The knowledge points of the new curriculum standard deletion are: fractional inequality (only regarded as the application of quadratic inequality)

(A) Analysis of test sites

1. Inequality Relationship and Inequality: In the college entrance examination, this part mainly focuses on the nature of inequality, and the questions are mostly multiple-choice questions or fill-in-the-blank questions, which are easy questions.

2. One-dimensional quadratic inequality and its solution: in the college entrance examination proposition, if the solution of one-dimensional quadratic inequality appears in the form of multiple-choice questions and fill-in-the-blank questions, it will directly solve the inequality, or it is often combined with set and necessary and sufficient conditions, and it is not difficult. If it appears in the form of a solution, it will generally be related to parameters, or discuss parameters in categories, or find the range of parameters. The difficulty is mainly intermediate questions.

3. Simple linear programming: linear programming problems often appear in the form of multiple-choice questions and fill-in-the-blank questions. The questions are mainly easy questions and intermediate questions, which examine the area of plane area and the optimal solution; With the deepening of curriculum reform, in recent years, in order to test students' ability to solve practical problems, problem-solving questions have appeared from time to time.

4. Basic Inequality: The college entrance examination proposition focuses on the mean inequality and the common methods to prove inequality. The proposition of simple inequality mainly appears in multiple-choice questions or fill-in-the-blank questions, which is generally not too difficult.

5. Comprehensive application of inequality: the comprehensive application of inequality is mostly based on application problems, which belong to problem solving and have certain difficulty.

6. Proof of inequality: The proof of inequality mostly appears in the form of intersection and solution, which is a moderately difficult exam.

(B) the law of proposition

In recent years, there are multiple-choice questions, fill-in-the-blank questions and analytical questions in the college entrance examination, which not only examines the basic knowledge, skills and methods of inequality, but also examines the ability to analyze and solve problems. Solving problems is based on the intersection of function, inequality and derivative of sequence. The problem of combining functions with inequalities is mostly solved by derivatives. The combination of function and inequality is mostly solved by intuitive thinking, recursion and mathematical induction, which has certain flexibility.

From the above analysis, it is expected that the nature of inequality, the solution of inequality and important inequality knowledge will appear in the form of multiple-choice questions or fill-in-the-blank questions; Solving inequality and proving inequality may appear in solving problems. If it is possible to solve inequality with parameters, and if it is proved that the problem will be a comprehensive problem of inequality combined with sequence, function, derivative and vector, then it is worth noting to solve this kind of problem with derivative. Sometimes this is a difficult question.

3) Review recommendations

The proof of 1. inequality is difficult in this chapter, because the types of questions are changeable, the proof ideas are diverse and skillful, and there is no one-size-fits-all procedure to follow. The key to overcome the difficulties is to master the nature and basic inequalities skillfully, and to deeply understand and grasp the mathematical transformation thought in inequality proof.

In review, we should master the common thinking methods of proving inequality: comparison method; Comprehensive method; Analytical methods; Scaling method; Reduction to absurdity; Function method; Alternative methods; Derivative method.

2. In reviewing the process of solving inequalities, we should pay attention to cultivating, strengthening and improving the mathematical thinking methods of functions and equations, equivalent transformation, classified discussion and combination of numbers and shapes, so as to gradually improve our mathematical literacy and improve our ability to analyze and solve comprehensive problems. Based on the characteristics of various inequalities and the particularity of deformation, we can summarize the solutions, ideas and concrete solutions of various inequalities.

3. Master the basic properties of inequality, the solutions of common inequalities (such as quadratic inequality in one variable), the application of inequality in practical problems, and the common methods of inequality proof.

plane analytic geometry

The knowledge points required by the new curriculum standard are: only a general understanding of hyperbola, and the knowledge points deleted by the new curriculum standard are: the second definition.

(A) Analysis of test sites

1. Location relationship of points, lines and circles: This part is generally based on multiple-choice questions or fill-in-the-blank questions, which is not difficult and easy.

2. Equation problems of straight lines and circles: Equation problems of straight lines and circles mostly appear in the form of multiple-choice questions and fill-in-the-blank questions, which are easy questions.

3. Solving the curve (trajectory) equation: Trajectory problems mostly appear as problem solving in the college entrance examination, which is an intermediate problem.

4. Questions about the definition of conic section: Fill-in-the-blank questions and multiple-choice questions are moderately easy questions.

5. Geometric properties of conic section

6. Relationship between straight line and conic curve: The relationship between straight line and conic curve involves mathematical thinking methods such as function and equation, combination of numbers and shapes, classified discussion and reduction, so this part is often used as the finale of the college entrance examination, and the main intention of the proposition is to examine the ability of operation and logic.

