law of numbers changes endlessly, so it is not easy to grasp the general law of solving problems. Therefore, attaching importance to the study of series synthesis requires mastering relevant basic knowledge and cultivating the ability to explore and discover laws.

In a word, the direction of Shanghai college entrance examination reform can be further clarified from the 20 10 spring college entrance examination, and I hope these problems can play a certain guiding role for candidates who are reviewing the college entrance examination.

Second, the characteristics of questioning

1. Multiple choice problem

(1) Strong concept: Every term, symbol and even idiom in mathematics often has a clear and specific meaning. This feature is reflected in multiple-choice questions, which shows that the concept of question type is very strong. The presentation of test questions and the transmission of information are based on the discipline rules and habits of mathematics, and will never be unconventional.

(2) Outstanding quantity: The study of quantity relation is an important part of mathematics, and it is also a major content of mathematics examination. Quantitative questions account for a large proportion of multiple-choice mathematics questions in the college entrance examination. Moreover, many multiple-choice questions are quantitative in form, but in fact they are not simple or mechanical calculation questions, and often contain an examination of concepts, principles, properties and laws. This examination is closely combined with quantitative calculation, forming the characteristics of quantitative outstanding questions.

(3) Full of speculation: This feature stems from the high abstraction, systematicness and logicality of mathematics. As a multiple-choice math problem, especially for selecting exams, there are not many questions that can be answered correctly only by simple calculation or intuitive perception, which can almost be said to be non-existent. In most multiple-choice questions, in order to answer correctly, candidates are always required to have certain ability of observation, analysis and logical reasoning, and speculative requirements are filled between the lines of the questions.

(4) Both form and number: the research object of mathematics is not only number, but also figure. The discussion and research of logarithm and figure are not carried out in isolation, but combined and dialectical. This feature has been fully demonstrated in senior high school mathematics. Therefore, in the mathematics multiple-choice questions of the college entrance examination, it embodies the characteristics of both shape and number, which shows that algebra questions are often hidden in geometry multiple-choice questions, and geometry questions are often contained in algebra multiple-choice questions. Therefore, the combination of numbers and shapes and the separation of numbers and shapes are important and effective thinking methods and problem-solving methods for multiple-choice questions in mathematics in college entrance examination.

(5) Diversification of solutions: Compared with other disciplines, the phenomenon of "multiple solutions to one problem" in mathematics is outstanding. In particular, the multiple-choice questions in mathematics, because of their options, provide rich and useful information for the answers to test questions, which is quite enlightening, showing a broad world for problem-solving activities and greatly increasing the ways and methods of answering questions. Very clever solutions are often hidden among them, which is conducive to examining the depth of thinking of candidates.

2. Fill-in-the-blank questions and multiple-choice questions are objective questions, and they have many common features: short and pithy forms, focused examination objectives, short, clear and specific answers, no need to fill in the problem-solving process, and objective, fair and accurate grading. But there is a qualitative difference between fill-in-the-blank questions and multiple-choice questions. First of all, there is no substitute for filling in the blanks. Therefore, the answer has the advantage of not being disturbed by induced errors, and it also lacks the help of hints. Candidates' ability to think and solve problems independently will be higher. For a long time, the correct answer rate of fill-in-the-blank questions has been lower than that of multiple-choice questions, which may be an important reason Secondly, the structure of fill-in-the-blank questions is often in a correct proposition or judgment, in which some contents (both conditions and conclusions) are removed, leaving room for candidates to fill in independently and the examination method is more flexible. In reading comprehension of topics, it sometimes seems more difficult than multiple-choice questions. Of course, this is not always the case, it will depend on the design intention of the proponent.

There are few test sites and concentrated goals in the fill-in-the-blank questions, otherwise the discrimination of the questions is poor, and its test reliability and validity are difficult to be guaranteed.

This is because: if there are many test sites, the answering process is long, and there are many factors that affect the conclusion, then it is difficult for candidates who answer wrong to know the real reason for their mistakes. Some of them may be ignorant and make mistakes at the beginning, and some may just make mistakes at the last step, but they show the same situation on the answer sheet and get the same result, although the level is very different.

3. Compared with fill-in-the-blank questions, answering questions is to provide questions, but there are also essential differences. First of all, when answering questions, candidates should not only provide the final conclusion, but also write or tell the main steps of the answering process and provide reasonable and legal explanations. There is no such requirement for fill-in-the-blank questions. Just fill in the results and omit the process. The results should be concise, general and accurate. Secondly, the content and answers of the test questions are much richer than the fill-in-the-blank questions. There are relatively many test sites for solving problems, which are comprehensive and difficult. The evaluation of the result of solving problems depends not only on the final conclusion, but also on the process of deduction and demonstration. Scores are evaluated according to the situation to reflect their differences, so the freedom of solving problems is much greater than that of filling in the blanks.

In normal times, you must ask yourself to fill in the blanks in one minute. Solving the problem of filling in the blanks at high speed by mathematical thinking.

Be careful not to do stupid things, and learn to be smart. Choosing to fill in the blanks and the first three solutions are the basic points of mathematics. The last three questions are not just the first question. We should guess the grading standard from front to back according to the steps and strive for high scores.

We should use the spirit of "pig eight quit" to overcome the difficult problem. Arch from front to back, you can often arch to 4 points first, then arch forward to 8 points until 10 points, and finally forget the remaining 2 points and 4 points. Because the scores at the back are difficult, you need a genius.