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Mathematics liberal arts scope of college entrance examination
Liberal arts mathematics

I. Knowledge requirements

Knowledge refers to the mathematical concepts, properties, laws, formulas, axioms, theorems and mathematical thinking methods embodied in the compulsory courses and elective courses series 1 and series 4 stipulated in the Mathematics Curriculum Standard for Ordinary Senior High Schools (hereinafter referred to as the Curriculum Standard), and also includes basic skills such as operation, data processing and drawing charts according to certain procedures and steps.

The general requirements and positioning of each part of knowledge refer to the relevant descriptions of the corresponding modules of the curriculum standards.

The requirements for knowledge are in turn three levels: understanding, understanding and mastering.

1. Understanding: It is required to have a preliminary perceptual understanding of the meaning of the listed knowledge, know what the content of this knowledge is, imitate it according to certain procedures and steps, and be able to (or will) understand and understand the relevant issues.

The main behavioral verbs involved in this level are: understanding, cognition, identification, imitation, cognition and understanding.

2. Understanding: It is required to have a profound and rational understanding of the contents of the listed knowledge, know the logical relationship between the knowledge, be able to correctly describe the listed knowledge and express it in mathematical language, be able to compare, judge and discuss related issues with what you have learned, and have the ability to solve simple problems with what you have learned.

The main behavioral verbs involved in this level are: description, explanation, expression, speculation, imagination, comparison, discrimination and preliminary application.

Wait a minute.

3. Mastery: It is required to be able to deduce and prove the listed knowledge, and use the learned knowledge to analyze, study, discuss and solve problems.

The main action verbs involved in this level are: mastering, deducing, analyzing, deducing, proving, researching, discussing, applying and solving problems.

Second, the ability requirements

Ability refers to spatial imagination ability, abstract generalization ability, reasoning ability, operational solving ability, data processing ability, application consciousness and innovation consciousness.

1. Space imagination: can make correct graphics according to conditions, and imagine intuitive images according to the graphics; Can correctly analyze the basic elements and their relationships in graphics; Can decompose and combine graphics; Will use graphics and charts to vividly reveal the essence of the problem.

Spatial imagination ability is the ability to observe, analyze and abstract spatial form, which is mainly manifested in the ability to recognize, draw and imagine graphics. Drawing refers to converting written language and symbolic language into graphic language, adding auxiliary graphics to graphics or making various transformations to graphics; Graphic imagination mainly includes pictographic and non-pictographic, which is a high-level symbol of spatial imagination.

2. Abstract generalization ability: Abstraction refers to abandoning the non-essential attributes of things and revealing their essential attributes; Generalization refers to the thinking process of distinguishing * * * from attributes. Abstraction and generalization are interrelated. There can be no generalization without abstraction, and generalization must draw some opinions or conclusions on the basis of abstraction.

Abstract generalization ability is to find the essence of the research object by analyzing and refining concrete and vivid cases; Summarize some conclusions from a large number of given information materials and apply them to solve problems or make new judgments.

3. Reasoning and argumentation ability: reasoning is one of the basic forms of thinking, which consists of two parts: premise and conclusion; Argumentation is a series of reasoning processes from the existing correct premise to the conclusion to be demonstrated. Reasoning includes both deductive reasoning and perceptual reasoning. Argumentation methods include deductive induction according to form, direct proof and indirect proof according to thinking method. Generally, reasonable reasoning is used to guess, and then deductive reasoning is used to prove.

Mathematical reasoning ability in middle school is the primary reasoning ability to demonstrate the truth value of a mathematical proposition according to known facts and correct mathematical propositions.

4. Ability of operation and solution: correct operation, deformation and data processing can be carried out according to laws and formulas, reasonable and simple operation paths can be found and designed according to the situation of problems, and data can be estimated and approximately calculated as needed.

Operational solving ability is the combination of thinking ability and operational skills. Operations include calculation, estimation and approximate calculation of numbers, combination and decomposition of formulas, calculation and solution of geometric quantities of geometric figures, etc. Operational ability includes the thinking ability in a series of processes, such as analyzing operating conditions, exploring operating direction, selecting operating formulas and determining operating procedures, and the ability to adjust operations when encountering obstacles in operation implementation.

5. Data processing ability: I can collect, sort out and analyze data, and I can extract useful information from a large number of data and make judgments.

Data processing ability mainly refers to the particularity of the research object, choosing reasonable methods to collect data, choosing appropriate statistical methods to sort out data according to the specific situation of the problem, constructing models to analyze and infer the data and drawing conclusions.

6. Application consciousness: being able to comprehensively apply the learned mathematical knowledge, ideas and methods to solve problems, including solving simple mathematical problems in related disciplines, production and life; Be able to understand the materials stated in the question, summarize, sort out and classify the information provided, and abstract the actual problem into a mathematical problem; Can apply relevant mathematical methods to solve problems and then verify them, and can correctly express and explain them in mathematical language. The main process of application is to extract relevant quantitative relations according to the real life background, transform real problems into mathematical problems, build mathematical models and solve them.

7. Innovative consciousness: be able to find and ask questions, comprehensively and flexibly use the learned mathematical knowledge and thinking methods, choose effective methods and means to analyze information, think, explore and study independently, put forward ideas to solve problems, and solve problems creatively.

Innovative consciousness is the advanced expression of rational thinking. Observing, guessing, abstracting, summarizing and proving mathematical problems is an important way to find and solve problems. The higher the degree of transfer, combination and integration of mathematical knowledge, the stronger the sense of innovation will be.