(B) the law of proposition

Analytic geometry is an important content of high school mathematics. Judging from the college entrance examination in recent years, there are generally two multiple-choice questions, one to fill in the blanks and one to answer. Multiple-choice questions and fill-in-the-blank questions are mostly intermediate, and the answers are generally low. The content of the test involves the relationship between curve equation, straight line and curve position, and combines the knowledge of function, equation, inequality, plane vector and derivative to comprehensively examine students' ability to solve problems flexibly.

(3) Review recommendations

1. Strengthen the basic knowledge of straight lines and conic curves, and initially master the basic skills and methods to solve problems related to straight lines and conic curves.

2. Because straight lines and conic curves are the key contents of college entrance examination, they are flexible in choosing and filling in the blanks, with strong thinking ability, novel and comprehensive problem-solving background and strong algebraic reasoning ability, so it is necessary to conduct in-depth research on the key contents of straight lines and conic curves and hot issues in college entrance examination.

3. Through vertical deepening and horizontal connection, we can further master the ideas and methods to solve the problems of straight lines and conic curves, and improve the ability to analyze and solve problems. Find the curve (trajectory) equation. In particular, the problem of finding the curve (trajectory) equation and the position relationship between straight line and conic curve is a hot spot.

4. The problem of fixed value, parameter range, maximum and minimum values are also the most important.

solid geometry

The knowledge points added in the new curriculum standard are: three views.

The knowledge points deleted are: three vertical theorems and their inverse theorems;

The knowledge points to reduce the requirements are as follows: only the structural characteristics of columns, cones, platforms, spheres and simple assemblies are required to be understood, and the structural characteristics are summarized through examples, without proof or in-depth exploration of the properties of prisms, regular pyramids and solutions.

(A) Analysis of test sites

1. Structure, three views and intuition of space geometry: the structural features of cylinders, cones, platforms, spheres and their simple combinations have appeared in old textbooks, but three views are new. Generally, we will focus on new content, and the three views are hot topics. Most of the questions are multiple-choice questions and fill-in-the-blank questions, and some of them appear in the answers, such as the 2007 Guangdong college entrance examination.

2. Surface area and volume of space geometry: The surface area and volume of cylinders, cones, platforms and spheres are mainly based on formulas. According to the requirements of the new curriculum standard, the volume formula does not need to be memorized, just master the calculation method of surface area and volume. Therefore, the topic belongs to the intermediate easy topic in difficulty.

3. The positional relationship between points, lines and surfaces: It mainly examines the basic properties of planes and the positional relationship between two straight lines in space, and mostly focuses on multiple-choice questions and fill-in-the-blank questions, which are not difficult.

4. The judgment and nature of line and plane, plane and plane parallelism: mainly examine the judgment and nature of line and plane parallelism, mostly in the form of multiple-choice questions and solutions, mainly proving that line and plane parallelism are intermediate questions. The judgment and nature of line and plane, plane and plane perpendicular: This paper mainly examines the judgment and nature of line and plane perpendicular, mostly in the form of multiple-choice questions and solutions, and mainly proves that line and plane perpendicular, plane and plane perpendicular, belong to intermediate problems.

(B) the law of proposition

The propositional form involving the content of solid geometry changes the most.

In addition to retaining the traditional "four-choice one" multiple-choice questions, we also tried to develop questions such as "multiple-choice fill in the blank", "cloze" and "structural fill in the blank". 20 10 college entrance examination solid geometry questions generally have 1-2 multiple-choice questions or fill-in-the-blank questions, 1 big questions, and the difficulty is mostly medium to low. Small questions focus on the understanding of basic knowledge and basic theorems, especially the judgment and nature of three parallel (or vertical) relationships: line, line and surface, and surface and surface. Usually there is a small topic that will intersect with propositions, necessary and sufficient conditions and other knowledge points, and another small topic is the recognition of three views and the calculation of surface area and volume. For big questions, simple geometry is often used as the carrier, and it appears in the form of 2-3 small questions, with lower slope and scattered difficulty. This paper mainly examines the positional relationship between points, straight lines and planes, as well as the calculation of surface area and volume of related distances or angles and space geometry. At the same time, it involves exploring problems, expanding three-dimensional graphics and folding plane graphics, setting values and maximum values. The liberal arts mainly examines the direct method, while the science pays equal attention to the direct method and the vector method, but tends to apply the vector method to solve it.

As a new content in the curriculum standard, the concept of "Three Views" requires higher spatial imagination and is a hot spot in the college entrance examination. Making three views of geometry and drawing or imagining geometry from three views are two kinds of problems in three views.

"Dynamic" Li Ji is a fresh blood injected into the solid geometry of the college entrance examination in recent years, and new tricks are often found in the exam. One of its characteristics is to implement basic knowledge and basic thinking methods, and the other is to pay attention to the organic combination of several kinds of knowledge and other knowledge (such as analytic geometry, functions, inequalities, derivatives, trigonometric functions, etc.). With the new curriculum reform, the topic of "dynamic" solid geometry should be appropriately added to the college entrance examination proposition in the future.