I. Nature of the examination

The national unified entrance examination for colleges and universities is a selective examination for qualified high school graduates and candidates with equivalent academic qualifications. Colleges and universities choose the best candidates according to their scores and established enrollment plans. Therefore, the college entrance examination should have high sex, validity, necessary discrimination and appropriate difficulty.

Two. Examination requirements

According to the requirements of ordinary colleges and universities for freshmen's cultural quality, and the teaching contents of compulsory courses and optional courses II in the Curriculum Plan of Full-time Ordinary Senior High School and the Mathematics Teaching Outline of Full-time Ordinary Senior High School promulgated by the Ministry of Education in 2002, the mathematics subject part in the National Unified Examination Outline for Enrollment of Ordinary Colleges and Universities (Science) in 20 12 is taken as the propositional scope of the mathematics subject examination of the college entrance examination for science, engineering, agriculture and medicine.

In the mathematics examination, according to the principle of "while examining the basic knowledge, we should pay attention to the ability", establish the guiding ideology of the ability-based proposition, integrate the examination of knowledge, ability and quality, and comprehensively test the mathematics literacy of candidates.

Mathematics examination should play the role of mathematics as a basic subject, which not only examines the knowledge and methods of mathematics in middle school, but also examines the ability of candidates to continue their studies in colleges and universities.

First, the knowledge requirements, ability requirements and personality quality requirements of the examination content

1, knowledge requirements

Knowledge refers to the mathematical concepts, properties, laws, formulas, axioms, theorems and mathematical ideas and methods in the teaching content stipulated in the mathematics syllabus of full-time senior middle schools.

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

(1) Understanding: It is required to have a preliminary perceptual understanding of the meaning and related background of the listed knowledge, and know what this knowledge content is, which can (or will) be identified in related issues.

(2) Comprehension and mastery: It requires a profound and rational understanding of the listed knowledge, the ability to explain, give examples or make inferences, and the use of knowledge to solve related problems.

(3) Flexible and comprehensive application: It requires a systematic grasp of the internal relationship of knowledge, and can use esoteric knowledge to analyze and solve more complex or comprehensive problems.

2, ability requirements

Ability refers to thinking ability, calculating ability, spatial imagination ability, practical ability and innovative consciousness.

(1) Thinking ability: observing, comparing, analyzing, synthesizing, abstracting and summarizing problems or data; Able to use analogy, induction and deduction for reasoning; Can be expressed logically and accurately.

Mathematics is the science of thinking, and thinking ability is the core of mathematical ability. Mathematical thinking ability is based on mathematical knowledge, through spatial imagination, intuitive guessing, inductive abstraction, symbolic representation, operational solution, deductive proof and pattern construction. Think and judge the spatial form, quantitative relationship and mathematical model in objective things, form and develop rational thinking and form the subject of mathematical ability.

(2) Calculation ability: it can perform correct operation, deformation and data processing according to laws and formulas; According to the conditions and objectives of the problem, find and design a reasonable and simple operation mode; Can estimate and approximate data as needed.

Computing ability is the combination of thinking ability and computing ability. Operations include numerical calculation, estimation and approximate calculation, combined deformation and decomposition deformation of formulas, calculation and solution of geometric quantities of geometric figures, etc. Computational ability includes thinking ability in a series of processes, such as analyzing operational conditions, exploring operational direction, selecting operational formulas, and determining operational procedures. It also includes the ability to adjust the operation when encountering obstacles in the execution of the operation, and the skills to realize the operation and calculation.

(3) Space imagination: being able to 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, combine and transform 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. Reading pictures refers to observing and studying the relationship between geometric elements in a given picture; Drawing refers to the transformation of text language into graphic language, and the addition or various transformations of auxiliary graphics to graphics; The imagination of graphics mainly includes two kinds: there are pictures and there are no pictures, which is a high-level symbol of spatial imagination.

(4) Practical ability: 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, abstract the actual problem into a mathematical problem and establish a mathematical model; Can apply relevant mathematical methods to solve problems and verify them, and can correctly express and explain them in mathematical language.

Practical ability is the ability to mathematize objective things. The main process is to refine the relevant quantitative relationship according to the real life background, build a mathematical model, and transform the real problem into a mathematical problem and solve it.

(5) Innovative consciousness: for novel information, situations and problems, choose effective methods and means to analyze information, comprehensively and flexibly use the learned mathematical knowledge, ideas and methods, conduct independent thinking, exploration and research, put forward ideas to solve problems, and creatively solve problems.

Innovative consciousness is the advanced expression of rational thinking. Observing, guessing, abstracting, generalizing 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.