Third, personality quality requirements.

Personality quality refers to the individual feelings, attitudes and values of candidates. Candidates are required to have a certain mathematical vision, understand the scientific value and humanistic value of mathematics, advocate the rational spirit of mathematics, form prudent thinking habits and appreciate the aesthetic significance of mathematics.

Candidates are required to overcome their nervousness, take the test with a peaceful mind, control the test time reasonably, answer the test questions with a scientific attitude of seeking truth from facts, establish confidence in overcoming difficulties, and embody the spirit of perseverance.

Fourth, the examination requirements

The systematicness and rigor of mathematics discipline determine the profound internal relations between mathematical knowledge, including the vertical and horizontal relations of each part of knowledge. We should be good at grasping these relations in essence, and then construct the framework structure of mathematics examination papers through classification, combing and synthesis.

1. The examination of the basic knowledge of mathematics should be comprehensive and focused. The key contents supporting the subject knowledge system should account for a large proportion and constitute the main body of the mathematics examination paper. We should pay attention to the internal relations of disciplines and the comprehensiveness of knowledge, and don't deliberately pursue the coverage of knowledge. It is necessary to consider the problem from the overall height of the subject and the height of thinking value, and design test questions at the intersection of knowledge networks to make the examination of basic mathematics knowledge reach the necessary depth.

2. The examination of mathematical thinking method is an abstract and generalized examination of mathematical knowledge at a higher level, which must be combined with mathematical knowledge to reflect the examinee's mastery of mathematical thinking method.

3. The examination of mathematical ability emphasizes "thinking with ability", that is, taking mathematical knowledge as the carrier, starting from problems, grasping the overall significance of the subject, organizing materials with a unified mathematical point of view, and paying attention to the understanding and application of knowledge, especially the comprehensive and flexible application, in order to test the ability of candidates to transfer knowledge to different situations, so as to test the breadth and depth of individual rational thinking of candidates and the potential for further study.

The examination of ability should be comprehensive, emphasizing comprehensiveness and application, and should conform to the reality of candidates. The examination of reasoning ability and abstract generalization ability runs through the whole volume, which is the focus of the examination, emphasizing its scientificity, rigor and abstraction; The examination of spatial imagination ability is mainly reflected in the mutual transformation of written language, symbolic language and graphic language; The examination of solving operation ability is mainly the examination of algorithm and reasoning, and the examination is mainly algebraic operation; The investigation of data processing ability is mainly to investigate the ability to solve practical problems by using the basic methods and ideas of probability and statistics.

4. The examination of application consciousness mainly adopts the form of solving application problems. The proposition should adhere to the principle of "close to life, fair background and controllable difficulty". The design of test questions should conform to the reality of middle school mathematics teaching and the age characteristics of candidates, and combine with practical experience to make the difficulty of mathematics application questions conform to the level of candidates.

5. The examination of innovation consciousness is an examination of advanced rational thinking. When creating novel question situations and constructing mathematical questions with certain depth and breadth in the examination, we should pay attention to the diversification of questions and reflect the divergence of thinking; Carefully design test questions, examine the main contents of mathematics, and reflect the quality of mathematics; There should also be questions that reflect the movement changes of numbers and shapes, as well as research, exploration and open questions.

On the basis of examining basic knowledge, mathematics subject proposition pays attention to examining mathematical thinking method and mathematical ability, highlights the scientific value and humanistic value of mathematics, pays attention to the foundation, comprehensiveness and application of test questions, pays attention to the hierarchy among test questions, reasonably regulates the comprehensive degree, insists on multi-angle and multi-level examination, and strives to meet the requirements of comprehensive examination of mathematical comprehensive literacy.

Ⅱ. Inspection scope and requirements

This part includes two parts: the required content and the selected content. The compulsory content is the compulsory content and elective part of the curriculum standard.

1 column; The content of the examination is two topics: coordinate system and parameter equation and inequality lecture in elective series 4 of curriculum standard.

Required test content

(1) assembly

The meaning and representation of a set.

(1) Understand the meaning of set and the relationship between elements and set.

(2) Natural language, graphic language and set language (enumeration or description) can be used to describe different specific problems. 2. The basic relationship between sets.

(1) Understanding the meaning of inclusion and equality between sets can identify subsets of a given set.

(2) Understand the meaning of complete works and empty sets in specific situations.

3. Basic operations of sets

(1) To understand the meaning of union and intersection of two sets, we need union and intersection of two simple sets.

(2) To understand the meaning of the complement of a subset in a given set, we need the complement of a given subset.

(3) venn diagram can be used to express the relations and operations between sets.

(2) Function concept and basic elementary function Ⅰ (exponential function, logarithmic function, power function)

1. function

(1) Knowing the elements that make up a function, we can find the domain and value of some simple functions; Understand the concept of mapping. (2) In actual situations, appropriate methods (such as image method, list method, analysis method, etc.) will be selected according to different needs.

Represents a function.

(3) Understand the simple piecewise function and apply it simply.

(4) Understand the monotonicity, maximum value, minimum value and geometric significance of the function; Combined with specific functions, understand the meaning of function parity.

(5) Understand and study the properties of functions by using function images.

2. Exponential function

(1) Understand the actual background of the exponential function model.

(2) Understand the meaning of rational exponential power, understand the meaning of real exponential power, and master the operation of power.

(3) Understand the concept of exponential function, understand the monotonicity of exponential function, and master the special points that exponential function images pass through.

(4) Know that exponential function is an important function model.