Examination is an important means and method to test students' learning effect, and it is necessary to reserve knowledge in all aspects before the examination. The following are the math knowledge points of the college entrance examination that I compiled for you, hoping to help you!

Summarize the first, function and derivative of liberal arts mathematics test center in college entrance examination. This paper mainly examines the concepts of * * * operation and function, such as the definition domain, value domain, analytical formula, limit, continuity and derivative of function.

Second, plane vector and trigonometric function, trigonometric transformation and their applications. This part is the key but not the difficult part of Weibo College Entrance Examination, which mainly contains some basic or intermediate topics.

Thirdly, sequence and its application. This part is the key and difficult part of the college entrance examination, which mainly produces some comprehensive questions.

Fourth, inequality. This paper mainly investigates the solution and proof of inequality, rarely alone, mainly through the size comparison in solving problems. It is the key and difficult point of the college entrance examination.

Fifth, probability statistics. This part is related to our life and is an applied problem.

Sixth, the qualitative and quantitative analysis of spatial position relationship is mainly to prove parallelism or verticality, and to find the angle and distance.

Seventh, analytic geometry. It is the difficulty of the college entrance examination, which requires a large amount of calculation and generally has quotations.

Hunan college entrance examination liberal arts mathematics test center 1: linear equation

1. Inclination angle of a straight line: the minimum positive angle formed by the upward direction of a straight line and the positive direction of the shaft is called the inclination angle of this straight line, where the inclination angle when the straight line is parallel or coincident with the shaft is 0, so the range of inclination angle of the straight line is.

Note: ① When or, the straight line is perpendicular to the axis, and its slope does not exist.

(2) Every straight line has a unique inclination, except the straight line perpendicular to the axis has a unique slope. When the slope of the straight line is constant, its inclination will be determined accordingly.

2. Several forms of linear equation: point skew, intercept, two points, skew.

In particular, when a straight line passes through two points, that is, the intercept and axis of the straight line on the axis are respectively, the straight line equation is:

Note: If it is the equation of a straight line, the equation of this straight line is, but if it is not this straight line.

Attachment: straight line system: for oblique equations of straight lines, when they are all fixed values, they represent a definite straight line. If they change, the corresponding straight line will also change. (1) When they change, they represent a straight beam passing through the fixed point 0. (2) when they are fixed values, they represent a set of parallel straight lines when changing.

3.( 1) Two straight lines are parallel:

∑ The conditions that two straight lines are parallel are: ① sum is two non-overlapping straight lines; ② It is obtained on the premise that the slope of sum exists. Therefore, we should pay special attention to the fact that removing or ignoring any "premise" will lead to wrong conclusions.

The general conclusion is: for two straight lines, their longitudinal intercept on the axis is 0, then the slope of ∨ or does not exist, which is a necessary and sufficient condition for parallelism, and

Inference: If the inclination of two straight lines is ∨.

(2) Two straight lines are vertical:

Conditions for two straight lines to be perpendicular: ① If the slopes of the sum of two straight lines are sum, then the premise here is that both slopes exist; ② The slopes of the two lines do not exist or, and the slopes of the two lines do not exist. That is a necessary and sufficient condition for verticality.

4. Angle of intersection of straight lines:

(1) Angle between the angle direction and the straight line; The angle of a straight line refers to the angle at which the straight line rotates counterclockwise around the intersection point and coincides with it, and its range is, at that time.

⑵ Angle between two intersecting straight lines and: The angle between two intersecting straight lines and refers to the smallest positive angle among the four angles formed by intersecting with, also called the angle formed by and, and its value range is, if, then.

5. The equation in which a straight line passes through the intersection of two straight lines is an independent variable and is not included.

Hunan college entrance examination liberal arts mathematics test site 2: trajectory equation

First, the basic steps of solving the moving point trajectory equation

1. Establish an appropriate coordinate system and set the coordinates of the dispatching point m;

4. Write the * * * of point M;

3. List the equation = 0;

2. Simplify the equation to the simplest form;

5. test.

Second, the common methods to solve the moving point trajectory equation: There are many methods to solve the trajectory equation, such as literal translation, definition, correlation point method, citation method, intersection method and so on.

1. Literal translation method: the conditions are directly translated into equations, and the trajectory equation of the moving point is obtained after simplification. This method of solving trajectory equation is usually called literal translation.