3, personality quality requirements

Personality quality refers to students' individual emotions, attitudes and values. Candidates are required to have a certain mathematical vision, understand the scientific and humanistic value of mathematics, advocate the rational spirit of mathematics, form the habit of prudent thinking, 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.

Second, the examination requirements

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

(1) The examination of the basic knowledge of mathematics should be comprehensive and focused, and the key contents supporting the subject knowledge system should occupy a large proportion, which constitutes the main body of the mathematics examination paper. Pay attention to the internal relations of disciplines and the comprehensiveness of knowledge, and do not deliberately pursue the coverage of knowledge. Considering the problem from the overall height of the subject and the height of thinking value, the test questions are designed at the intersection of knowledge networks, so that the examination of basic mathematics knowledge can 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 understanding of mathematical thinking method; Starting from the overall significance and ideological value of this topic, we should pay attention to general methods and downplay special skills, and effectively examine the examinee's mastery of mathematical ideas and methods contained in middle school mathematics knowledge.

(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 candidates' ability to transfer knowledge to different situations, so as to test the breadth and depth of candidates' individual rational thinking and the potential for further study.

The examination of ability takes thinking ability as the core, comprehensively examines various abilities, emphasizes comprehensiveness and application, and conforms to the reality of candidates. The examination of thinking ability runs through the whole volume, focusing on the examination of rational thinking, emphasizing the scientific, rigorous and abstract thinking. The examination of computing ability is mainly the examination of arithmetic and logical reasoning, mainly algebraic operation, estimation and simplification. The examination of spatial imagination ability is mainly reflected in the mutual transformation of written language, symbolic language and graphic language, and in the recognition, understanding and processing of graphics. The examination should combine the ability of calculation and logical thinking.

(4) The examination of practical ability mainly adopts the form of solving application problems. The proposition should adhere to the principle of "close to life, fair background, and control difficulty", and the design of test questions should conform to the reality of mathematics teaching in middle schools in China, taking into account the age and practical experience of candidates, so that the difficulty of mathematics application questions can meet the level of candidates.

(5) The examination of innovative consciousness is an examination of advanced rational thinking. In the examination, we should create relatively novel question situations, construct mathematical questions with certain depth and breadth, and pay attention to the diversification of questions to reflect the divergence of thinking. Carefully design test questions, examine the main contents of mathematics, and reflect the quality of mathematics; Test questions that reflect the movement changes of numbers and shapes; Research-oriented, exploratory and open questions.

Mathematics subject proposition, on the basis of examining basic knowledge, pays attention to the examination of mathematical thinking method, mathematical ability, scientific value and humanistic value of mathematics, takes into account the foundation, comprehensiveness and reality 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 realize the requirement of comprehensive examination of mathematics literacy.

Ⅲ. Examination contents and requirements

Mandatory (1 14)

First, the plane vector (12 class hours, 8)

Content:

1. vector; 2. Addition and subtraction of vectors; 3. Product of real number and vector; 4. Coordinate representation of plane vector; 5. The demarcation point of the line segment; 6. The product of plane vectors; 7. The distance between two points on the plane; 8. Translation.

Requirements:

1. Understand the concept of vector, master the geometric representation of vector, and understand the concept of * * * line vector.

2. Master the addition and subtraction of vectors.

3. Master the product of real numbers and vectors, and understand the necessary and sufficient conditions for the connection of two vectors.

4. Understand the basic theorem of plane vector, understand the coordinate concept of plane vector, and master the coordinate operation of plane vector.

5. Mastering the quantitative product of plane vector and its geometric meaning, understanding the quantitative product of plane vector can deal with the problems about length, angle and verticality, and master the conditions of vector verticality.

6. Master the distance formula between two points in the plane and the coordinate formula of the fixed point and midpoint of the line segment, and skillfully use it. Master the translation formula.

Second, set, simple logic (14 class, 8)

Content:

1. setting; 2. subset; 3. supplement; 4. Intersection; 5. Trade unions; 6. Logical connector; 7. Four propositions; 8. Necessary and sufficient conditions.

Requirements:

1. Understand the concepts of set, subset, complement, intersection and union. Understand the meaning of empty set and complete set. Understand the meaning of belonging, tolerance and equality. Master related terms and symbols, and use them to represent some simple sets correctly.

2. Understand the meaning of logical conjunctions "or" and "and". Understand four propositions and their relationships. Grasp the significance of sufficient conditions, necessary conditions and necessary and sufficient conditions.

