Sorting out the knowledge points of ninth grade mathematics
Space and graphics
Understanding of graphics:
1, point, line, surface
Points, lines and faces:
① Graphics are composed of points, lines and surfaces.
(2) The line where the surface intersects and the point where the line intersects.
(3) Points become lines, lines become surfaces, and surfaces become bodies.
Expand and collapse:
(1) In a prism, the intersection of any two adjacent faces is called an edge, and a side is the intersection of two adjacent edges. All sides of the prism have the same length, the upper and lower bottom surfaces of the prism have the same shape, and the side surfaces are cuboids.
(2) N prism is a prism with N faces on its bottom.
Cutting a geometric figure: cutting a figure with a plane, and the cutting surface is called a section.
Views: main view, left view and top view.
Polygon: It is a closed figure composed of some line segments that are not on the same straight line.
Arc, sector:
(1) A graph consisting of an arc and two radii passing through the end of the arc is called a sector.
② The circle can be divided into several sectors.
corner
Line:
① A line segment has two endpoints.
(2) The line segment extends infinitely in one direction to form a ray. A ray has only one endpoint.
③ A straight line is formed by the infinite extension of both ends of a line segment. A straight line has no end.
Only one straight line passes through two points.
Comparison length:
① Of all the connecting lines between two points, the line segment is the shortest.
② The length of the line segment between two points is called the distance between these two points.
Measurement and representation of angles;
The (1) angle consists of two rays with a common endpoint, and the common endpoint of the two rays is the vertex of the angle.
② One degree of 1/60 is one minute, and one minute of1/60 is one second.
Angle comparison:
The angle (1) can also be regarded as a light rotating around its endpoint.
(2) The ray rotates around its endpoint. When the ending edge and the starting edge are on a straight line, the angle formed is called a right angle. The starting edge continues to rotate, and when it coincides with the starting edge again, the angle formed is called fillet.
(3) The ray from the vertex of an angle divides the angle into two equal angles, and this ray is called the bisector of the angle.
Sorting out the knowledge points of ninth grade mathematics
algebraic expression
1, algebraic formula and rational formula
Formulas that associate numbers or letters representing numbers with operational symbols are called algebraic expressions. A single number or letter is also algebraic.
Algebraic expressions and fractions are collectively called rational forms.
2. Algebraic expressions and fractions
Algebraic expressions involving addition, subtraction, multiplication, division and multiplication are called rational expressions.
Rational expressions without division or division but without letters are called algebraic expressions.
Rational number formula has division, and there are letters in division, which is called fraction.
3, monomials and polynomials
Algebraic expressions without addition and subtraction are called monomials. (product of numbers and letters-including single numbers or letters)
The sum of several monomials is called polynomial.
Description:
(1) Distinguish algebraic expressions from fractional expressions according to whether there are letters in the division method; According to whether there are addition and subtraction operations in algebraic expressions, monomial and polynomial can be distinguished.
② When classifying algebraic expressions, the given algebraic expressions are taken as the object, not the deformed algebraic expressions.
4, similar projects and their merger
Conditions: ① The letters are the same; ② The indexes of the same letters are the same.
Basis of merger: law of multiplication and distribution.
5. Radical type
The algebraic expression of square root is called radical.
Algebraic expressions that involve square root operations on letters are called irrational expressions.
6. Similar quadratic root, simplest quadratic root, denominator of rational number.
After being transformed into the simplest quadratic root, the quadratic roots with the same number of roots are called similar quadratic roots.
The following conditions are satisfied: ① the factor of the root sign is an integer and the factor is an algebraic expression; (2) The number of roots does not include exhausted factors or factors.
Crossing out the root sign in the denominator is called denominator rationalization.
Mathematics learning methods in grade three
conceptual class
We should attach importance to the teaching process, actively experience the process of knowledge generation and development, find out the ins and outs of knowledge, understand the process of knowledge generation, understand the derivation process of formulas, theorems and laws, change the method of rote learning, and experience the fun of learning knowledge from the process of knowledge formation and development; In the process of solving the problem, I felt the joy of success.
Exercise class
It is necessary to master the trick of "I would rather watch it once, not do it once, not tell it once, not argue it once". In addition to listening to the teacher and watching the teacher do it, you should also do more exercises yourself, and you should actively and boldly tell everyone about your experience. When encountering problems, you should argue with your classmates and teachers, stick to the truth and correct your mistakes. Pay attention to the problem-solving thinking process displayed by the teacher in class, think more, explore more, try more, find creative proofs and solutions, and learn the problem-solving methods of "making a mountain out of a molehill", that is, take objective questions such as multiple-choice questions and fill-in-the-blank questions seriously, and never be careless, just like treating big questions, so as to write wonderfully; For a topic as big as a comprehensive question, we might as well decompose the "big" into "small" and take "retreat" as "advance", that is, decompose or retreat a relatively complex question into the simplest and most primitive one, think through these small questions and simple questions, find out the law, and then make a leap and further sublimation, thus forming a big question, that is, settle for second best. If we have this ability to decompose and synthesize, coupled with solid basic skills, what problems can't beat us?
recite
In the process of mathematics learning, we should have a clear review consciousness and gradually develop good review habits, so as to gradually learn to learn to learn. Mathematics review should be a reflective learning process. We should reflect on whether the knowledge and skills we have learned have reached the level required by the curriculum; It is necessary to reflect on what mathematical thinking methods are involved in learning, how these mathematical thinking methods are used, and what are the characteristics in the process of application; It is necessary to reflect on basic issues (including basic graphics, images, etc.). ), whether the typical problems have been really understood, and which problems can be attributed to these basic problems; We should reflect on our mistakes, find out the reasons and formulate corrective measures. In the new semester, we will prepare a "case card" for math learning, write down the mistakes we usually make, find out the "reasons" and prescribe a "prescription". We will often take it out and think about where the mistakes are, why they are wrong and how to correct them. Through your efforts, there will be no "cases" in your mathematics by the time of the senior high school entrance examination. And math review should be carried out in the process of applying math knowledge, so as to deepen understanding and develop ability. Therefore, in the new year, we should do a certain number of math exercises under the guidance of teachers, so as to draw inferences from others and use them skillfully to avoid the tactics of "practicing" rather than "repeating".
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