3. Definition method: If it can be determined that the trajectory of the moving point meets the definition of the known curve, the equation can be written by using the definition of the curve. This method of solving trajectory equation is called definition method.

13. Associated point method: express the coordinates x0 and y0 of the associated point P with the coordinates x and y of the moving point Q, and then substitute them into the curve equation satisfied by the coordinates x0 and y0 of the point P, and get the trajectory equation of the moving point Q simply and clearly. This method of solving trajectory equation is called correlation point method.

4. Deduction method: When it is difficult to find the direct relationship between the coordinates of the moving point X and Y, the relationship between X and Y and a variable T is often found first, and then the equation is obtained by eliminating the parameter T, that is, the trajectory equation of the moving point. This method of solving trajectory equation is called derivative method.

5. Trajectory method: eliminate the independent variables in the equations of two dynamic curves, and get the equation without independent variables, that is, the trajectory equation of the intersection of two dynamic curves. This method of solving trajectory equation is called trajectory method.

Hunan college entrance examination liberal arts mathematics test center 3: derivative

First of all, the monotonicity of the function

The differentiable functions fx and f ′ x in A and B are not always equal to 0 in any subinterval of A and B. 。

f′x≥0？ Fx is the increasing function on A and B.

f′x≤0？ Fx is the subtraction function on a and b.

Second, the extreme value of the function

1, the minimum value of the function:

The function value f'a = 0 of function y=fx at point x=a is smaller than other points near point x=a, f'a = 0, on the left side near point x=a, f' x.

2. The maximum value of the function:

The function value fb of function y=fx at point x=b is greater than that at other points near point x=b, f ′ b = 0, on the left side of point x=b, f ′ x >: 0, and on the right side f ′ x.

The minimum point and the maximum point are collectively referred to as extreme points, and the maximum value and minimum value are collectively referred to as extreme values.

Third, the maximum value of the function.

1. The continuous function fx in the closed interval [a, b] must have a maximum value and a minimum value in [a, b].

2. If the function fx monotonically increases in [a, b], then fa is the minimum value of the function and fb is the maximum value of the function; If the function fx monotonically decreases in [a, b], then fa is the maximum value of the function and fb is the minimum value of the function.

Fourthly, the general steps and methods to find the monotone interval of differentiable functions.

1, which determines the domain of the function fx;

2. Find f ′ x, make f ′ x = 0, and find all its real roots on the domain;

3. Arrange the discontinuous points of the function fx, that is, the abscissa of the undefined points of fx, and the real number roots in the order from small to large, and then use these points to divide the defined interval of the function fx into several cells;

4. Determine the sign of f ′ x in each open interval, and judge the increase or decrease of function fx in each corresponding small open interval according to the sign of f ′ x. 。

Hunan college entrance examination liberal arts mathematics test site 4: inequality

The properties of 1 understanding inequality and its proof.

Guide reading

The nature of inequality is the theoretical support of inequality, and its basic nature comes from the comparison of numbers. Please note the following points:

Strengthen the sense of reduction, and transform the problem of comparative size into the operation of real numbers;

By examining the conditional "operation" of strengthening inequality. For example, a>b, only c>d can start ac & gtBD；;

Strengthen the important role of function properties in size comparison and strengthen the connection between knowledge;

The nature of inequality is the basis of solving and proving inequality. For any two real numbers a and b, a-b >; 0a & gt； b，a-b=0 a=b，a-b & lt； 0 a

On the basis of understanding, we must remember the nature of inequality accurately and familiarly, and pay attention to its flexible and accurate application in solving problems;

When two or more inequalities are added or multiplied, we must pay attention to whether the inequalities are in the same direction and greater than zero;

Compare the size of problems with parameters, and pay attention to classified discussion.

Master the theorem that the arithmetic mean of two nonexpansive packages to three positive numbers is not less than its geometric mean, and simply apply it.

Guide reading

1. Among all kinds of methods to prove inequality, comparison is the most basic and important method. It uses the difference between two sides of inequality to prove inequality. It is widely used and must be mastered skillfully.

2. For formulas a+b≥ 2√ab and ab≤a+b/22, we need to know their functions, conditions of use and internal relations. The two formulas also reflect the transformation relationship between ab and A+B.

3. When applying the mean value theorem to find the maximum value, we should grasp three conditions for the theorem to be established: "First, it is positive-everything is positive; The binary product or sum is a fixed value; Three levels-whether you can get an equal sign. " If a condition is ignored, an error will occur.