III. Functions (30 class hours, 12)

Content:

1. mapping; 2. Function; 3. Monotonicity and parity of functions; 4. Inverse function; 5. The relationship between function images of reciprocal function; 6. Extension of the concept of index; 7. Operational properties of rational exponential power: 8. Exponential function; 9. Logarithm; 10. Operational properties of logarithm; 1 1. logarithmic function; 12. Examples of functions.

Requirements:

1. Understand the concepts of mapping and function.

2. Understand the concepts of monotonicity and parity of functions, and master the judgment methods of monotonicity and parity of some simple functions.

3. Understand the relationship between the concept of inverse function and the function image as inverse function, and you will find the inverse function of some simple functions.

4. Understand the concept of exponential power of fractions, and master the operational properties of exponential power of rational numbers. Master the concept, image and properties of exponential function.

5. Understand the concept of logarithm and master the operational nature of logarithm. Master the concept, image and properties of logarithmic function.

6. Be able to use the properties of functions, exponential functions and logarithmic functions to solve some simple practical problems.

Four. Inequality (22 class hours, 5)

Content:

1. Inequality; 2. Basic properties of inequality; 3. Proof of inequality; 4. Solving inequality; 5. Inequalities with absolute values.

Requirements:

1. Understand the essence of inequality and its proof.

2. Grasp the theorem that the arithmetic mean of two (not extended to three) positive numbers is not less than its geometric mean, and simply apply it.

3. Master the analysis, synthesis and comparison to prove simple inequalities.

4. Master the solution of simple inequality.

5. Understand the inequality |a|-|b|≤|a+b|≤|a|+|b|.

Trigonometric function (46 class hours, 16)

Content:

The generalization of the concept of 1. angle; 2. Curvature system; 3. Trigonometric function at any angle; 4. The trigonometric function line in the unit circle; 5. Basic relations of trigonometric functions with the same angle (square relation, quotient relation and reciprocal relation); 6. Inductive formulas of sine and cosine; 7. Sine, cosine and tangent of sum and difference of two angles; 8. Sine, cosine and tangent of double angles; 9. Images and properties of sine function and cosine function; 10. Periodic function; Image of 1 1. function; 12. Images and properties of tangent function; 13. Find the angle with the known trigonometric function value; 14. Sine theorem; Cosine theorem; 16. oblique triangle solution

Requirements:

1. Understand the concept of arbitrary angle and the meaning of radian. Can correctly convert radian and angle.

2. Understand the definition of sine, cosine and tangent at any angle. Understand the definitions of cotangent, secant and cotangent. Master the basic relationship between trigonometric functions and angles. Master the inductive formulas of sine and cosine. Understand the meaning of periodic function and minimum positive period.

3. Master the sine, cosine and tangent formulas of the sum and difference of two angles. Master the sine, cosine and tangent formulas of double angles.

4. Can correctly use trigonometric formula to simplify, evaluate and prove the identities of simple trigonometric functions.

5. Understand the images and properties of sine function, cosine function and tangent function, draw the graphs of sine function, cosine function and function with "five-point method", and understand the physical meaning of a and sum.

6. The angle will be obtained from the known trigonometric function values and represented by the symbols arcsinx, arccosx and arctanx.

7. Master sine theorem and cosine theorem, and use them to solve oblique triangles.

VI. Series (12 class hours, 5)

Content:

1. sequence; 2. arithmetic progression and its general formula; 3. arithmetic progression's first N terms and formulas; 4. Geometric series and its topping formula; 5. The first n terms and formulas of geometric series.

Requirements:

1. Understand the concept of sequence, and understand the meaning of the general term formula of sequence. Knowing the recursive formula is a way to give the sequence, and the first few items of the sequence can be written according to the recursive formula.

2. Understand the concept of arithmetic progression, master arithmetic progression's general formula and the first N summation formulas, and solve simple practical problems.

3. Understand the concept of geometric series, master the general formula of geometric series and the first n summation formulas, and solve simple practical problems.

VII. Equation of Line and Circle (22 class hours, 12)

Content:

1. Angle and slope of straight line; 2. Point-oblique and two-point linear equations; 3. General formula of linear equation;

4. Conditions for two straight lines to be parallel and vertical; 5. Angle of intersection of two straight lines; 6. Distance from point to straight line; 7. The plane area is expressed by binary linear inequality; 8. Simple linear programming problem; 9. Concepts of curves and equations; 10. The curve equation is listed by known conditions; Standard equation and general equation of 1 1. circle; 12. The parametric equation of the circle.

Requirements:

1. Understand the concepts of inclination angle and slope of a straight line and master the slope formula of two points of a straight line. Master the point-oblique formula, two-point formula and general formula of one-dimensional linear equation, and be able to skillfully solve one-dimensional linear equation according to conditions.

