catalogue
Knowledge points of plane vector in senior one mathematics.
Senior one mathematics knowledge points
Mathematics learning methods in senior one.
Knowledge point vector of mathematics plane vector in senior one: both size and direction.
Quantity: only size, no directional quantity.
Three elements of a directed line segment: starting point, direction and length.
Zero vector: length vector.
Unit vector: A vector with a length equal to the unit.
Equal vector: a vector with equal length and same direction.
& vector operation
Add operation
AB+BC=AC, this calculation rule is called triangle rule of vector addition.
It is known that the two vectors OA and OB starting from the same point O are parallelogram OACB, and the diagonal OC starting from O is the sum of the vectors OA and OB. This calculation method is called parallelogram rule of vector addition.
For zero vector and arbitrary vector a, there are: 0+a = a+0 = a.
|a+b|≤|a|+|b| .
The addition of vectors satisfies all the laws of addition.
subtraction
The vector with the same length and opposite direction as A is called the inverse quantity of A, -(-a)=a, and the inverse quantity of zero vector is still zero vector.
( 1)a+(-a)=(-a)+a = 0(2)a-b = a+(-b).
multiply operation
The product of real number λ and vector A is a vector, and this operation is called vector multiplication, which is denoted as λa, | λa | = | λ| A|. When λ > 0, the direction of λ A is the same as that of A. When λ
Let λ and μ be real numbers, then: (1) (λ μ) a = λ (μ a) (2) (λ μ) a = λ μ a (3) λ (ab) = λ a λ b (4) (-λ) a =-(λ a).
The addition, subtraction and multiplication of vectors are collectively called linear operations.
Quantity product of vector
Given two nonzero vectors a and b, then |a||b|cos θ is called the product or inner product of a and b, and is denoted as a? B, θ is the included angle between A and B, and |a|cos θ(|b|cos θ) is called the projection of vector A in direction B (B is in direction A). The product of zero vector and arbitrary vector is 0.
Geometric meaning of a.b: the product of a.b is equal to the product of the length of a |a| and the projection of b in the direction of a |b|cosθ.
The product of two vectors equals the sum of the products of their corresponding coordinates.
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Structural characteristics of 1, column, cone, table and ball, the knowledge point of senior one mathematics.
(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 Pyramid
Definition: One face is a polygon, the other faces are triangles with a common vertex, and the geometric figure enclosed by these faces.
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 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) Cylinder:
Definition: Geometry surrounded by surfaces that rotate on one side of a rectangle and on 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: Geometry surrounded by the surface formed by the circle rotating 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 of a cone:
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.
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) and top view (from top to bottom)
Note: the front view reflects the position relationship of the object, that is, it reflects the height and length of the object;
The top view reflects the position relationship between the left and right of the object, that is, the length and width of the object;
The side view reflects the up-and-down and front-and-back positional relationship of the object, that is, it reflects the height and width of the object.
3. Intuition of space geometry-oblique two-dimensional drawing method.
Characteristics of oblique mapping;
(1) the original line segment parallel to the X axis is still parallel to X, with the same length;
② The line segment originally parallel to the Y axis is still parallel to Y, and its length is half of the original.
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High school mathematics learning methods Listen carefully and take notes.
It is very important to cultivate good listening habits in classroom teaching. Of course, listening is the main thing. Listening can help you concentrate. You should understand and listen to the key points of the teacher. Pay attention to thinking and analyzing problems when listening, but only listening without remembering, or just remembering without listening, it is inevitable to pay attention to one thing and lose sight of another, and the classroom efficiency is low. Therefore, we should take notes appropriately and purposefully to understand the main spirit and intention of the teacher in class. Scientific notes can improve the efficiency of a 45-minute class.
Grasp the textbook to understand.
Improve math ability, of course, through the classroom. We should make full use of the classroom. The process of mathematics learning in senior one is alive, so is the object of teachers' teaching, which changes with the development of teaching process, especially when teachers pay attention to ability teaching, the teaching materials can't be reflected. Mathematical ability is formed simultaneously with the occurrence of knowledge. Whether forming a concept, mastering a law or doing an exercise, we should cultivate and improve it from different ability angles. Through the teacher's teaching in the classroom, we can understand the position of what we have learned in the textbook and the relationship with the previous knowledge. Only by mastering the teaching materials can we master the initiative in learning.
Improve the agility of thinking
If there is no certain speed in math class, it is ineffective learning. Slow learning can't train the speed of thinking, the agility of thinking and the ability of mathematics, which requires that mathematics learning must have rhythm, so that over time, the agility of thinking and the ability of mathematics will gradually improve.
Avoid legacy problems
In math class, teachers usually ask questions and perform, sometimes accompanied by discussion, so they can hear a lot of information. These questions are very valuable. For those typical problems, problems with universality must be solved in time, and the symptoms of the problems cannot be left behind or even solved. Valuable problems should be grasped in time, and the remaining problems should be supplemented in a targeted manner and pay attention to practical results.
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Summary of knowledge points of plane vector in senior one mathematics;
★ Summary of knowledge points of plane vector in senior one mathematics.
★ Knowledge points of plane vectors in senior one mathematics.
★ Summary of compulsory 4-plane vector knowledge points in senior high school mathematics.
★ Mathematics required 4 vector formula induction
★ Analysis of knowledge points of plane vector in senior one mathematics.
★ Summary of mathematics knowledge points in senior three and senior one.
★ Summary of compulsory 4-plane vector formula in mathematics
★ Four required knowledge points of plane vector in senior high school mathematics
★ Summary and induction of mathematics knowledge points in senior one.
★ High school mathematics plane analytic geometry knowledge points induction.
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