Induction of a compulsory knowledge point in senior high school mathematics
Mathematics required for senior one 1 knowledge point induction (1)
The Meaning and Expression of 1. Set
1, the meaning of set: a set is the sum of some different things, and people can realize these things and judge whether a given thing belongs to the whole.
The research objects are collectively called elements, and the whole composed of some elements is called set, which is called set for short.
2. Three characteristics of elements in a set:
(1) Determinism of elements: If the set is certain, then whether an element belongs to this set is certain: yes or no.
(2) Mutual dissimilarity of elements: the elements in a given set are affirmative and unrepeatable.
(3) The disorder of elements: the position of elements in the set can be changed, and changing the position does not affect the set.
3. Representation of set: {…}
(1) indicates the set in capital letters: A={ basketball players in our school}, B={ 1, 2,3,4,5}.
(2) Representation of sets: enumeration and description.
Enumeration: Enumerate the elements in the set one by one {a, B, c...}
B, description method:
① Interval method: describe the common attributes of the elements in the set, and write them in braces to represent the set.
{x？ r | x-3 & gt； 2}，{ x | x-3 & gt； 2}
② Language description: Example: {A triangle that is not a right triangle}
③ venn diagram: Draw a closed curve, which represents the set.
4, the classification of the set:
(1) finite set: a set with finite elements.
(2) Infinite set: a set containing infinite elements.
(3) Empty set: a set without any elements.
5, the relationship between elements and sets:
(1) If an element is in a set, it belongs to the set, that is, a? A
(2) If the element is not in the set, it does not belong to the set, that is, a ￠ a
Note: Commonly used digit sets and their symbols:
The set of nonnegative integers (i.e. natural number set) is recorded as n.
Positive integer set N* or N+
Integer set z
Rational number set q
Real number set r
Mathematics required for senior one 1 knowledge point induction (2)
Structural characteristics of 1, column, cone, platform and ball
(1) prism:
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: 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) 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: 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: A Zhou Suocheng is rotated with a right-angled side of a 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 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: 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 with the diameter of the semicircle as the rotation axis and the semicircle surface rotating 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.
3. Intuition of space geometry-oblique two-dimensional drawing method.
The characteristics of oblique bisection method are as follows: ① The line segment originally parallel to the X axis is still parallel to X, and its length remains unchanged;
② The line segment originally parallel to the Y axis is still parallel to Y, and its 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.
Mathematics required for senior one 1 knowledge point induction (3)
(1) inclination angle of straight line
Definition: The angle formed by the positive direction of the X axis and the upward direction of the straight line is called the inclination angle of the straight line. Especially when the 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.
(2) the slope of the straight line
① Definition: The tangent of a straight line whose inclination angle is not 90 is called the slope of the straight line. The slope of a straight line is often expressed by k, that is, the slope reflects the inclination of the straight line and the axis.
At that time,; At that time,; It didn't exist then.
② Slope formula of straight line passing through two points:
Pay attention to the following four points: (1) At that time, the right side of the formula was meaningless, the slope of the straight line did not exist, and the inclination angle was 90;
(2)k has nothing to do with the order of P 1 and P2; (3) The slope can be obtained directly from the coordinates of two points on a straight line without inclination angle;
(4) The inclination angle of a straight line can be obtained by calculating the slope through the coordinates of two points on the straight line.
(3) Linear equation
① Point-oblique type: the slope of the straight line is k, passing through the point.
Note: When the slope of the straight line is 0, k=0, and the equation of the straight line is y=y 1.
When the slope of the straight line is 90, the slope of the straight line does not exist, and its equation can not be expressed by point inclination. However, because the abscissa of each point on L is equal to x 1, its equation is x=x 1.
② Oblique section: the slope of the straight line is k, and the intercept of the straight line on the Y axis is b..
③ Two-point formula: () Two points on a straight line,
(4) Cutting torque type:
Where the straight line intersects the axis at the point and intersects the axis at the point, that is, the intercepts with the axis and the axis are respectively.
⑤ General formula: (A, B are not all 0)
Note: Various equations with special application scope, such as:
A straight line parallel to the X axis: (b is a constant); A straight line parallel to the Y axis: (A is a constant);
(5) Linear system equation: that is, a straight line with some * * * property.
(1) parallel linear system
A linear system parallel to a known straight line (a constant that is not all zero): (c is a constant)
(2) Vertical linear system
A linear system perpendicular to a known straight line (a constant that is not all zero): (c is a constant)
(3) A linear system passing through a fixed point
(i) Linear system with slope k: a straight line passes through a fixed point;
(ii) The equation of the line system at the intersection of two lines is
(is a parameter), where the straight line is not in the straight line system.
(6) Two straight lines are parallel and vertical.
Note: When judging the parallelism and verticality of a straight line with slope, we should pay attention to the existence of slope.
(7) The intersection of two straight lines
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The coordinates of the intersection point are the solutions of a set of equations.
These equations have no solution; The equation has many solutions and coincidences.
(8) Distance formula between two points: Let it be two points in the plane rectangular coordinate system.
(9) Distance formula from point to straight line: distance from point to straight line.
(10) Distance formula of two parallel straight lines
Take any point on any straight line and then convert it into the distance from the point to the straight line to solve it.
A compulsory catalogue of mathematics for senior one.
The first chapter is the concept of set and function.
1. 1 set
The number of elements in the reading and thinking set
1.2 function and its representation
The development of the concept of reading and thinking function
Basic properties of 1.3 function
The application of information technology draws function images with computers.
Practice homework
summary
Chapter II Basic Elementary Functions (Ⅰ)
2. 1 exponential function
The application of information technology explores the properties of exponential function with the help of information technology
2.2 Logarithmic function
Reading and thinking about the invention of logarithm
The exploration also found the relationship between two function images which are mutually inverse functions.
2.3 power function
summary
Review reference questions
Chapter III Functional Application
3. 1 functions and equations
Reading and thinking on solving equations in Chinese and foreign history
The application of information technology depends on the approximate solution of information technology equation.
3.2 Functional model and its application
Information technology applications collect data and build functional models.
Practice homework
summary
Review reference questions