2. Master the condition that two straight lines are parallel and vertical, the angle formed by two straight lines and the distance formula from point to straight line. Can judge the positional relationship between two straight lines according to the straight line equation.

3. Understand that binary linear inequalities represent plane regions.

4. Understand the significance of linear programming and apply it simply.

5. Understand the basic ideas of analytic geometry and coordinate method.

6. Master the standard equation and general equation of a circle, understand the concept of parametric equation and understand the parametric equation of a circle.

VIII. Conic Curve (18 7 class hours)

Content:

1 ellipse and its standard equation; 2. Simple geometric properties of ellipse; 3. Parametric equation of ellipse; 4. Hyperbola and its standard equation; 5. Simple geometric properties of hyperbola; 6. Parabola and its standard equation; 7. Simple geometric properties of parabola.

Requirements:

1. Master the definition, standard equation and simple geometric properties of ellipse, and understand the parameter equation of ellipse.

2. Master the definition of hyperbola, standard equation and simple geometric properties of hyperbola.

3. Master the definition, standard equation and simple geometric properties of parabola.

4. Understand the preliminary application of conic curve.

Nine, (2) straight line, plane, simple (36 hours, 28 hours)

Content:

1. plane and its basic properties; 2. Intuitive drawing of plane graphics; 3. Parallel straight lines; 4. Determination and nature of parallelism between straight line and plane: 5. Determination of perpendicularity between straight line and plane; 6. Three vertical theorems and their inverse theorems; 7. The positional relationship between two planes; 8. Space vector and its addition, subtraction, multiplication and division; 9. Coordinate representation of space vector; 10. the product of space vectors; 1 1. The direction vector of the straight line; 12. angles formed by straight lines on different planes; 13. Common perpendicular of straight lines on different planes; 14 straight line distance in different planes; 15. Verticality of straight line and plane; 16. The normal vector of the plane; 17. Distance from point to plane; 18. The angle formed by a straight line and a plane; 19. The projection of the vector on the plane; 20. Determination and nature of parallel planes; 2 1. Distance between parallel planes; 22. dihedral angle and its plane angle; 23. Determination and nature of verticality of two planes; 24. Polyhedron; 25. Regular polyhedron; 26. Prism; 27. pyramids; 28. Ball.

Requirements:

1. Understand the basic properties of the plane, and draw a vertical view of the horizontally placed plane figure with oblique survey. Can draw a graph of the position relationship between two straight lines and a plane in space. You can imagine their positional relationship according to the graph.

2. Master the judgment theorem and property theorem of parallel lines and planes. Understand the concept of vertical line and plane, and master the judgment theorem of vertical line and plane. Master the three vertical theorems and their inverse theorems.

3. Understand the concept of space vector and master the addition, subtraction, multiplication and division of space vector.

4. Understand the basic theorem of space vector. Understand the concept of space vector coordinates and master the coordinate operation of space vectors.

5. Master the definition and properties of the product of space vector, and master the calculation formula of the product of rectangular coordinate space vector. Master the distance formula between two points in space.

6. Understand the concepts of the direction vector of a straight line, the normal vector of a plane and the projection of the vector on the plane.

7. Master the concepts of angles and distances between straight lines, between straight lines and planes, and between planes. For the distance of straight lines in different planes, only the distance in the given common vertical line or coordinate representation needs to be calculated. Master the property theorem of vertical line and plane. Master the judgment theorem and property theorem of two parallel vertical planes.

8. Understand the concepts of polyhedron, convex polyhedron and regular polyhedron.

9. Understand the concept of prism, master the nature of prism, and draw a direct view of straight prism.

10. Understand the concept of the pyramid, master the properties of the regular pyramid, and draw a direct view of the regular pyramid.

1 1. Understand the concept of the ball, master the properties of the ball, and master the surface area formula and volume formula of the ball.

Ten, permutation, combination, binomial theorem (18 class, 8)

Content:

1. Classification counting principle and step-by-step counting principle; 2. Arrangement; 3. Formula of permutation number; 4. combination; 5. Combination number formula; 6. Two properties of combinatorial numbers: 7. Binomial theorem; 8. The nature of binomial expansion.

Requirements:

1. Master the principles of classified counting and step counting, and use them to analyze and solve some simple application problems.

2. Understand the meaning of permutation, master the calculation formula of permutation number, and use it to solve some simple application problems.

3. Understand the meaning of combination, master the calculation formula of combination number, and use it to solve some simple application problems.

