I. Overall analysis
Compared with previous years, the examination paper structure of Beijing 20 16 spring exam has changed greatly. However, the content and difficulty of the test paper are basically the same as those of the previous exams. The examination paper covers a wide range of knowledge, focusing on the main knowledge of high school mathematics. The examination paper attaches importance to the examination of basic knowledge, basic skills and basic methods. Most of the questions come from textbooks, and students are familiar with them. The examination paper highlights the examination of mathematical core concepts, thinking ability and mathematical thinking methods.
This paper continues and strengthens the kindness, liveliness and keeping up with the times of the 20 15 spring examination and 20 15 college entrance examination, and strengthens the curriculum reform and examination reform, which has important guiding significance for senior high school mathematics teaching and preparing for the 20 16 college entrance examination. We must attach great importance to it!
Second, the structural analysis
1. Problem structure
Compared with previous years, the design of Beijing 20 16 spring exam mathematics papers has changed greatly, and the number of multiple-choice questions has increased from 20 to 25. There are four fill-in-the-blank questions, but they are scattered to the first questions of 26, 28, 29 and 30. The number of solutions changed from four to five. Only one of the 27 problems is the structure of the whole solution. Fill in the blanks of the other four questions and solve the puzzle.
The multiple-choice part of Beijing 20 16 spring test paper emphasizes the comprehensive examination of basic knowledge, basic skills and basic thinking methods. The examination paper covers almost all the contents of the compulsory module of senior high school mathematics. It is easy for students to start by examining the general methods. The examination paper focuses on students' understanding and mastery of concepts, theorems, formulas and rules.
Multiple choice questions are the same as 20 15, and focus on the main knowledge at the same time. The multiple-choice question * * * has eight questions based on different functions. The analytic formula, definition range, range, monotonicity, parity, periodicity and image of the function are investigated respectively, which almost comprehensively examines the students' mastery of the main knowledge of middle school mathematics and improves the reliability of the whole set of test papers.
Fill in the blanks in Mathematics Volume 26 of Beijing 20 16 Spring Exam. The first question is the basic relation of trigonometric function with the same angle, which examines students' understanding level and operation ability of trigonometric function definition and transformation. The first question of 28 questions examines the quantitative analysis of the relationship between the position of a straight line and a circle, and examines the students' understanding and operation ability of the combination of shape and number. Question 29 examines students' understanding and application of the recursive formula of arbitrary series. Examine the function consciousness of students' sequence. The first question of 30 questions examines students' understanding and expression of the concept of function zero. The above four fill-in-the-blank questions are all easy questions. The function of this kind of fill-in-the-blank questions is no longer that the fill-in-the-blank questions in all previous exams are responsible for the difficulty and discrimination of the whole test paper. It is the performance of the test reform in solving problems! In essence, Beijing 20 16 spring examination mathematics test paper has cancelled the fill-in-the-blank question. This is a brave attempt by the Beijing 20 16 spring examination mathematics examination paper proposition Committee to pay attention to practical results and break the model!
Problem solving is the main carrier to test students' comprehensive application of knowledge to analyze and solve problems. Compared with previous exams, the problem-solving content of Beijing 20 16 spring test paper is both continuous and changeable. The five questions examine the main knowledge of trigonometric function, solid geometry, straight line and circle, sequence and function synthesis respectively. Compared with the 20 15 spring examination paper, the positions of solid geometry and trigonometric function solutions are interchanged. The content of trigonometric function solution is diluted, and the simplification and operation of trigonometric function are emphasized. The geometry of solid geometry has also changed, focusing on the calculation of volume, diluting the investigation of parallel and vertical relations. Analytic geometry or investigating the positional relationship between a straight line and a circle. The third question is added to the series. In the answer part, three function synthesis questions are added. Continuity is conducive to guiding high school mathematics teaching to pay attention to the main knowledge. Changing the teaching mode is helpful to break the teaching mode, cultivate students' independent thinking ability and play a good guiding role in teaching.
Compared with previous exams, the answer questions of Beijing 20 16 spring exam have changed unprecedentedly, which not only fully reflects the effectiveness of considering the actual value and function of multiple-choice questions and fill-in-the-blank questions in the exam, but also dilutes the examination of intermediate comprehensive questions, lowers the threshold of medium grades and increases the difficulty of high or full marks! This exam is a passing exam, not an optional exam, which is consistent with the function!
2. Knowledge structure
Knowledge structure analysis of Beijing 20 16 spring exam mathematics paper
Problem group
function
trigonometric function
solid geometry
Analytic geometry
Ordered sequence
other
full marks
29
17
1 1
17
eight
18
As can be seen from the above table, the knowledge structure of the test questions in Beijing 20 16 spring test paper is basically consistent with the requirements of curriculum standards and test notes. This paper focuses on the functions, trigonometric functions, analytic geometry, solid geometry, sequence and other parts that run through the senior high school mathematics curriculum, and maintains a high proportion of test paper scores. Among them, the examination of functions is particularly prominent, involving 9 test questions. The score is 29. This conforms to the position of function as a model to describe the laws of daily life, and also conforms to the position of other disciplines, which is closely related to equations, inequalities, series and so on. And it is a main line running through high school mathematics. The test paper also examines knowledge such as set, algorithm, linear programming and statistics. It not only focuses on the main knowledge and core knowledge, but also realizes the overall coverage of knowledge.
