A comprehensive survey of the mathematics test questions in Beijing senior high school entrance examination in 2006, 2007, 2008, 2009 and 20 10 shows that the basic structure, types and quantity of the test questions are basically the same. From the content of the examination, functions, equations and inequalities, triangles, quadrilaterals, circles, statistics and probability are all the key contents.
1, knowledge points have changed.
Judging from the examination of knowledge points, the knowledge points of senior one and senior two are almost 60%, 6 1%, 62% and 63% each year, while the knowledge content of senior three only appears about 25% in the senior high school entrance examination papers. Of course, there are also some test questions, which are not easy to distinguish. According to the above situation, two problems can be explained. One is the content of the senior high school entrance examination in recent years, and the mathematics content has not changed much. The knowledge of senior one and senior two is about 62%, and that of senior three is about 25%. In other words, this is definitely a stable requirement. 20 1 1 Needless to say, this level will not be reached. In the senior high school entrance examination papers, the knowledge assessment score of senior one and senior two accounts for more than 60%, which is close to 2/3. The knowledge content of grade three is less than 1/3. Before 2006, when we were reviewing the senior high school entrance examination, we often said, "The math content in Grade Three is the focus of study, and it is the focus of the senior high school entrance examination." Now this sentence has to be changed. For example, the last few questions in the past exams always focused on quadratic functions, circles and similar shapes. However, in the past five years, the difficulty and content of the questions in the senior high school entrance examination have been obviously reduced, especially the round and similar shapes. From these two points of view, I think you can do some analysis yourself. First, the difficulty of the test questions will not change much. Secondly, what is the key content of knowledge point assessment? What conclusions can be drawn? It is worthy of self-evaluation by parents and classmates.
2. The requirement for students' learning ability has been improved.
The current curriculum standards require students' learning knowledge, but it is more important to pay attention to the cultivation of students' ability in the learning process. It is more important for students to cultivate some mathematical qualities in the process of learning. This is what teachers strive to implement in the classroom according to the requirements of teaching materials and curriculum standards. But this problem is more prominent in the senior high school entrance examination papers. Why? Because in the senior high school entrance examination papers, we should try our best to reflect the spirit of the new curriculum standards promulgated by the state. So I will take the five-year senior high school entrance examination paper from another angle, that is, from the perspective of ability evaluation, see what I have already taken in the senior high school entrance examination and what I will take in the future, and talk about my views.
First, computing power and computing habits.
In the test paper, in addition to some simple calculations in filling in the blanks (10 has 8 places, with 32 points), there are also direct calculation questions, such as the calculation of numbers, solving equations and algebraic evaluation, and the three questions remain unchanged, with 15 points. There are still two problems to understand, one is solving equations, and the other is a statistical problem with a score of 10. Both calculations require students to be accurate. For example, the first 32 points, everyone scores. If you make a mistake, you will lose 4 points. The first score 15, everyone gets points, and you lose 1 point, which is not good. Strong computing ability. But generally speaking, what is more important? 23 or 24 questions, one-dimensional quadratic equation or quadratic function questions. In this problem, it is often calculated that there are letters in the coefficients of a quadratic function and a quadratic equation. But some calculations are needed, which is even more demanding. If you have no past in this calculation, there is a wrong symbol and a wrong number. After the whole question, can it be done? There is no score of 1. So the calculation will appear on the senior high school entrance examination paper. As long as a calculation error is found in the test paper, it is often an understatement. I shouldn't be wrong. I was so careless. I didn't see it clearly. The implication is that there is no problem. As a result, the next time, not in the same place, but in other places. If it happens once or twice, we can take advantage of carelessness and not see clearly. If it happens many times, this is a problem, and solving this problem is a problem of ability and habit.
Second, the ability to demonstrate and prove problems.
There are four fixed questions in the senior high school entrance examination paper.
A simple triangle proof problem (about 15),
This is a very simple proof of congruence. Looking at the mathematics test papers of Beijing senior high school entrance examination in recent years, there is a relatively simple geometric proof every year: you only need to prove congruence once, without auxiliary lines, and the conditions of congruence are obvious. Difficulty coefficient: 0.9. This problem is a geometric 1 problem in the solution. The difficulty is small because all candidates have a smooth start after entering the solution, thus avoiding fear, so that the exam can have the confidence to do the more difficult questions later.
