Summary of two knowledge points of compulsory mathematics in senior one and senior two.
Basic concept axiom 1: If two points on a straight line are in a plane, then all points on this straight line are in this plane.
Axiom 2: If two planes have a common point, then they have only one common straight line passing through this point.
Axiom 3: When three points that are not on a straight line intersect, there is one and only one plane.
Inference 1: Through a straight line and a point outside this straight line, there is one and only one plane.
Inference 2: Through two intersecting straight lines, there is one and only one plane.
Inference 3: Through two parallel straight lines, there is one and only one plane.
Axiom 4: Two lines parallel to the same line are parallel to each other.
Equiangular Theorem: If two sides of one angle are parallel and in the same direction as two sides of another angle, then the two angles are equal.
Summary of two knowledge points of compulsory mathematics in senior two
There are only three positional relationships between two straight lines in space: parallel, intersecting and nonplanar.
According to whether * * * surface can be divided into two categories:
(1)*** plane: parallel intersection.
(2) Different planes:
Definition of non-planar straight lines: two different straight lines on any plane are neither parallel nor intersecting.
Judgment theorem of out-of-plane straight line: use the straight line between a point in the plane and a point out of the plane, and the straight line in the plane that does not pass through this point is the out-of-plane straight line.
The angle formed by two straight lines on different planes: the range is (0,90) esp. Space vector method
Distance between two straight lines in different planes: common vertical line segment (only one) esp. Space vector method
From the point of view of whether they have something in common, they can be divided into two categories:
(1) has only one thing in common-intersecting straight lines; (2) There is nothing in common-parallel or non-parallel.
The positional relationship between a straight line and a plane:
There are only three positional relationships between a straight line and a plane: within the plane, intersecting the plane and parallel to the plane.
(1) The straight line is in the plane-there are countless things in common.
(2) A straight line intersects a plane-there is only one common point.
Angle between a straight line and a plane: the acute angle formed by the diagonal of a plane and its projection on the plane.
Space vector method (finding the normal vector of a plane)
Provisions: a, when the straight line is perpendicular to the plane, the angle formed is a right angle; B, when the line is parallel or in the plane, the angle is 0.
The included angle between the straight line and the plane is [0,90].
Minimum angle theorem: the angle formed by the diagonal line and the plane is the smallest angle between the diagonal line and any straight line in the plane.
Three Verticality Theorems and Inverse Theorems: If a straight line in a plane is perpendicular to the projection of a diagonal line in this plane, it is also perpendicular to this diagonal line.
This line is perpendicular to the plane.
Definition of vertical line and plane: If straight line A is perpendicular to any straight line in the plane, we say that straight line A and plane are perpendicular to each other. The straight line A is called the perpendicular of the plane, and the plane is called the vertical plane of the straight line A. ..
Theorem for judging whether a straight line is perpendicular to a plane: If a straight line is perpendicular to two intersecting straight lines in a plane, then the straight line is perpendicular to the plane.
Theorem of the property that straight lines are perpendicular to a plane: If two straight lines are perpendicular to a plane, then the two straight lines are parallel. ③ The straight line is parallel to the plane-there is nothing in common.
Definition of parallelism between straight line and plane: If straight line and plane have nothing in common, then we say that straight line and plane are parallel.
Theorem for determining the parallelism between a straight line and a plane: If a straight line out of the plane is parallel to a straight line in this plane, then this straight line is parallel to this plane.
Theorem of parallelism between straight lines and planes: If a straight line is parallel to a plane and the plane passing through it intersects with this plane, then the straight line is parallel to the intersection line.
Summary of two knowledge points of compulsory mathematics in grade three and grade two of senior high school
Derivative is an important basic concept in calculus. When the independent variable x of the function =f(x) generates the increment δ x at the point x0, if there is a limit a of the ratio of the increment δ of the output value of the function to the increment δ x of the independent variable when δ x approaches 0, then A is the derivative at x0, which is denoted as f'(x0) or df(x0)/dx. Derivative is the local property of function. The derivative of a function at a certain point describes the rate of change of the function near that point. If the independent variables and values of the function are real numbers, then the derivative of the function at a certain point is the tangent slope of the curve represented by the function at that point. The essence of derivative is the local linear approximation of function through the concept of limit. For example, in kinematics, the derivative of the displacement of an object with respect to time is the instantaneous velocity of the object.
Not all functions have derivatives, and a function does not necessarily have derivatives at all points. If the derivative of a function exists at a certain point, it is said to be derivative at this point, otherwise it is called non-derivative. However, the differentiable function must be continuous; Discontinuous functions must be non-differentiable.
For the derivative function f(x), xf'(x) is also a function, which is called the derivative function of f(x). The process of finding the derivative of a known function at a certain point or its derivative function is called derivative. Derivative is essentially a process of finding the limit, and the four algorithms of derivative are also among the four algorithms of limit. Conversely, the known derivative function can also reverse the original function, that is, indefinite integral. The basic theorem of calculus shows that finding the original function is equivalent to integral. Derivation and integration are a pair of reciprocal operations, both of which are the most basic concepts in calculus.
Let the function =f(x) be defined in the neighborhood of point x0. When the independent variable x has an increment Δ x at x0 and (x0+Δ x) is also in the neighborhood, the corresponding function gets the increment Δ = f (x0+Δ x)-f (x0); If the ratio of Δ to Δ x has a limit when Δ x→ 0, the function =f(x) can be derived at point x0, and the derivative of this limit at point x0 is denoted as f'(x0), or as' │x=x0 or d/dx│x=x0.
Summary of two knowledge points of compulsory mathematics in senior four and senior two.
Linear inclination angle:
Definition: The angle between the positive direction of the X axis and the upward direction of the straight line is called the inclination angle of the straight line. In particular, when a straight line is parallel or coincident with the X axis, we specify that its inclination angle is 0 degrees. Therefore, the range of inclination angle is 0 ≤α.