3. Capability structure
Analysis on the Ability Structure of Mathematics Test Paper in Beijing 20 16 Spring Examination.
Problem group
Operational solution
Analyze and solve
Spatial imagination
Reasoning argument
Abstract generalization
data processing
full marks
48
22
1 1
10
six
three
As can be seen from the above table, Beijing 20 16 spring exam math questions highlight the examination of the ability to calculate and analyze problems. The scores in the test paper are 48 and 22 respectively, indicating that the test questions pay attention to the examination of the essential ability of mathematics.
4. Analysis of basic test questions and development test questions
Problem group
Basic test questions
Development test problem
Title number
1 ~ 10 and 19, 12 ~ 22 and 26 ~ 28.
1 1、23、24、25、29、30
score
Seventy-eight
22
As can be seen from the above table, the proportion of basic questions and development questions is appropriate, which is in line with the functional orientation of HKCEE. The basic questions focus on students' double basics, while the development questions focus on students' ability to use knowledge flexibly and their potential to continue learning. The number of developmental questions in HKCEE mathematics test paper in the spring of Beijing 20 16 increased, but the score decreased. Is this to ensure the functional orientation of HKCEE, and also to give consideration to the top students of key universities according to HKCEE's achievements? It is worth pondering!
Second, analyze the change of topic
1. Closure of fill-in-the-blank questions and answers
Fill-in-the-blank problem is embedded in solution problem, which is a pioneering work in form! Considering from the value, it is the careful design of the title form. It is to save time by omitting the steps with low thinking content in the solution process, and concentrate on thinking and expressing the follow-up answers! It is an idea put forward by the proposition Committee, which fully understands the reality of students and is inspired by the proposition form of Beijing college entrance examination in recent years.
Compared with previous years, the last two questions increase the examination of inquiry ability, which is the need to find top students through examinations. The score of each answer is only 5 points, which is 2 points lower than previous exams. This is to make the basic part get enough scores and fully reflect the value of the exam!
2. The number of applied questions has increased, and the number of patriotic education topics has increased.
The above two increases are the new trend of HKCEE, which is an important inspiration for preparing for the 20 16 college entrance examination, and it is worth our reflection!
Third, the preparation suggestions
1. Suggestions for Senior Three
In the solid geometry module, science candidates turn to solving the calculation and exploration problems of solid geometry with space vectors, and adhere to the principle of simplifying point coordinates, methods and paths and finding normal vectors skillfully. The practice of turning solid geometry for liberal arts students is more comprehensive and more difficult than the examination questions. It is necessary to comprehensively, systematically and emphatically master all the theorems for verifying the spatial parallel and vertical relations. Liberal arts candidates should ensure that the big questions of solid geometry can get full marks quickly and accurately! In the usual practice, students should have great patience to improve the whole process of answering this question, and teachers should also have great patience and a high sense of responsibility to check the details of the students' answering process, whether it is the best, simplest and most skilled.
In analytic geometry module, liberal arts candidates should strengthen the training of linear and elliptical comprehensive questions. Adhere to the principle of strategic optimization and simplification of derivation process, operation and expression of algebraic geometry problems. Solving analytic geometry problems requires not only challenging spirit and tenacious willpower, but also a calm and sophisticated attitude!
In derivative module, to keep an optimistic and open mind, we must step out of the traditional derivative problem-solving thinking and gradually realize the change of thinking! That is to eliminate the change from thinking to displaying thinking! Teachers should take the initiative to guide, but also select typical topics, and must focus on the derivatives in the Beijing college entrance examination papers after 20 13!
The majority of teachers and students should devote themselves to studying the developmental test questions in the Beijing college entrance examination papers and papers after 20 13, and realize that proposition experts embody the intention of educational fairness through examination reform! And advocate independent thinking, establish a sense of origin, and actively respond to the new trend of "trying to break the pattern and dilute the review effect" in the college entrance examination!
2. Advice for Senior Two
Unswervingly aim at obtaining the highest level of HKCEE and lay a solid foundation. The concept should be clear, the method should be skilled, and the expression should be standardized! Don't do a lot of extra-curricular problems, but dare to spend time and energy to study the ins and outs of knowledge! For the modules that will not be tested in the hot-spot exam of the college entrance examination, such as derivatives, conic curves and space vector questions, we must master the most basic level, and do not blindly expand and extend, leaving "potential energy space" for the sprint stage of the college entrance examination.
After 20 13, teachers and students should devote themselves to studying the developmental test questions in Beijing test papers and realize that proposition experts embody the intention of educational fairness through test questions reform! In order to promote independent thinking and establish original consciousness, on the one hand, we should actively respond to the new trend of "trying to break the pattern and dilute the review effect" in the college entrance examination! On the other hand, strive for excellent results in HKCEE!