There is also a simple quadrilateral argument (about 18).
Test sites of this topic: properties of trapezoid, isosceles right triangle, properties of special quadrilateral, Pythagorean theorem. Difficulty coefficient: 0.6.
There is also a round of proof (about 20 questions). This problem is a comprehensive problem related to the circle. The first problem is the conventional tangent proof, and the second problem can be solved by integrating knowledge such as similarity, trigonometric function and Pythagorean theorem. This is a good question to evaluate students' comprehensive ability. Test sites of this topic: the determination of the tangent of the circle, the related properties of the circle (vertical diameter theorem, right angle between the circle and the diameter), similarity (or trigonometric function, Pythagorean theorem) difficulty coefficient: the first question: 0.6; Question 2: 0.5
The fourth question is the geometric finale (23 or 24 questions). This topic is called exploratory geometry synthesis problem. The test sites of this problem are: the nature of diamond, congruent triangles, trigonometric function, the nature of equilateral triangle, the folding of figure, the nature of parallelogram, etc.
Third, about induction and speculation.
This kind of topic exists every year now, such as a certain data, find out its law and judge the result of the nth data. Generally speaking, some topics like this give data directly, and some don't give data, so you need to find them yourself. Finally, it is more difficult to find a pattern. The simplest one, guessing, guessing an answer, of course, must have a certain basis for guessing, and it is ok to guess completely, but it is too far from the correct answer. After guessing, induction, and this ability of induction is not easy, which is not easy for us to come into contact with in our usual study.
Fourth, operational ability and drawing ability.
What is the operation? The ability to stack, rotate and flip paper. What is painting ability? I can't do the problem. I want to draw a new picture, whether it is a function problem or a geometry problem. Or the picture is complete, complicated and looks messy as soon as it is picked up. I want to do it well. I'll take it apart and do it bit by bit. This ability is obvious in the present examination paper. There is no time to solve it in the test paper. There is a problem of overlapping papers every year. You said that time is not allowed to overlap papers in the exam, which may look like cheating. What do you depend on? To cultivate this ability at ordinary times, it is necessary to start work, and the painting of this painting will cultivate a kind of spatial imagination ability, which will only work when the exam is held.
Fifth, we call it reading analysis ability.
Everyone can read, but it is a question whether they can read well. For example, the last question, the last question this year is a triangle question, and last year was a function question. If you have finished reading this kind of question, it means that you don't understand. You don't know how to do this problem. In order to understand, it is usually necessary to cultivate the ability to find one word at a time, dig out the content contained in each sentence and the hidden conditions behind it, continue to play with this condition, and then continue to find. This ability depends on the usual training. For a simple example, when I tell you that y=x+ 1, it is a linear function. If I say nothing else, what will you tell me? Students will ask, what do you ask? I don't ask anything, I'll give you this. What can you tell me? Why? Our senior high school entrance examination 100% will give you a formula without asking anything. At this time, you need to have analytical skills. In fact, the information given by this equation is as follows: first, it is called a linear function; The second image is a straight line; The third k is equal to1; The fourth image rises through the first, second and third quadrants; Fifth, the intersection of the image and the Y axis (0, 1, 0); And the intersection of the sixth line and the x axis (-1, 0). After giving the students this formula, do the latter things react? If not, there will be obstacles in doing difficult problems. If you react, such conditions will become the conditions you will use in the future. This is whether you have analytical ability. In particular, the eighth multiple-choice question and the fourth fill-in-the-blank question are often difficult. If you want to solve it, you must be able to read the problem and interpret it word for word. What does this question give me? Function, what the horizontal axis represents, what the vertical axis represents, and what kind of story the image tells, we must make it clear, and the problem will come out, otherwise we don't know how to start.
