1. plane vector

Examination contents: vector, vector addition and subtraction, product of real number and vector, coordinate representation of plane vector, fixed point of line segment, quantitative product of plane vector, distance and translation between two points in plane.

Examination 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) Grasp the product of real number and vector, and understand the necessary and sufficient conditions of two vector lines.

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

(5) Grasp the quantitative product of plane vector and its geometric meaning, understand that the quantitative product of plane vector can deal with problems related to length, angle and verticality, and grasp the conditions of vector verticality.

(6) Master the distance formula between two points on the plane and the coordinate formula of the bisector and midpoint of the line segment, and skillfully use it. Master the translation formula.

2. Set and simple logic

Examination content: set, subset, complement set, intersection, union set, logical connectives, four propositions, sufficient conditions and necessary conditions.

Examination requirements:

(1) Understand the concepts of set, subset, complement set, intersection set and union set, understand the meanings of empty set and complete set, understand the meanings of ownership, inclusion and equality, master relevant terms and symbols, and correctly use them to represent some simple sets.

(2) Understand the meanings of logical conjunctions "OR", "Qi" and "Fei", understand the four propositions and their relationships, and master the meanings of sufficient conditions, necessary conditions and necessary and sufficient conditions.

3. Functional test content:

Mapping, function, monotonicity, parity, inverse function, relationship between function image and inverse function, generalization of exponential concept, operational properties of rational exponential power, exponential function, logarithm, logarithmic function.

Application of functions. Examination 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) Understanding the concept of inverse function and the relationship between function images which are mutually inverse functions, we will find the inverse functions of some simple functions.

(4) Understand the concept of fractional exponential power, master the operational properties of rational exponential power, and 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) We can use the properties of function, exponential function and logarithmic function to solve some simple practical problems.

4. Inequality

Examination contents: inequality, its basic properties, its proof, its solution and inequality with absolute value.

Examination requirements:

The properties of (1) understanding 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) Mastering 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 │.

5. Trigonometric function

Exam content: the generalization of angle concept, radian system, trigonometric function at any angle, trigonometric function line in the unit circle, and the basic relationship of trigonometric function with the same angle: sin2α+cos2α= 1, sinα/cosα=tanα, Tan α Cot α = 1. Inductive formulas of sine and cosine. Sine, cosine and tangent of sum and difference of two angles. Sine, cosine and tangent of a double angle. Images and properties of sine function and cosine function. Periodic function. The image of function y=Asin(ωx+φ). Images and properties of tangent function. Find the angle by knowing the value of trigonometric function ..

Examination requirements:

(1) Understand the concept of arbitrary angle and the meaning of radian, and 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, and understand the significance 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) The trigonometric formula can be used correctly 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, and draw the graphs of sine function, cosine function and function y=Asin(ωx+φ) with the "five-point method" to understand the physical meanings of a, ω and φ.

(6) The angle will be obtained from the known trigonometric function value and represented by the symbol arcsinx arccosx arctanx.

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

6. Series

Exam content: series, arithmetic progression and its general formula, arithmetic progression's first n summation formulas, geometric progression and its general formula, and geometric progression's first n summation formulas.

Examination requirements:

(1) Understand the concept of sequence, understand the meaning of general term formula of sequence, and understand recursive formula is a way to give sequence, and write the first few terms of sequence according to 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.

7. Equations of straight lines and circles

Examination contents: inclination angle and slope of straight line, point inclination and two-point formula of straight line equation, general formula of straight line equation, parallel and vertical conditions of two straight lines, intersection angle of two straight lines, distance from point to straight line, plane area expressed by binary linear inequality, simple linear programming problem, concept of curve and equation, listing curve equation, standard equation and general formula of circle and parameter equation of circle from known conditions.

Examination requirements:

(1) Understand the concepts of inclination angle and slope of a straight line, master the slope formula of a straight line passing through two points, master the point inclination formula, two-point formula and general formula of a straight line equation, and skillfully solve the straight line equation according to conditions.

(2) Knowing 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, we can judge the positional relationship of two straight lines according to the equation of straight lines.

(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 and understand the concept of parametric equation. Understand the parametric equation of a circle.

8. Conic curve equation

Examination contents: ellipse and its standard equation, simple geometric properties of ellipse, parametric equation of ellipse, hyperbola and its standard equation, simple geometric properties of hyperbola.

Parabola and its standard equation. Simple geometric properties of parabola.

Examination 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.

Article 9(A). Straight line, plane and simple geometry (candidates can choose one of 9 (a) and 9(B))

Examination contents: plane and its basic properties, drawing method of orthographic drawing of plane graphics, parallel straight lines, angles formed by parallel sides, common perpendicularity of lines in different planes, distance of lines in different planes, determination and properties of parallelism between lines and planes, determination and properties of perpendicularity between lines and planes, distance from points to planes, projection of diagonal lines on planes, angles formed by lines and planes, three perpendicularity theorems and their inverse theorems, and determination and properties of parallel planes.

