Based on the foundation, pay attention to skill examination. Basic knowledge, basic skills, basic thinking methods and basic activity experience are well grasped in the proposition design. The science 18 question examines the proof and writing of the inverse theorem of the three vertical theorems, which is an important part of the core knowledge. The most basic method in solid geometry is used to solve the problem. Candidates can use vector method or geometric method to prove it, which has been proved in the textbook (chapter 1 of compulsory 2). Compared with the proof of cosine theorem last year, the proposer obviously lowered the threshold and improved the scoring rate of the test questions. This design is commendable.
Moderate and comprehensive, difficult to control. The examination of cosine theorem in triangle, organically combined with mean inequality to find the maximum value, is moderately difficult and well designed. 14 fill-in-the-blank problem combines the derivative and tangent of piecewise function and its curve with linear programming, which has more knowledge without showing its complexity and combines the characteristics of examination ability.
Mathematics experiment, showing the highlights of the test questions. This year's math problem 10 is to estimate the approximate value of pi by using the simulation experiment method of random numbers. Candidates are not required to design programs, but still focus on reading block diagrams and examining mathematical knowledge such as block diagrams and geometric probabilities. The design of the test questions is novel, which highlights the experimental characteristics of mathematics.
Increase thinking and reduce the length of operation. 17 series problem comprehensively investigates the related knowledge of geometric series and arithmetic progression. The amount of thinking is not reduced, and the amount of calculation is not large. Moreover, the two questions are not necessarily related, so we can think independently, which undoubtedly improves the scoring rate; The probability scenario of question 20 is very complicated. The key to solve the gas problem is to apply the simple case background of queuing theory system in operational research, read the problem and think about classification, with little calculation.
Pay attention to reality and show the charm of mathematics. Mathematics is a tool, and the universality of application is a major feature of mathematics. Practical application problems are better reflected in this year's test paper. The eighth question of science examines the calculation of the total number of times of the best-of-five system in table tennis matches, which is close to life and easy to use, but difficult to classify and calculated step by step; 13 the calculation of the water surface width of parabolic arch bridge comes from the original scene of the textbook, which highlights the life atmosphere; What's more worth mentioning is the waiting time problem in the process of handling the banking service window business of 20 questions in science. This problem has a strong atmosphere of real life and plays a good demonstration role in the examination of mathematical analysis and problem-solving ability.
Avoid hot spots and keep the focus of the examination. This year's science test questions avoided many hot issues in mathematics, such as three views, the positional relationship of conic curves, histograms, and the properties of trigonometric functions. However, the investigation of the nature of the function has not weakened. The second question of science examines monotonicity and parity, and the question 16 examines the image, period and evaluation of trigonometric functions. Question 20 highlights the calculation of probability, the distribution list of random variables and expectations-this is the core content of probability statistics. 2 1 question examines the monotonicity, zero point, constant establishment, inequality proof and other main knowledge of functions.
Arts and sciences are different, taking into account the requirements of the discipline. There are 8 ways to fill in the blanks and 2 ways to solve problems in different questions of arts and sciences. The sequence problem of 16 problem and the function problem of 2 1 problem belong to sister problems and are well designed. The probability problem of liberal arts topic 19 is the same as last year. It is difficult to estimate the block diagram of the fifth question of liberal arts, so it is more appropriate to adjust the similarity in the future. Liberal arts basically maintains the style of last year's proposition, but reducing the difficulty is more conducive to daily teaching and students' level.
Lowering the threshold is conducive to candidates' play. The fifth question of science, directly give the figure, establish the spatial coordinate system, examine the cosine value of the line angle, which is uncharacteristic-the practice of asking candidates to establish the spatial coordinate system; The sixth question gives the stem-leaf diagram of the actual problem and examines the size of the average and median. The situation is simple, you can know the answer by mental arithmetic, without specific operation, and it has characteristics; 19 Question examines how to use the undetermined coefficient method to solve elliptic equations. Although the second question is to examine the positional relationship between a straight line and an ellipse and give it a vector form to guide candidates, it is simple to operate and is a good question in analytic geometry. Especially the last question of 2 1 has obvious geometric significance, which provides a clear direction for candidates to explore conclusions and plays a navigation role in solving algebraic means.
The overall impression of this year's test questions is mediocre, but it is not easy to show the comprehensiveness and charm of the test questions in the middle. Unlike some simulation questions, guide candidates to play their level in a peaceful atmosphere. It should be said that this year's math exam has brought candidates a sense of intimacy and pleasure that is rare over the years. It is expected that the average branch of mathematics will be more than that of Big bounce in previous years. The improvement of the average score is helpful to give full play to the weight of mathematics in the total score of the college entrance examination, but the reduction of the difficulty of the examination questions will not be conducive to the distinction of some top students in mathematics. It is reasonable to believe that Shaanxi's mathematics college entrance examination proposition will be further explored in grasping the difficulty, paying attention to the degree of discrimination, highlighting the essence of mathematics, connecting with the reality of life, and attaching importance to the ability examination, which will surely play a good evaluation effect and be widely recognized by all walks of life.