1. It has a wide range of knowledge and focuses on the backbone.
Except probability statistics, the test questions cover all the knowledge modules in the textbook, and the coverage rate of knowledge items is about 50%. In addition to the main knowledge, it also covers complex number, set, three views, program block diagram, logic and reasoning, permutation and combination, linear programming, plane vector and so on. It also pays attention to the reality and history and culture of mathematics, such as questions 7 and 9 of science 14 and 18, and questions 5 and 19 of liberal arts.
The main contents of functions and derivatives, triangles, series, solid geometry, analytic geometry, inequalities and other disciplines occupy a high proportion in the test paper, and the overall structure is reasonable, reaching the necessary depth of investigation.
The examination paper also pays attention to the examination of knowledge intersection, such as the fifth question of science, 14, and the seventh question of liberal arts, 1 1, 19.
2. Pay attention to the way of thinking and highlight the ability and accomplishment.
Seven basic mathematical ideas are all involved in the examination paper. There are coordinate method, trigonometry method, vector method, undetermined coefficient method, method of substitution method, elimination method, collocation method and method of substitution method.
The six core qualities of mathematics: the ability to solve problems is reflected in most topics, and logical reasoning is also clearly reflected. Intuitive imagination is embodied in the combination of numbers and shapes. Mathematical modeling and data analysis are the processes of abstracting practical problems, expressing and solving them with mathematical language. At the same time, it is natural to examine the ability of reading comprehension and knowledge transfer, and also pay attention to the application of mathematics.
3. Close to the improvement of teaching materials and increase the difficulty of thinking.
The knowledge composition and question composition of the test paper are strictly in accordance with the outline system, and nearly 80% of the questions reflect the basic knowledge, skills and methods of the textbook. Most of the topics are directly derived from the basic concepts, methods, and operations of the textbooks, or are simply deformed, with a low starting point and a large slope. Most of them only involve two or three knowledge items, and only take two or three steps of calculus, which is in line with the reality of most students. Although the last two or three questions increase the amount of thinking and calculation, it is still a bit difficult in the middle. Science 10, 1 1 2, liberal arts 8,112, multiple-choice thinking. Fill in the blanks are science questions 15 and 16, and liberal arts questions 15 and 16. Science problem solving 18(2), 20, 2 1, liberal arts 19(2), 20, 2 1.
4. Reflect the target level, and the differences between arts and sciences complement each other.
Each question type is easy to match, from easy to difficult.
Except for four small questions (question 3 of arts and sciences, question 6 of arts and sciences, question 10 of arts and sciences, question 13 of arts and sciences, question 4 of arts and sciences, and question 22 of multiple-choice questions), everything else is different. The main ways to realize the difference are to replace the contents that are not tested in liberal arts (such as arrangement and combination), reduce the difficulty of the topic (sister topic) and change the position before and after. For the exponential function of science, liberal arts should take more tests.
5. Pay attention to mathematical culture and present innovative elements.
The new syllabus highlights the content of mathematical culture, and science papers have made some efforts and attempts to examine mathematical culture. Through the innovative design of materials, candidates can deeply understand the characteristics of focusing on algorithms in the excellent traditional culture of the Chinese nation and inject new vitality into the examination paper.
In China's ancient problem-solving methods, there appeared a big derivative problem in the test questions. The problem of Dayan stems from the problem of "uncountable things" in Sun Tzu's calculation: "There are things today, but I don't know their number. Three or three numbers leave two, five or five numbers leave three, and seven or seven numbers leave two. What is the geometry of things? " This belongs to the problem of solving linear congruence equations in modern number theory In Nine Chapters (written in 1247), Qin, a mathematician in the Song Dynasty, made a systematic exposition of the solution to this kind of problem, and called it "the skill of seeking a skill through great development". German mathematician C.F. Gauss established the congruence theory in 180 1 year, and the great achievements of ancient mathematics in China were reflected by the great derivation. Among the working people in ancient China, mathematical games such as "partition calculation", "cutting pipes" and "Qin Wang secretly ordered soldiers" have been circulating for a long time. There is a song "The Art of War", which even crossed the ocean and was introduced to Japan:
"Three people walk seventy times, five trees and twenty-one sticks.
