Summary of knowledge points in the first volume of junior two mathematics
Triangle knowledge point
1, the corresponding sides and angles of congruent triangles are equal.
2. The Angle and Edge Axiom (SAS) has two congruent equilateral triangles.
3. Angle and Angle Axiom (ASA) has congruences between two triangles and two angles and their corresponding edges.
4. Inference (AAS) has two angles, and the opposite side of one angle corresponds to the congruence of two triangles.
5. The edge axiom (SSS) has two triangles and three corresponding equilateral sides.
6. Axiom of hypotenuse and right-angled edge (HL) Two right-angled triangles with hypotenuse and a right-angled edge are congruent.
7. Theorem 1 The distance between a point on the bisector of an angle and both sides of the angle is equal.
8. Theorem 2 The point where two sides of an angle are equidistant is on the bisector of this angle.
9. The bisector of an angle is the set of all points with equal distance to both sides of the angle.
10, the property theorem of isosceles triangle, the two base angles of isosceles triangle are equal (that is, equilateral and equilateral).
Knowledge points of functions and equations
1, a linear function is also called a linear function, which is generally represented by a straight line on the x and y coordinate axes. When the value of one variable in a linear function is determined, the value of another variable can be solved by a linear equation.
2. Any one-dimensional linear equation can be transformed into the form of ax+b=0 (A, B is constant, a≠0), so solving one-dimensional linear equation can be transformed into: when a linear function value is 0, find the value of the corresponding independent variable (from the digital point of view); From the image point of view, it is equivalent to knowing the straight line y=ax+b and determining the value of the abscissa of its intersection with the X axis (from the shape point of view).
3. Using the function image to solve the equation: -2x+2=0 can be transformed into finding the abscissa of the intersection of the linear function y=-2x+2 and the X axis. And the abscissa of the intersection of y=-2x+2 and X axis is 1, then the solution of equation -2x+2=0 is x= 1.
Note: Solving the unary linear equation ax+b=0(a≠0) and finding the abscissa of the intersection of the image and the function y=ax+b(a≠0) are the same problem. The difference is that the former solves the problem from the angle of number, while the latter solves the problem from the angle of form.
4. Each set of binary linear equations corresponds to two linear functions. From the numerical point of view, solving equations is equivalent to considering the values of two functions when the independent variables are equal and what the functions are; Formally speaking, solving the equation is equivalent to determining the coordinates of the intersection of two straight lines, so that the equation can be solved.
5. The simplest method to solve linear function is list method. Take the coordinates of two points that satisfy a linear function expression and determine the value of another unknown. There is another way to trace it. Generally take two points. According to the principle that two points determine a straight line, it can also be called "two-point method". Generally, the image of y=kx+b(k≠0) can be drawn after (0, b) and (-b/k, 0).
Induction of knowledge points in the first volume of junior two mathematics
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) 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) The characteristics of the coordinates 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) Coordinate characteristics 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).
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.
Math review method in junior two
orderly
Mathematics is an interlocking subject, and any link will affect the whole learning process. Therefore, don't be greedy when studying. You should pass the exam chapter by chapter, and don't leave questions that you don't understand or understand deeply easily.
Emphasize understanding
Concepts, theorems and formulas should be memorized on the basis of understanding. Every time you learn a new theorem, first try to do an example without looking at the answer to see if you can correctly apply the new theorem; If not, compare the answers to deepen the understanding of the theorem.
basic skill
You can't learn mathematics without training. Usually do more exercises with moderate difficulty. Of course, don't fall into the misunderstanding of dead drilling questions, be familiar with the questions of the college entrance examination, and be targeted in training.
Pay attention to mistakes
Booking the wrong book and collecting the wrong questions by yourself is often your weakness. When reviewing, this wrong book has become a valuable review material.
Mathematics learning is a step-by-step process, and it is unrealistic to dream of reaching the sky in one step. After reciting the contents of the book, carefully write the exercises at the back of the book. Some students may think that the exercises after the book are too simple to do. This idea is highly undesirable. The function of the exercises after the book is not only to help you remember the contents in the book, but also to help you standardize the writing format, make your problem-solving structure compact and tidy, make proper use of formulas and theorems, and reduce unnecessary marks in the exam.
The usual mathematical research:
○ 1 preview carefully before class. The purpose of preview is to listen to the teacher better. Through preview, the mastery level should reach 80%. Listen to the teacher answer these questions with questions that you don't understand in the preview. Preview can also improve the overall efficiency of attending classes. Specific preview method: finish the topics in the book and draw the knowledge points. The whole process lasts about 10.
○2 Let math class combine with practice. It's no use just listening in math class. When the teacher asks the students to do calculus on the blackboard, they should also practice on the draft paper. You must ask questions you don't understand, or you may not do it if you encounter similar problems in the exam. When listening to the teacher's lecture, you must concentrate on the details, otherwise, "the embankment of a thousand miles will collapse in the ant nest."
○3 Review in time after class. After finishing your homework, sort out what the teacher said that day, and you can do extracurricular problems for about 25 minutes. You can choose the extracurricular books that suit you according to your own needs. The content of the extracurricular problem is probably today's class.
The fourth unit test is to test your recent study. In fact, the score represents your past. The key is to sum up and learn from each exam so that you can do better in the mid-term and final exams. Teachers often take exams without notice and review them in time after class.
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