A, 20 10 college entrance examination focus on mathematics:
According to "20 10 Mathematics Examination Outline for College Entrance Examination", we mainly investigate nine chapters, such as function, sequence, trigonometric function, plane vector, inequality, solid geometry, analytic geometry, probability statistics and derivative. As a college entrance examination, focus on the following sections:
(1) function and derivative: This section focuses on monotonicity and maximum of quadratic function, higher-order function, fractional function and composite function. Candidates pay special attention to the monotonicity of fractional function and the solution method of compound function value domain. At the same time, candidates should attach importance to the combination of function and sequence, function and inequality, flexibly master the methods and skills to deal with such comprehensive problems, and grasp typical examples to cope with constant changes.
(2) Plane vector and trigonometric function: This section takes vector as a tool to examine trigonometric function, focusing on three aspects: ① Simplification and evaluation of trigonometric function, examining simplification and evaluation, focusing on five groups of trigonometric formulas, including basic formula of the same angle, induced formula, bi-half formula, sum-difference formula and auxiliary angle formula; ② Images and properties: Here, we focus on the images and properties of sine and cosine functions. To master the properties of sine and cosine functions, we should master them from seven aspects: domain, range, monotonicity, parity, images, periodicity and symmetry, especially the properties of sine and cosine functions are the focus of the college entrance examination, so we should pay special attention to them. (3) Triangle identity deformation. This part focuses on the application of some basic formulas to remind candidates to strengthen their understanding and memory of basic formulas.
(3) Series: This section focuses on the general term and summation of series. This paper focuses on several common methods to find the general term, including formula method and undetermined coefficient method. In summation, we mainly introduce several common summation methods, including formula method, split term addition, dislocation subtraction and so on. The emphasis here is to master what kind of series each method is suitable for. Generally speaking, passing the college entrance examination is the key and difficult point, especially to master the recursive formula between the items. For the summation of series, we should pay special attention to the restrictive conditions of common ratio in the summation formula of equal proportion series, which is an error-prone point in the college entrance examination, so we should pay special attention to it!
(4) Space Vector and Solid Geometry: The new curriculum standard of 20 10 has lowered the requirements for this part. Especially for liberal arts students, the calculation of angle and distance is limited to geometric line angle and point-surface distance, surface area and volume. In the proof, the straight line is parallel to the plane, and the straight line is perpendicular to the plane. For science students, here I suggest that you should master the problem of proof and calculation in solid geometry by using space vectors. In particular, when solving with space vector, we must remember the calculation formulas of angle and distance accurately, then understand the meaning of each letter in the formula and find the conditions according to the formula. For this part of the candidates, in addition to mastering the traditional proof and calculation key points, we should also strengthen the training of flip and moving point problems in solid geometry, so as to calmly deal with the new questions and problems in the college entrance examination.
(5) Probability statistics: In senior high school, three basic models, namely classical probability, geometric probability and random variable, are mainly studied. This part appears in the form of college entrance examination application questions. Here I want to emphasize that the question of probability in the college entrance examination is often not so difficult. Candidates only need to read the questions carefully, understand the meaning of the questions and distinguish the types. For the 20 10 college entrance examination, candidates should pay attention to the study of statistics, especially linear regression and statistical methods, and candidates should accurately understand the basic concepts and simply apply them.
(6) Analytic geometry: In this section, I have summarized five models commonly used in college entrance examination: the first category: the positional relationship between straight lines and curves and the calculation of vectors. This kind of topic is the most common topic in the college entrance examination, and candidates should master its general methods. The second kind: fixed point problem (parameter elimination method), here we should pay attention to the range limit satisfied by fixed points. The third category: chord length problem (formula method), candidates only need to be able to use chord length formula; The fourth category: symmetry problem (replacement method), that is, finding the midpoint to replace; The fifth category: midpoint problem (point difference method). Analytic geometry is often the most computationally intensive topic in the whole test paper. Many students will learn to do but can't calculate. This situation is very common in the college entrance examination. This requires us to insist on calculation every time we do a problem from beginning to end, form good habits for a long time, and our calculation ability will naturally improve. These five types of model candidates should focus on mastering. Although the college entrance examination analysis is difficult, it is more than enough to deal with this big problem as long as you master the basic model skillfully.
(7) Sequence, function and inequality: This section is often the finale, mainly focusing on the proof of inequality, which is often very difficult. Candidates should focus on accumulating some methods to prove inequalities, including scaling, mathematical induction and so on. Although it is difficult, I suggest that candidates take a step-by-step grading and leave no blank. For this part of the review, I suggest that it can be put in the later stage. After May, you can take a proper look at the final exam questions, broaden your thinking, and don't make key requirements for most candidates.