The seven sons were reunited for half a month, and they didn't know until 105. "
These interesting math games introduced the solutions to the world-famous "grandson problem" in various forms, and popularly reflected an outstanding achievement of ancient mathematics in China. Sun Tzu's problem is a congruence problem in modern number theory, which first appeared in Sun Tzu's mathematical classics in the fourth century A.D.. The title of Sun Tzu's Mathematical Classics, Unknown Things, says: If there are unknown things, three counts as more than two, five counts as more than three, and seven counts as more than two. What is the total number of things? Obviously, this is equivalent to finding the positive integer solutions of the indefinite equations N=3x+2, N=5y+3 and N=7z+2, or using modern number theory symbols, it is equivalent to solving the following linear congruence groups: n 2 (mod 3) 3 (mod 5) 2 (mod 7) ② The answer given in Sun Tzu's calculation is N=23. Because Sun Tzu's question data is relatively simple, this answer can also be obtained through trial calculation. But Sun Tzu's calculations failed to do this. The skill of "not knowing the number of things" points out the method of solving problems: take 70 from three or three and multiply it with the remainder 2; Among five or five numbers, take the number twenty-one and multiply it by the remainder three; For the number 77, multiply the remainder 2 by 15. Add up the products and subtract the multiple of 105. The column formula is:
n = 70×2+2 1×3+ 15×2-2× 105 .
Where 105 is the least common multiple of module 3, module 5 and module 7. It is easy to see that Sun Tzu has given the smallest positive integer that meets the conditions. For the general remainder, Sun Tzu's Art of War points out that it is only necessary to replace the remainder 2, 3 and 2 in the above algorithm with new ones respectively. R 1, R2, R3 are used to represent these remainders, and Sun Tzu's calculation is equivalent to giving a formula.
N = 70× r1+2/kloc-0 /× R2+15× R3-p×105 (p is an integer).
By setting comprehensive, open and exploratory test questions, the test paper has the characteristics of situational innovation, diverse situations and flexible thinking, which not only examines students' basic knowledge and skills, but also examines students' basic ideas and basic experience activities, and examines students' innovative ability.
Second, suggestions for accurate preparation and efficient review in the next stage.
First: further lay a solid foundation.
To achieve 100% mastery, clear understanding, accurate application and mastery.
Second: Pay more attention to general methods.
Regression is simple, special skills are diluted, and the basic methods and skills of applying concepts, properties and theorems to solve problems are mastered, that is, the basic thinking methods of applying mathematical ideas to analyze problems, understand problems, grasp problems and explore solutions.
Third, the most important thing is to form the core literacy of mathematics.
Guided by the cultivation of basic ability and comprehensive ability, we will guide the implementation of the three basics, enhance our ability in deepening our understanding and application of knowledge, and form vegetarian buckwheat.
Fourth, re-emphasize the return to teaching materials.
Familiar with the examples and related conclusions in the textbook. Although some conclusions can't be used as theorem formulas, they can inspire ideas and simplify the thinking process.
Fifth, it comes from the "independence" of solving problems.
In the face of examination questions, candidates need to analyze their own problems, judge themselves, choose their own methods, and make breakthroughs when encountering difficulties. This requires students to have the ability of independent thinking, the ability to distinguish between simple and simple problem-solving methods, the ability of logical expression, and the ability to judge the reasonable and correct answers to conclusions. These abilities need to be studied and trained in the usual problem-solving process, and have their own understanding and experience under the guidance of teachers, so as to truly prepare for the exam accurately and review efficiently.
