1. summary of compulsory mathematics knowledge points in senior two.
1, structural features of prism, such as column, cone, stage and sphere (1);
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 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:
Geometric features: the upper and lower bottom surfaces are similar parallel polygons, the side surfaces are trapezoidal, and the side edges intersect with the vertices of the original pyramid.
(4) Cylinder: Definition: It is formed by taking a straight line on one side of a rectangle as the axis and rotating the other three sides.
Geometric features: the bottom is an congruent circle; The bus is parallel to the shaft; The axis is perpendicular to the radius of the bottom circle; The profile is a rectangle.
(5) Cone: Definition: A Zhou Suocheng is rotated with a right-angled side of a right-angled triangle as the rotation axis.
Geometric features: the bottom is round; The generatrix intersects with the apex of the cone; The side spread is a fan.
(6) frustum of a cone: Definition: Take the vertical line of the right-angled trapezoid and the waist of the bottom as the rotation axis, and use Zhou Suocheng to rotate.
Geometric features: the upper and lower bottom surfaces are two circles; The side generatrix intersects with the vertex of the original cone; The enlarged side view shows an arch.
(7) Sphere: Definition: Geometry formed by taking the straight line with the diameter of the semicircle as the rotation axis and the semicircle surface rotating once.
Geometric features: the cross section of the ball is round; The distance from any point on the sphere to the center of the sphere is equal to the radius.
2. Three views of space geometry
Define three views: front view (light is projected from the front of the geometry to the back); Side view (from left to right),
Top view (from top to bottom)
Note: the front view reflects the height and length of the object; The top view reflects the length and width of the object; The side view reflects the height and width of the object.
3. Intuition of space geometry-oblique two-dimensional drawing method.
The characteristics of oblique bisection method are as follows: the line segment originally parallel to X axis is still parallel to X, and its length remains unchanged;
The line segment parallel to the Y axis is still parallel to Y, and the length is half of the original.
4. Surface area and volume of cylinders, cones and platforms.
The surface area of a (1) geometry is the sum of all the surfaces of the geometry.
(2) The surface area formula of special geometry (C is the perimeter of the bottom, H is the height, and L is the generatrix)
(3) Volume formulas of cylinders, cones and platforms.
2. Summary of compulsory mathematics knowledge points in Senior Two.
There are several positional relationships between a straight line and a plane. There are three relationships between a straight line and a plane: straight line is on the plane, straight line intersects with the plane, and straight line is parallel to the plane. Among them, the line intersects with the plane, and it is divided into two subcategories: the oblique intersection of the line and the plane and the vertical of the line.
The straight line is in the plane-there are countless things in common; A straight line intersects a plane-there is only one common point; The straight line is parallel to the plane-there is no common point. The intersection and parallelism of a straight line and a plane are collectively called out-of-plane straight lines.
Judging whether a straight line is perpendicular to the plane: If the straight line L is perpendicular to any straight line in the plane α, we say that the straight line L and the plane α are perpendicular to each other, which is called L⊥α. The straight line L is called the perpendicular of the plane α, and the plane α is called the perpendicular of the straight line L. ..
Line-plane parallelism: A straight line out of the plane is parallel to a straight line in the plane, then the straight line is parallel to the plane. A straight line out of the plane is perpendicular to the perpendicular of this plane, so this straight line is parallel to this plane.
Angle range between straight line and plane
[0,90] or [0,π/2].
When two straight lines intersect non-perpendicularly, four angles are formed, which are divided into two groups. Two acute angles and two obtuse angles. According to the regulations, a pair of diagonal angles with acute angles are selected as the included angle between straight lines.
The direction vector of the straight line is m = (2,0, 1), the normal vector of the plane is n=(- 1, 1, 2), the angle between m and n is θ, cos θ = (m _ n)/| m | n |, and the result is equal to 0. That is to say. The angle between l and the plane is 0.
3. Summary of compulsory mathematics knowledge points in Senior Two.
Spatial Angle Problem (1) Angle between straight lines
① Angle formed by two parallel straight lines: specified as.
(2) The angle formed by the intersection of two straight lines: the angle formed by the intersection of two straight lines is not greater than the right angle, which is called the angle formed by these two straight lines.