Examination requirements:

(1) To understand the basic properties of a plane, he can draw a vertical view of a horizontally placed plane figure by oblique sides. He can draw graphs of various positional relationships between two straight lines and a plane in space, and can imagine their positional relationships according to the graphs.

(2) Master the judgment theorem and property theorem of two straight lines being parallel and vertical, and master the concepts of the angle and distance formed by two straight lines. For the distance of straight lines in different planes, it is only necessary to calculate the distance given the common perpendicular.

(3) Mastering the concepts of judging theorem and property theorem of straight line parallel to plane, judging theorem and property theorem of straight line perpendicular to plane, projection of oblique line on plane, angle formed by straight line and plane, three perpendicular theorems and their inverse theorems.

(4) Master the judgment theorem and property theorem of two planes being parallel, the concepts of dihedral angle, its plane angle and the distance between two parallel planes, and the judgment theorem and property theorem of two planes being perpendicular.

(5) Simple problems can be proved by reduction to absurdity.

(6) Understand the concepts of polyhedron, convex polyhedron and regular polyhedron.

(7) Understand the concept and properties of prism and draw a straight prism.

(8) Understand the concept of the pyramid, master the nature of the regular pyramid, and draw a direct view of the regular pyramid.

(9) Understand the concept of the ball, master the properties of the ball, and master the surface area formula and volume formula of the ball.

Article 9 (b). Straight line, plane, simple geometry

Examination contents: plane and its basic properties, drawing method of plane figure, parallel straight lines, determination and properties of parallelism between straight lines and plane, determination of perpendicularity between straight lines and plane, theorem of three perpendicular lines and its inverse theorem, and positional relationship between two planes.

Space vector and its addition, subtraction, multiplication and division. Coordinate representation of space vector. Quantity product of space vector.

Direction vector of straight line, angle formed by non-planar straight line, common perpendicular of non-planar straight line, and distance of non-planar straight line.

Verticality of straight line and plane, normal vector of plane, distance from point to plane, angle between straight line and plane, projection of vector on plane.

Determination and properties of parallel planes. Distance between parallel planes. Dihedral angle and its plane angle. Determination and properties of two planes being perpendicular.

Polyhedron Regular polyhedron Prism. Pyramid. Ball.

Examination requirements:

(1) To understand the basic properties of a plane, he can draw a vertical view of a horizontally placed plane figure by oblique survey. He can draw graphs of various positional relationships between two straight lines and a plane in space, and can imagine their positional relationships according to the graphs.

(2) To master the judgment theorem and property theorem of parallel lines and planes, the judgment theorem of vertical lines and planes, the three perpendicular lines theorem and its inverse theorem.

(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 vector.

(5) Master the definition and properties of the product of space vector, the calculation formula of the product of space vector in rectangular coordinates, and the calculation formula of the distance 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 formed by straight lines, straight lines and planes, and planes and planes. For the distance of straight lines in different planes, we only need to calculate the distance given by the common perpendicular or the distance in the coordinate representation, master the property theorem of the perpendicularity between straight lines and planes, and master the judgment theorem and property theorem of the parallelism and perpendicularity between two planes.

(8) Understand the concepts of polyhedron and convex polyhedron. Understand the concept of regular polyhedron.

(9) Understand the concept and properties of prism and draw a straight prism.

(10) Understand the concept of pyramids and master the properties of regular pyramids. You can draw a regular pyramid directly.

(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.

10. permutation, grouping and binomial theorem

Examination contents: classification counting principle and step counting principle, permutation, permutation number formula, combination, combination number formula, two properties of combination number, binomial theorem, properties of binomial expansion.

Examination requirements:

(1) Master the principles of classified counting and step-by-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 formulas and properties of combination numbers, and use them 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.

1 1. Possibility

Examination content:

Probability of random events. Probability of equal possibility events. Mutually exclusive events has a probability of occurrence. The probability of mutually independent events happening at the same time. Independent repeat test.

Examination requirements:

(1) It is meaningful to know the regularity and probability of random events.

(2) Knowing the significance of the probability of equal possibility events, we 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 that the event happens exactly κ times in n independent repeated tests.

12. Statistics

Examination content: sampling method, estimation of population distribution, estimation of population expectation and variance.

Examination requirements:

(1) Understand the significance of random sampling and stratified sampling, and use them to sample simple practical problems.

(2) The sample frequency distribution will be used to estimate the overall distribution.

(3) The sample will be used to estimate the overall expectation and variance.

13. derivative

Exam content: the background of derivative, the concept of derivative, the derivative of polynomial function, using derivative to study the monotonicity and extreme value of function, the maximum and minimum value of function.

Examination requirements:

(1) Understand the practical background of the concept of derivative.

(2) Understand the geometric meaning of derivatives.

(3) Mastering the derivative formulas of functions y=c(c is a constant) and y=xn(n∈N+), we can find the derivative of polynomial function.

(4) Understand the concepts of maxima, minima, minima and minima, and use derivatives to find maxima and minima of monotone intervals, maxima and minima of polynomial functions and closed intervals.

(5) Using derivatives to find the maximum and minimum of some simple practical problems.