Induction of mathematical knowledge points in the last semester of senior two.
Triangular knowledge concept
1, triangle: A figure composed of three line segments that are not on the same line end to end is called a triangle.
2. Trilateral relationship: the sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side.
3. Height: Draw a vertical line from the vertex of the triangle to the line where the opposite side is located, and the line segment between the vertex and the vertical foot is called the height of the triangle.
4. midline: in a triangle, the line segment connecting the vertex and its relative midpoint is called the midline of the triangle.
5. Angular bisector: The bisector of the inner angle of a triangle intersects the opposite side of this angle, and the line segment between the vertex and the intersection of this angle is called the angular bisector of the triangle.
6. Stability of triangle: The shape of triangle is fixed, and this property of triangle is called stability of triangle.
7. Polygon: On the plane, a figure composed of some line segments connected end to end is called polygon.
8. Interior Angle of Polygon: The angle formed by two adjacent sides of a polygon is called its interior angle.
9. Exterior angle of polygon: The angle formed by the extension line of one side of polygon and its adjacent side is called the exterior angle of polygon.
10, diagonal of polygon: the line segment connecting two non-adjacent vertices of polygon is called diagonal of polygon.
1 1, regular polygon: a polygon with equal angles and sides in a plane is called a regular polygon.
12, plane mosaic: a part of the plane is completely covered by some non-overlapping polygons, which is called covering the plane with polygons.
13, formula and properties:
(1) Sum of internal angles of triangle: The sum of internal angles of triangle is 180.
(2) the nature of the triangle exterior angle:
Property 1: One outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it.
Property 2: The outer angle of a triangle is larger than any inner angle that is not adjacent to it.
(3) The formula of the sum of polygon internal angles: Is the sum of polygon internal angles equal to? 180
(4) Sum of polygon external angles: the sum of polygon external angles is 360.
(5) Number of diagonal lines of a polygon: ① Starting from a vertex of a polygon, a diagonal line can be drawn to divide the polygon into triangles. ② The polygon * * * has a diagonal line.
Position and coordinates
1, determine the location
In a plane, two data are usually needed to determine the position of an object.
2. Plane rectangular coordinate system
Meaning: In a plane, two mutually perpendicular axes with a common origin form a plane rectangular coordinate system.
(2) Usually, the two number axes are placed in horizontal and vertical positions respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, and the vertical axis is called Y axis and vertical axis, both of which are collectively called coordinate axes, and their common origin O is called the origin of rectangular coordinate system.
③ Establish a plane rectangular coordinate system, and the points on the plane can be represented by a set of ordered real number pairs.
(4) In the plane rectangular coordinate system, two coordinate axes divide the coordinate plane into four parts, the upper right part is called the first quadrant, and the other three parts are called the second quadrant, the third quadrant and the fourth quadrant counterclockwise, and the points on the coordinate axes are not in any quadrant.
⑤ In the rectangular coordinate system, for any point on the plane, there is an ordered real number pair (that is, the coordinates of the point) corresponding to it; On the contrary, for any ordered real number pair, there is a point on the plane corresponding to it.
3. Axisymmetry and coordinate changes
Regarding the coordinates of two points about the axis symmetry of X, the abscissa is the same, and the ordinate is opposite; With regard to the coordinates of two points symmetrical about the Y axis, the ordinate is the same, and the abscissa is opposite.
Eighth grade mathematics knowledge point book 1
First of all, in a plane, two data are usually needed to determine the position of an object.
Second, the plane rectangular coordinate system and related concepts
1, plane rectangular coordinate system
In a plane, two mutually perpendicular axes with a common origin form a plane rectangular coordinate system. Among them, the horizontal axis is called X axis or horizontal axis, and the right direction is the positive direction; The vertical axis is called Y axis or vertical axis, and the orientation is positive; The x-axis and y-axis are collectively referred to as coordinate axes. Their common origin o is called the origin of rectangular coordinate system; The plane on which the rectangular coordinate system is established is called the coordinate plane.