Senior three mathematics examination paper analysis 2 multiple choice questions
The multiple-choice questions in the second-mode exam in Xicheng District are arranged as follows: 1, set, 2, vector, 3, function value domain, 4, parabola, 5, inequality and logic term, 6, linear programming, 7, three views, 8, and the range of function parameters. Many students should have done the fifth question before. These topics are basically simple adaptations of previous high-frequency problems. Question 8 requires students to master the problem-solving skills of special functions, inequalities and scope problems in an all-round way. Of course, for students, first of all, we should do a good job in basic questions. If there are problems in it, for example, the fourth question is not familiar with the relationship between the focal length and parameters of parabola, and the seventh question has problems in three-view restoration, which needs to be strengthened.
fill-in-the-blank question
The contents of the fill-in-the-blank exam are arranged as follows: 9. Complex number, 10, program block diagram, 1 1, triangle solution, 12, straight line and circle, 13, piecewise function, 14, counting principle.
Question 9 examines the concept of "* * * yoke" to help students further check the completeness of knowledge mastery. 12 involves the concept of "symmetry", and students need to master the algebraic transformation corresponding to this condition. 13 piecewise function, we must be familiar with the analysis method of combining numbers and shapes, and pay attention to the possibility of multiple solutions to fill-in-the-blank questions. The question 14 is a big topic. On the one hand, students' reading ability and key data extraction ability are examined. On the other hand, students are required to have clear logical thinking, and when necessary, they can draw pictures to assist analysis. In addition, students need to have good psychological quality and enough confidence to deal with problems. In fact, the topic is not difficult.
answer the question
In terms of big questions, 15 questions examine a tangent function, and the frequency of triangular modules in college entrance examination is low. Students should pay attention to the "acute angle" condition and the standardized solution process. The statistical probability of question 16, the theme of which is "restaurant satisfaction survey", contains a histogram and a frequency distribution table. This chart is a model that students usually train more, and it is easier to understand and ask questions, so most students can do it well. 17 is the simplest model. A arithmetic progression and a geometric progression form a new series, so we just need to pay attention to the examination of the questions. For the second question, the condition in the first question does not hold. 18 solid geometry, including the proof of vertical parallelism, is a very classic structure. Candidates should pay attention to writing norms in the process of solving problems, speed up analysis and save time for solving problems.
Finally, let's talk about the derivatives and cones that often do the finale questions. The second derivative of Xicheng this year is 19, and the cone is the last question. From the examination method, the derivative model of 19 is more complicated, with scores and logarithms. The proof of the second question is "the minimum value is greater than the maximum value", which is somewhat novel compared with the past, and it is also a considerable challenge for students. Many students usually have less practice from thought to process. After the second mode, for students who have mastered the basic knowledge to a certain extent, it is necessary to focus on strengthening the proof questions.
Question 20, the three questions are the standard equation, the maximum area and the judgment of the relationship between line segments. This question is a classic conic construction, and the analysis difficulty is generally lower than the previous derivative question, but the requirements for candidates' mathematical expression ability and calculation ability will be higher. In the final stage, students need to consolidate their computing ability again and keep their sense of touch, so as to cope with the problem of large amount of computation that may occur in the college entrance examination.
Generally speaking, the title of the second model of Xicheng is "stability", which well tests the students' basic skills and ability to deal with popular investigation routines. For students with higher level, the final selection of big questions can play a certain training effect. At the same time, pay attention to strengthen the practice of later proof questions, strengthen the practice of the details of the answering process, summarize the reasons for losing points in time, refine the "final summary written to yourself before the exam", pay attention to reasonable arrangement of time, find the point with the largest "increment" of scores, strengthen and pay attention to the monitoring of the time allocation for solving problems, so as to think about the coping strategies when encountering problems. I hope that candidates can grasp the last point that can be strengthened in the last month's college entrance examination sprint, make a breakthrough, adjust their state and achieve ideal results in the college entrance examination.