Teacher's comments: Liu, a special math teacher in the middle school affiliated to Harbin Normal University, is a national backbone teacher and a senior coach of China Mathematical Olympics.

First, the basic characteristics of the test paper

Judging from this year's test paper and examinee's response, the 20 10 national college entrance examination mathematics test paper (Jilin, Heilongjiang, Ningxia) is the same in structure as the 2009 test paper (Ningxia, Hainan). Multiple choice questions are easier than last year's national second volume, and the fill-in-the-blank questions are basically the same as last year's national second volume. It is slightly more difficult to solve solid geometry and analytic geometry in the questions than last year. Among the three problems, parametric equation is a little more difficult than plane geometry and inequality. Most students feel that they are not fluent in answering questions, so it is expected that the average math branch this year will be lower than last year.

20 10 national college entrance examination mathematics volume (Jilin, Heilongjiang, Ningxia volume) has the following characteristics:

First, based on teaching materials, closely follow the syllabus.

None of the questions on the test paper are out of the question. Half of the multiple-choice questions and fill-in-the-blank questions in science and liberal arts come from textbooks, and 17 and 19 in the solution questions also come from textbooks. The questions of arts and sciences 17 are all the contents of the investigation series. Liberal arts highlights arithmetic progression's basic quantitative thought and function viewpoint, while science highlights the basic methods of finding general terms by accumulation method and summing by double difference method.

Second, highlight the foundation and strengthen integration.

The examination paper examines concepts such as set, complex number, function parity, definite integral, three views, mathematical expectation, and the angle formed by a straight line and a plane.

Question 7 embodies the synthesis of algorithm and summation of sequence, question 1 1 embodies the synthesis of logarithmic function and linear function, equation and inequality, question 13 embodies the synthesis of definite integral and random simulation method, and question 19 embodies the synthesis of sampling method and independence test.

Third, intentional thinking, conception ability.

The examination paper is comprehensive, focusing on ability, especially the ability to imagine space, reason and demonstrate, calculate and solve, data processing, application consciousness and innovation consciousness. 14 moderately requires students' spatial imagination, while 18 excessively requires students' spatial imagination. Questions 13 and 19 are just right for students' mathematical data processing ability and application consciousness, and questions 14 and 19 are open to some extent. Questions 16 and 20 put forward higher requirements for students' rational thinking ability. Question 2 1 The second question tests the students' reasoning ability well. The first issue of science 18 is entitled: It is known that the bottom of the quadrangular cone P-ABCD is an isosceles trapezoid, AB//CD, AC⊥BD, the vertical foot is H, the PH is the height of the quadrangular cone, and E is the midpoint of AD. (1) proves that PE ⊥ BC; (2) If ∠APB=∠ADB=60 degrees, find the sine value of the angle formed by the straight line PA and the plane PEH. This problem is the second problem in solving problems. The proposer didn't want to embarrass the students, but in fact he really stumped many students. The reason is worth pondering. On the one hand, the requirement of this topic for spatial imagination is a little divorced from the reality of students and textbooks, on the other hand, the over-patterning of usual training is also the reason for students' poor adaptability. The function of question 2 1 is the algebraic sum of an exponential function and a quadratic function with parameters. It is a basic problem to find the value of a given parameter and the monotone interval. The second question is a constant question, and the range of parameters is similar to the second question of derivative questions in 2006 and 2008, which requires high reasoning ability and is difficult to get full marks.

Fourth, reflect the curriculum reform and pay attention to innovation.

The examination of the new contents of the textbook is comprehensive and moderately difficult, which not only reflects the progress of basic knowledge with the times, but also is beneficial to middle school mathematics teaching. Algorithm, three views, sampling method and independence test, geometric probability and definite integral concept are all examined in place. Examination paper 3 small questions 2 big questions to examine the new curriculum content, * * * 37 points. The open questions of 14 and 19 are an innovation, and the new background of 18 and 2 1 is also an innovation. Science problem 14 is about three views. The original title is: the geometry of the front triangle can be (written in three ways) with moderate difficulty and some innovation. The question "Arts and Sciences 19" examines the preliminary application of sampling method and independence test. The original title is: In order to investigate whether the elderly in a certain area need the help of volunteers, 500 elderly people in this area were investigated by simple random sampling method, and the results are as follows:

(1) Estimate the proportion of elderly people in need of volunteer help in this area;

(2) Is 99% sure whether the elderly in this area need the help of volunteers related to gender?

(3) According to the conclusion of (2), can you propose a better survey method to estimate the proportion of elderly people who need volunteer help in this area? Explain why. (chi-square table)

This question is a combination of compulsory three and elective two or three. (1) and (2) questions will be fine as long as they are reviewed systematically, and (3) questions need to be mastered in various sampling methods in textbooks to be answered well. Through this question, the proposer explained to us the requirements of the new curriculum outline of statistics. The three options are plane geometry, parametric equation and absolute value inequality. Plane geometry and absolute inequality are equivalent to the level of usual training questions, which makes it easier for students to get started. It is difficult to find the trajectory of the second question of parametric equation, and it is difficult for students to get full marks. Therefore, reasonable choice is also a test of students' ability.

Throughout this year's college entrance examination teaching questions, closely following the mathematics examination syllabus, we emphasize both foundation and ability, inheritance and innovation, and realize the smooth transition from the old college entrance examination mathematics paper to the new one. It has played a positive guiding role in the teaching of new courses. The disadvantage is that the proposer may not know enough about the textbooks and students studying the new curriculum, which leads to the inconsistency between the requirements of solving the second problem of solid geometry and the reality of the textbooks and students, thus affecting the play of most candidates.

Second, the inspiration for future teaching and review

The enlightenment of 20 10 college entrance examination math problems to future math teaching and review is: pay attention to returning to textbooks, lay a solid foundation, strive to improve students' ability, guide students to master new and old contents in new textbooks, embody process teaching in teaching, select exercises and train effectively. Advocating rational thinking and strengthening the cultivation of inquiry ability is the general trend of mathematics teaching and learning in senior high schools, and respecting students' personality differences, teaching students in accordance with their aptitude and highlighting the pertinence and effectiveness of review are the best ways to succeed.