6. What does reading and learning ability mean?
As can be seen from the five-year senior high school entrance examination, there is at least one such topic every year. What topic? It tells you something you have never learned. He told you all the conditions, processes and answers. I want you to solve the problem immediately according to what you have just learned. Without this ability, the following question 100% will not be done. Why? Because often the following questions need you to understand and see through some of the connotations you have learned in order to solve the following problems. You just understand the above, no, you can't solve the problem. In other words, can you teach yourself? These abilities are reflected in the examination paper of the senior high school entrance examination, which is the final exam. These abilities must be cultivated by ourselves. Of course, teachers are more responsible for cultivating your ability in this area. The usual mathematical knowledge itself contains many such abilities. You notice that this ability will gradually increase, and with it, the problem will become easier.
The percentage of an assessment, the content of an assessment ability and the content of a five-year assessment are all inseparable from these. Of course, I don't think students need to care too much about other difficulty factors and the difficulty of the topic. There are 65438+ 10,000 participants in the senior high school entrance examination in Beijing this year. The examination questions are easy for everyone, but difficult for everyone. In 2007, there was a question in Beijing that few people gave, and everyone didn't score, just like there was no such question. Don't care too much about the difficulty, it's easy for everyone. Candidates are most concerned about these basic things, and how to grasp them is the key. As for the prediction of the 20 1 1 senior high school entrance examination paper, I think it is inseparable from what I said. The title can be changed literally and the content can be changed, but the substance will not change.
In recent five years, the test questions have put more emphasis on application, increased inquiry and paid more attention to comprehensiveness. On the one hand, it pays attention to the foundation, highlights the examination of basic knowledge, basic skills and basic mathematical thinking methods, and has a good teaching orientation; On the other hand, it focuses on students' basic mathematical ability. So suppose that the math proposition of the senior high school entrance examination of 20 1 1 has the following possibilities:
The scope of the examination will still be the learning content stipulated in the Curriculum Standard for Full-time Compulsory Education formulated by the Ministry of Education, involving three sections: number and algebra, space and graphics, statistics and probability.
The examination paper will consist of the first volume and the second volume. The first volume is a multiple-choice question with 32 points. The second volume is fill-in-the-blank questions and solutions (including fill-in-the-blank questions 16, and solution questions 72). The distribution of knowledge content is: number and algebra are about 60 points; Space and graphics are about 46 points; Statistics and probability are about 14 points. The distribution of difficulty is as follows: 60 points for easy questions; About 36 points in the mid-range test questions; The more difficult questions are about 24 points. The exam time is still 120 minutes.
20 1 1 The trend of mathematics proposition in senior high school entrance examination will still focus on the examination of basic knowledge, basic skills and basic thinking methods. Highlight the most basic and core content of junior high school, that is, the core concepts, thinking methods, basic knowledge and common skills that all students must master in the process of learning mathematics and applying mathematics to solve problems, reflecting the foundation and popularization of mathematics curriculum in compulsory education stage.
In terms of basic knowledge, starting with the topic 1 and looking at the topic 1 and 2 in recent 5 years, we can find the law:
The reciprocal of (06) 1. Yes ()
A.B. C. D。
The reciprocal of (07) 1. Yes ()
A.B. C. D。
The absolute value of (08) 1 Equal to ()
A.B. C. D。
The reciprocal of (09) 1. 7 yes
A.B. C. D。
( 10) 1.？ The reciprocal of 2 is
(1)? (2) (3)? 2 (D) 2 .
The mid-term exam questions in these five years, 1 questions are all concepts of reciprocal, absolute value and reciprocal, which is the so-called "low starting point". Let's look at question 2 again:
(06) 2. The Qinghai-Tibet Plateau is the highest plateau in the world, with an area of about 1000 square kilometers.
A.B. C. D。
(07) 2. National Aquatics Center-"Water Cube" is one of the venues of Beijing 2008 Olympic Games, and its outer membrane area is about 260,000 square meters, so the scientific notation of 260,000 should be ().
A.B. C. D。
(08) 2. As of May 19, 2008, 2 1600 Chinese and foreign journalists have become registered journalists for the Beijing Olympic Games, the highest in previous Olympic Games. The scientific notation for 2 1 600 should be ().
