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.
(4) Characteristics of the coordinates of points on a straight line parallel to the coordinate axis
The ordinate of each point on the straight line parallel to the X axis is the same.
The abscissa of each point on the straight line parallel to the Y axis is the same.
(5) Coordinate characteristics of points symmetrical about the X axis, Y axis or origin.
The abscissa of point P and point P' is equal to the X axis, and the ordinate is opposite, that is, the symmetrical point of point P(x, y) relative to the X axis is P'(x, -y).
The axisymmetrical ordinate of point P and point P' with respect to Y is equal, and the abscissa is opposite, that is, the symmetrical point of point P(x, y) with respect to Y axis is P'(-x, y).
Point P and point P' are symmetrical about the origin, and the abscissa and ordinate are opposite, that is, the symmetrical point of point P(x, y) about the origin is P'(-x, -y).
Summary of Mathematics Review Methods in Grade Two of Junior High School
First, junior high school math exam review method:
Mathematician Hua once said: "Cleverness lies in learning, and genius lies in diligence." Diligence is good training, and one effort is one talent.
1. Review must be diligent.
Diligent hands-on: Don't look at the questions, count them, and write down the knowledge points that you can't, and write them down in a notebook.
Diligent: No, you must ask the teacher if you have any questions. Time waits for no one, there is no time to waste. And learn to discuss problems with classmates.
Be diligent: Be sure to listen to the teacher's review class. Don't think that this problem is solved, and the teacher can slip the number. You should know that you can learn new things by looking back on the past.
Think hard: be good at thinking and think positively-absorb and store information.
Exercise your legs regularly: Don't take part in too intense exercise to prevent injuries from affecting your study, but keep exercising, jog for 30 minutes every day and report to the country.
2. Junior high school math review should also emphasize two points:
One is to do, and the other is to use your head.
Thinking is to learn to observe and analyze problems, learn to think, don't just do problems, find the connection between known and unknown, ask more why, and know more about what knowledge points to test.
Hands-on is to practice more, do more problems, and never leave your mouth. Students just stick to the subject. These two points should be remembered and adhered to. Only through thinking and action can the efficiency of the brain be fully exerted. This is also the teacher's experience.
Step 3 do it with your heart three times
Listen carefully in class: listen to the teacher's knowledge about methods and so on
Hand-made: do it according to the teacher's idea and see if the effect is good.
Think carefully: think about why you did it and what knowledge you took.
4. Pay attention to the simple learning process
Reading a textbook well is the main basis for teaching and senior high school entrance examination;
The knowledge of note-taking methods is the crystallization of teachers' years of experience, and everyone prepares a set of wrong questions;
Do a good job of cleaning up a problem set, which is to broaden the knowledge;
These seemingly ordinary and simple, but it is a true portrayal of the teacher's personal experience and careful observation of our senior high school entrance examination and college entrance examination. In fact, what they repeat every day is not what the teacher just said.
There is no magical power, only ordinary. The most valuable thing is persistence.
If resources are available, find several sets of final exam questions in previous years, all from your own county and other counties (the test sites are similar). Within the specified time, find out the bottom, be familiar with the questions in each chapter, and practice the efficiency of doing the questions yourself. Many students make mistakes in exercises for the first time. If they don't correct and reflect in time, but only correct their answers, then they don't really understand where they are wrong or how to apply this knowledge, which will eventually lead to similar problems in the future.
Shanghai science edition eighth grade mathematics knowledge points summary related articles;
★ Shanghai Science Edition Grade 8 Volume I Mathematics Review Outline
★ Knowledge points of Grade 8 Mathematics Shanghai Science Edition
★ Eight Grade Mathematics Knowledge Points Shanghai Campus Edition
★ Grade 8 Mathematics Review Knowledge Outline Volume I Shanghai Sub-volume
★ Sort out and summarize the knowledge points of eighth grade mathematics.
★ Summary of Junior High School Mathematics Knowledge Points (Shanghai Science Edition)
★ Knowledge points of the first volume of eighth grade mathematics in Shanghai Science Edition
★ The first volume of eighth grade mathematics review materials.
★ Review Outline of Grade Eight Mathematics in Shanghai.
★ Summary of the knowledge points in the first volume of the second grade mathematics.