4. Grasp the properties of binomial theorem and binomial expansion, and use them to calculate and prove some simple problems.

XI。 Probability (12 class hours, 5)

Content:

1. Probability of random events; 2. The probability of this possible event; 3. mutually exclusive events has the probability of occurrence; 4. The probability of mutually independent events occurring simultaneously; 5. Repeat the test independently.

Requirements:

1. It is very meaningful to understand the regularity and probability of random events.

2. In order to understand the significance of the probability of equal possibility events, we will use the basic formula of permutation and combination to calculate the probability of some equal possibility events.

3. In order to understand the meaning of mutually exclusive events and independent events, we will use mutually exclusive events's probability addition formula and independent event probability multiplication formula to calculate the probability of some events.

4. Calculate the probability of the event happening k times in n independent repeated tests.

Elective 2 (24)

XII. Probability and Statistics (14 class hours, 6)

Content:

1. Distribution table of discrete random variables; 2. Expected value and variance of discrete random variables; 3. Sampling method; 4. Estimation of the overall distribution; 5. Normal distribution; 6. Linear regression.

Requirements:

1. Knowing the meaning of discrete random variables will lead to some simple distribution lists of discrete random variables.

2. Understand the meaning of expectation and variance of discrete random variables, and work out expectation and variance according to the distribution table of discrete random variables.

3. We will use common sampling methods such as random sampling, systematic sampling and stratified sampling to extract samples from the population.

4. The sampling frequency will be used to estimate the overall distribution.

5. Understand the significance and main properties of normal distribution.

6. Understand the method and simple application of linear regression.

Thirteen. Restrictions (12 class hours, 6)

Content:

1. Mathematical induction; 2. The application of mathematical induction; 3. Limit of sequence; 4. Limit of function; 5. Four operations of limit; 6. Functional continuity.

Requirements:

1. Understand the principle of mathematical induction, and use mathematical induction to prove some simple mathematical propositions.

2. Understand the concepts of sequence limit and function limit.

3. Four algorithms to master the limit. Will find the limits of some sequences and functions.

4. Understand the meaning of function continuity and the property that continuous functions have maximum and minimum values in a closed interval.

Fourteen Derivative (18 class hour, 8)

Content:

The concept of 1. derivative; 2. Geometric meaning of derivative; 3. Derivatives of several common functions; 4. Derivative of sum, difference, product and quotient of two functions; 5. Derivative of composite function; 6. Basic derivative formula; 7. Using derivatives to study monotonicity and extremum of functions: 8. Maximum and minimum values of functions.

Requirements:

1. Understand some practical background of the concept of derivative (such as instantaneous velocity, acceleration, slope of tangent of smooth curve, etc.). ); Master the definition of the derivative of a function at a point and the geometric meaning of the derivative; Understand the concept of derivative function.

2. Memorize the basic derivative formulas (derivatives of C, xm(m is a rational number), sinx, cosx, ex, ax, lnx and logax); Master the derivation rules of sum, difference, product and quotient of two functions. Knowing the law of derivative of compound function, we will find the derivative of some simple functions.

3. Understand the relationship between monotonicity of differentiable function and its derivative; Understand the necessary and sufficient conditions for the derivative function to obtain the extreme value at a certain point (the sign of the derivative is different on both sides of the extreme value point); You will find the maximum and minimum of some practical problems (generally referring to unimodal functions).

Fifteen, plural (4 class hours, 4)

Content:

The concept of 1. complex number; 2. Addition and subtraction of complex numbers; 3. Multiplication and division of complex numbers; 4. Expansion of digital system.

Requirements:

1. Understand the related concepts of complex numbers, their algebraic expressions and geometric meanings.

2. Master the algorithm in the form of complex algebra, and be able to perform addition, subtraction, multiplication and division in the form of complex algebra.

3. Understand the relationship between natural number system and complex number system and the basic idea of expansion.

Ⅳ. Examination form and examination paper structure

The examination takes the form of closed book and written test. Full paper 150 points, examination time 120 minutes.

The whole volume includes the first volume and the second volume. The first volume is a multiple-choice question; Volume 2 is a multiple-choice question.

Examination papers generally include multiple-choice questions, fill-in-the-blank questions and solution questions. Multiple choice questions are single choice questions of four choices and one type; Fill in the blanks only by filling in the results directly, without writing out the calculation process or derivation process; Solution questions include calculation questions, proof questions, application questions, etc. The solution should be written in words, calculation steps or derivation process.

The test paper should be composed of easy questions, medium problems and difficult problems, with appropriate overall difficulty, with medium problems as the main problem.