(3) Angle formed by two straight lines with different planes: when passing through any point o in space, make the straight line parallel to the two straight lines with different planes A and B to form two intersecting straight lines, and the angle formed by these two intersecting straight lines is called the angle formed by two straight lines with different planes.
(2) The angle formed by a straight line and a plane
① The angle formed by the parallel lines between the plane and the plane: specified as.
② The angle between the plane and the perpendicular to the plane: specified as.
(3) The angle formed by the oblique line of the plane and the plane: the acute angle formed by an oblique line of the plane and its projection in the plane is called the angle formed by this straight line and this plane.
The idea of finding the angle between diagonal and plane is similar to finding the angle formed by straight lines on different planes: "one work, two certificates and three calculations"
When making an angle, project according to the definition key. From the definition of projection, the key lies in the point on the diagonal to the perpendicular to the surface.
When solving problems, pay attention to mining two main information in the problem setting:
(1) The vertical line from a point on the diagonal to the surface;
(2) The diagonal or a point on the plane of the diagonal is perpendicular to the known surface, and the vertical line can be easily obtained from the vertical nature of the surface.
(3) The dihedral angle of dihedral angle and plane angle
① Definition of dihedral angle: The figure formed by two half planes starting from a straight line is called dihedral angle, this straight line is called the edge of dihedral angle, and these two half planes are called the faces of dihedral angle.
② Plane angle of dihedral angle: Take any point on the edge of dihedral angle as the vertex and make two rays perpendicular to the edge in two planes. The angle formed by these two rays is called the plane angle of dihedral angle.
③ Straight dihedral angle: A dihedral angle whose plane angle is a right angle is called a straight dihedral angle.
If the dihedral angle formed by two intersecting planes is a straight dihedral angle, then the two planes are vertical; On the contrary, if two planes are perpendicular, the dihedral angle formed is a straight dihedral angle.
(4) Calculation method of dihedral angle
Definition method: select the relevant point on the edge, and make a ray perpendicular to the edge in two planes through this point to get the plane angle.
Vertical plane method: when the vertical lines from one point to two surfaces in dihedral angle are known, the angle formed by the intersection of two vertical lines as the intersection of plane and two surfaces is the plane angle of dihedral angle.
4. Summary of compulsory mathematics knowledge points in senior two.
(1) population and sample: ① In statistics, the whole research object is called population.
② Call each research object an individual.
The total number of individuals in a group is called the total capacity.
④ In order to study the related properties of the population, we generally randomly select a part from the population: x 1, x2, ..., _ research, which we call samples. The number of individuals is called sample size.
(2) Simple random sampling, also known as pure random sampling.
In other words, the survey units are randomly selected from the population, without any grouping, classification, queuing, etc. The characteristics are: the probability of each sample unit being extracted is the same (the probability is equal), and each unit of the sample is completely independent, and there is no certain correlation and exclusion between them. Simple random sampling is the basis of other sampling forms. This method is usually only used when the difference between the whole units is small and the number is small.
(3) Common methods of simple random sampling:
(1) draw lots
② Random number table method
③ Computer simulation method
In the sample size design of simple random sampling, we mainly consider:
① General variation;
② Allowable error range;
③ Degree of probability assurance.
(4) draw lots:
(1) Number each object in the measurement group;
(2) Prepare the lottery tool and implement it;
③ Measure or investigate each individual in the sample.
5. Summary of compulsory mathematics knowledge points in senior two.
1. Definition of geometric probability: If the probability of each event is only proportional to the length (area or volume) of the event area, such a probability model is called geometric probability model, or geometric probability model for short. 2. Probability formula of geometric probability: P(A)= the length (area or volume) of the region that constitutes event A; The length (area or volume) of the area formed by all test results.
3, the characteristics of geometric probability:
1) There are infinitely many possible results (basic events) in the test;
2) The possibility of each basic event is equal,
4. Comparison between geometric probability and classical probability: on the one hand, classical probability is limited, that is, the test results are countable; Geometric probability is that there are infinitely many results in the test, and it is related to length (or area, volume, etc.). ), that is, the test results are infinite. This is the difference between the two; On the other hand, the experimental results of classical probability and geometric probability have the same possibility, which is their * * * property.