2. In order to describe the position of a point in the coordinate plane conveniently, the coordinate plane is divided into four parts, namely the first quadrant, the second quadrant, the third quadrant and the fourth quadrant.
Note: The points on the X axis and Y axis (points on the coordinate axis) do not belong to any quadrant.
3. The concept of point coordinates
For any point P on the plane, the intersection point P is perpendicular to the X-axis and Y-axis respectively, and the numbers A and B corresponding to the vertical feet on the X-axis and Y-axis are respectively called the abscissa and ordinate of the point P, and the ordered number pair (A, B) is called the coordinate of the point P. ..
The coordinates of points are represented by (a, b), and the order is abscissa before, ordinate after, and there is a ","in the middle. The positions of horizontal and vertical coordinates cannot be reversed. The coordinates of points on the plane are ordered real number pairs. At that time, (a, b) and (b, a) were the coordinates of two different points.
There is a one-to-one correspondence between points on the plane and ordered real number pairs.
4. Coordinate characteristics of different locations
(1), the coordinate characteristics of the midpoint of each quadrant.
Point P(x, y) is in the first quadrant: x; 0，y； 0
Point P(x, y) is in the second quadrant: x; 0，y； 0
Point P(x, y) is in the third quadrant: x; 0，y； 0
Point P(x, y) is in the fourth quadrant: x; 0，y； 0
(2) Characteristics of points on the coordinate axis
The point P(x, y) is on the x axis, y=0, and x is an arbitrary real number.
The point P(x, y) is on the y axis, x=0, and y is an arbitrary real number.
Point P(x, y) is on both X and Y axes, and both X and Y are zero, that is, the coordinate of point P is (0,0), that is, the origin.
(3) Coordinate characteristics of points on the bisector of two coordinate axes.
Point P(x, y) is on the bisector of the first and third quadrants (straight line y=x), and x and y are equal.
Point P(x, y) is on the bisector of the second and fourth quadrants, and x and y are reciprocal.
Math review method in junior two
(1) Organize the knowledge and methods learned this semester: 1. Chapters 1 and 7 are geometry parts. These three chapters mainly introduce the application of Pythagorean theorem, the nature and discrimination of parallel lines, the theorem of triangle interior angle sum and its application. So remember that nature is the key, learning to judge is the key, and flexible use is the goal. To learn the choice of judgment methods, the differences and connections between different figures should be very familiar and form an organic whole. Practice and summarize common proof questions. 2. Chapter 456 is mainly about the teaching of concepts. Students may not be familiar with these chapters. Therefore, it is necessary to focus on the training questions synchronized with the teaching materials, and list or draw them so that students can actively operate and draw conclusions. In class, teachers should give as many lectures and practice as possible, and do as much as they should. Students should try their best to summarize the common analysis methods of geometry problem demonstration. 3. The second chapter is mainly about calculation. Teachers review concepts, properties and methods in advance, add appropriate exercises and practice calculations. Explain the easy-to-mistake problems one by one in class, and emphasize the pertinence of problem-solving methods. Finally, in view of the problems existing in the usual practice, check for leaks and fill gaps.
(2) In the problem-solving activities you have experienced, choose a challenging problem and write down the problem-solving process, including the difficulties encountered, the methods and processes to overcome the difficulties and the experience gained, and choose the reasons for this problem.
(3) Ask the students to sum up the harvest of this semester's mathematics study; Where improvement is needed.
Summary of knowledge points of mathematics department of senior two;
★ Guidance of eighth grade learning methods
★ Knowledge points in the second volume of Grade Two Mathematics compiled by the Ministry
★ Grade 8 Mathematics Review Knowledge Outline Volume I Shanghai Sub-volume
★ The Department compiles the second volume of Grade 8, and arranges the knowledge points in Lesson 8.
★ Make up the seventh volume of the second volume of the eighth grade and sort out the knowledge points.
★? Learning method guidance
★ Best learning method recommendation
★ Encyclopedia of seventh grade mathematics knowledge points