Master simple inequalities proved by analysis, synthesis and comparison.

Guide reading

1. In the process of proving inequality, analytical method and synthetic method are inseparable. If it is difficult to prove inequality by comprehensive method, analytical method is often used to explore the way to prove the problem, and then the proof process is written in the form of comprehensive method. Sometimes it is difficult to prove the problem, and analytical synthesis method is often used to achieve the purpose of proof by tilting both ends to the middle.

2. Because there is no single inequality proof problem in the college entrance examination questions, they are often combined with functions, sequences, triangles and equations. So in learning, in addition to the three commonly used methods, there are other ways to prove inequality, such as comparing sizes. The common methods to prove inequality are: difference method, quotient comparison method, function property method, analytical synthesis method and scaling method. We should be able to understand the commonly used scaling methods, such as using the properties of increase and decrease, fraction, monotonicity and boundedness of functions, basic inequalities and absolute inequalities, mathematical induction and so on. Proving inequality sometimes requires equivalent deformation, and sometimes several proving methods are used comprehensively.

There are two forms of comparative law: one is to make a difference, not to make a difference. It is the most basic and commonly used method to prove inequality by difference method. It is based on the basic properties of inequality. The steps are: difference quotient → deformation → judgment. The purpose of deformation is to judge. If it is poor, judge its relationship with 0. In order to make it easier to judge, the form is often changed into a product or a completely flat way. If the vendors on both sides are positive, use 1 to judge the relationship.

Hunan college entrance examination liberal arts mathematics test site 5: geometry

1 prism:

Definition: Geometry surrounded by two parallel faces, the other faces are quadrangles, and the common edges of every two adjacent quadrangles are parallel to each other.

Classification: According to the number of sides of the bottom polygon, it can be divided into three prisms, four prisms and five prisms.

Representation: Use the letter of each vertex, such as a five-pointed star, or use the letter at the opposite end, such as a five-pointed star.

Geometric features: the two bottom surfaces are congruent polygons with parallel corresponding sides; The lateral surface and diagonal surface are parallelograms; The sides are parallel and equal; The section parallel to the bottom surface is a polygon that is congruent with the bottom surface.

2 pyramids

Definition: One face is a polygon, and the other faces are triangles with a common vertex. These faces enclose a geometric figure.

Classification: According to the number of sides of the bottom polygon, it can be divided into three pyramids, four pyramids and five pyramids.

Representation: Use the letters of each vertex, such as a pentagonal pyramid.

Geometric features: the side and diagonal faces are triangles; The section parallel to the bottom surface is similar to the bottom surface, and its similarity ratio is equal to the square of the ratio of the distance from the vertex to the section to the height.

3 prism:

Definition: Cut off the part between the pyramid, the section and the bottom with a plane parallel to the bottom of the pyramid.

Classification: According to the number of sides of the bottom polygon, it can be divided into triangular, quadrangular and pentagonal shapes.

Representation: Use the letters of each vertex, such as a pentagonal pyramid.

Geometric features: ① The upper and lower bottom surfaces are similar parallel polygons; ② The side is trapezoidal; ③ The sides intersect with the vertices of the original pyramid.

4 cylinders:

Definition: Geometry surrounded by a surface with one side of a rectangle and the other three sides rotating around a straight line.

Geometric features: ① The bottom is an congruent circle; ② The bus is parallel to the shaft; ③ The axis is perpendicular to the radius of the bottom circle; ④ The side development diagram is a rectangle.

5 cone:

Definition: Rotate the geometry surrounded by the surface of Zhou Suocheng with the right-angled side of the right-angled triangle as the rotation axis.

Geometric features: ① the bottom is round; (2) The generatrix intersects with the apex of the cone; ③ The side spread diagram is a fan.

6 frustum:

Definition: Cut the part between the cone, the section and the bottom with a plane parallel to the bottom of the cone.

Geometric features: ① The upper and lower bottom surfaces are two circles; (2) The side generatrix intersects with the vertex of the original cone; (3) The side development diagram is an arch.

7 sphere:

Definition: Geometry formed by taking the straight line where the diameter of the semicircle is located as the rotation axis and the semicircle surface rotates once.

Geometric features: ① the cross section of the ball is round; ② The distance from any point on the sphere to the center of the sphere is equal to the radius. See "Knowledge Points of Mathematics in Hunan College Entrance Examination";