A.B. C. D。
(09)2. Since the reform and opening up, China's GDP has increased from 654.38+364.5 billion yuan in 0978 to 3006.7 billion yuan in 2008. The scientific symbol of 300670 should be
A.B. C. D。
(10) 2.2065438+00On June 3rd, the first manned space flight test "Mars -500" was officially launched. China volunteer Wang Yue and other six volunteers embarked on a12,480-hour "trip to Mars". 12480 should be expressed in scientific notation.
(1) 12.48? 103 (B) 0. 1248？ 105 (C) 1.248？ 104 (D) 1.248？ 103。
It is easy to see that the second questions are all based on the basic knowledge of the realistic background. According to the description of the Beijing senior high school entrance examination, "the distribution of test paper difficulty is: easy questions are about 60 points, medium questions are about 36 points, and difficult questions are about 24 points." What are the easier questions? Most of the easier questions come from the original textbook questions. What is the senior high school entrance examination? It's easier to change the intermediate test questions a little. If this is made clear, we should not have candidates with a score below 90.
Basic skills, let's take a look at the 13 questions in recent five years:
(06) 13. Calculation:
(07) 13. Calculation:
(08) 13. Calculation:.
(09) 13. Calculation:
(10) 13. Calculation: 1? 20 100? |? 4 |? tan60？ .
It is not difficult to see that these five questions are strikingly similar. The principles of setting the test questions for the senior high school entrance examination are: overall stability, seeking change in stability and innovation in change. The stable part should be in the first 96 points. That is, in terms of basic knowledge and skills. "Change" and "new" should be in basic mathematical thinking. If we carefully study questions 8, 12, 22, 23, 24 and 25 in the mid-term exam in recent five years, it is not difficult to find the law and direction of change.
Among them, the proposition of algebra will increase from "number and formula" to "equation and inequality" and then to "function" Investigate the "three basics", dilute the special skills, and pay attention to universality and generality;
The geometry part will further enrich the understanding and feeling of space graphics by exploring the basic properties of basic graphics and their relationships; By investigating the basic properties of graphics such as translation, rotation and symmetry, we can appreciate and experience the application of graphic transformation in real life. Using coordinate system to determine the position of objects and develop the concept of space; Triangle plate will attach importance to the understanding and understanding of the bisector, midline and height of any triangle; Pay attention to the understanding of triangle stability: pay attention to the exploration of the nature of the midline in the triangle; Attach importance to the exploration of congruence conditions of two triangles; Pay attention to the exploration of judgment conditions of isosceles triangle, equilateral triangle and right triangle; Attach importance to the exploration of the properties of isosceles triangle and right triangle; Attach importance to the experience of exploring Pythagorean theorem; Quadrilateral board will attach importance to the judgment and application of parallelogram, rectangle, diamond and square; The content of "circle" in the textbook itself is low, and there may be three problems in "vertical diameter theorem, determination of tangent and calculation of its nature and area", but in 2006, 2007, 2008, 2009 and 10, the finale was written on the basis of geometry. Looks like we need to work on dynamic geometry.
Although the score of statistics and probability is only 14, there are many concepts, which may investigate basic statistical problems such as census, sampling survey and sample selection. Check the statistical data reflecting the degree of concentration and dispersion; Or get information from statistical charts, supplement and draw statistical charts, and investigate the understanding and mastery of basic methods and skills of data processing (representation and analysis); Estimate the population through the analysis of sample data, or make reasonable decisions on some practical problems and question some statistical methods. , examine students' statistical concepts; Examine the basic concepts of probability such as inevitable events and random events; Even examine students' understanding and application of frequency and probability; Combine statistics and probability problems with knowledge in other fields to examine students' comprehensive practical ability.
At this point, we should have a more specific understanding of the "Examination Instructions" for the senior high school entrance examination in Beijing. About 60 points for "easier questions"; About 36 points in the mid-range test questions; The more difficult questions are about 24 points. "Yes", overall stability, seeking change in stability and innovation in change. "Understanding is more profound. If we put the mid-term exam topics in the past five years together, we should study them carefully. 20 1 1 The mid-term exam is coming soon.