Second, the problems that should be paid attention to in the last four months:
There are still more than four months before the 20 10 college entrance examination, which is the golden time to improve the comprehensive quality of candidates. This period is also called comprehensive review stage. Students need to systematize, organize and modularize some scattered knowledge points in front of them, look for macro clues in the discipline, outline and fully reach the designated position. Below, I will talk about the review suggestions in the last four months based on the previous math review experience of the college entrance examination and the learning experience of excellent candidates.
(a), the full implementation of the "two basics", to ensure easy to use.
At present, the examination of basic knowledge and basic methods accounts for about 80% of the mathematics papers in the college entrance examination. Even innovation questions or ability questions are based on double bases. Only by solidly and meticulously consolidating the double basics can we break through the difficult problems and overcome new problems. What I want to emphasize here is that the teaching materials are excellent, and only by grasping the teaching materials can we get to the point. Not only should we have a deep understanding of the knowledge in the textbook, but more importantly, we should pay attention to the thinking method of solving problems in the textbook, and we should also master the knowledge system in an all-round way so as not to let go. According to the exam instructions, determine the scope of the exam, carefully read and understand the relevant contents in the textbook, including every concept, every example, every note and every figure, accurately understand and remember the knowledge points, leaving no gaps and hidden dangers. In the final review stage, we should start with the textbook catalogue and connect it in series to form a system. At the same time, with proper practice, it is inevitable to encounter difficulties in practice. We must find out the crux of the problem and completely eliminate the obstacles by comparing the teaching materials. Go back to the textbook, read the textbook thoroughly, and never be an expert. For the review of teaching materials, it is suggested that we can focus on the examples in the chapters of probability statistics, sequence, function, derivative and conic curve.
(2) Pay attention to misjudged cases and make up in real time.
Misjudged cases are also wealth. Sometimes they expose our knowledge defects, sometimes our thinking deficiencies, sometimes our improper methods and our shortcomings, so we have the direction of treatment and the opportunity to correct mistakes. Therefore, I suggest that in the late sprint stage, we must establish a wrong question bank, especially those typical mistakes such as poor understanding of concepts, poor knowledge memory, poor thinking and improper use of methods, collect them into a book, comment on them, point out the reasons for the mistakes, and read them often.
(3), seize the typical cases, and strive to achieve mastery through a comprehensive study.
Now the college entrance examination is not far away, and time is tight. Therefore, in the final review stage, candidates should seize precious time and improve their learning efficiency to the maximum in the shortest time, so we can't do a lot of repetitive useless work. Therefore, to learn how to choose a topic, we need to grasp some typical problems, make full use of them and fully explore them. Specifically, it is reflection after solving the problem. Reflect on the meaning of the question, summarize the methods and skills to solve such problems, and at the same time learn the extended changes of typical problems to promote the series of knowledge and the sublimation of methods. So what is a typical example? That's the real question of the college entrance examination, especially the answer in the real question of the college entrance examination in the past three years (the focus is on the first five questions)
(4) Read the exam outline carefully to make sure it is clear at a glance.
Examination description is the basis of college entrance examination proposition. The outline clearly tells us what to take in the college entrance examination, how difficult it is and how to take it. Candidates must be clear about the knowledge requirements of the exam. Compare the teaching materials with the notes in the review one by one to see if they have been implemented, to ensure that there are no omissions, and never stop if they fail to meet the requirements. In particular, we should attach great importance to the contents adjusted in the syllabus. For example, the new curriculum standard of 20 10 has added three views, program and block diagram, polar coordinates, geometric probability, calculus and so on. , and clear requirements, improve the pertinence and effectiveness of the review. In addition, the form, type, test time, score and so on of the test paper should also be clear.
(5) Strengthen perseverance training to achieve perseverance.
The last four months are the most critical time for the college entrance examination sprint. Many candidates are physically and mentally exhausted, depending on who can persist to the end and win. In the final stage, we should also have a clear study plan every day, stick to it and make no excuses. As long as you don't touch any subjects for three days, you will feel that you have a bad start, poor thinking, low efficiency and easy to make mistakes when you get the topic. Don't practice for five days, don't retreat. Therefore, it is suggested that all subjects should be consolidated every day, and difficulties should be solved in time, and they should not be accumulated, otherwise confidence will be undermined and morale will be lost. If you want to succeed in the college entrance examination, you must have enthusiasm and perseverance!