Without double diligence, there is no talent, no genius. Genius is actually a person who can persevere. Diligence is a kind of good training, one point of hard work and one point of talent, and diligence has always been the best shortcut to success in learning. Here are some math knowledge points I have compiled for you, hoping to help you.

Mathematics knowledge points in the new semester of grade three

One-dimensional linear equation:

(1) In an equation, there is only one unknown, and the exponent of this unknown is

1, such an equation is called a linear equation.

② Adding or subtracting or multiplying or dividing (non-0) an algebraic expression on both sides of the equation at the same time, the result is still an equation.

Steps to solve a linear equation with one variable:

Denominator is removed, items are shifted, similar items are merged, and the unknown coefficient is changed to 1.

Binary linear equation: An equation that contains two unknowns and whose terms are 1 is called binary linear equation.

Binary linear equations: The equations composed of two binary linear equations are called binary linear equations. A set of unknown values suitable for binary linear equation is called the solution of this binary linear equation. The common * * * solution of each equation in a binary linear system of equations is called the solution of this binary linear system of equations.

Methods of solving binary linear equations: substitution elimination method/addition and subtraction elimination method.

2. Inequality and unequal groups

Inequality:

Formulas connected by "=" symbols are called inequalities.

② Add or subtract the same algebraic expression on both sides of the inequality, and the direction of the inequality remains unchanged.

③ Both sides of inequality are multiplied or divided by a positive number, and the direction of inequality remains unchanged.

④ Both sides of inequality are multiplied or divided by the same negative number, and the unequal numbers are in opposite directions.

Solution set of inequality;

(1) can make the value of an unknown inequality known as the solution of inequality.

(2) All solutions of an inequality with unknowns constitute the solution set of this inequality.

③ The process of finding the solution set of inequality is called solving inequality.

One-dimensional linear inequality: an inequality with algebraic expressions on both sides and only one unknown number of degree 1 is called one-dimensional linear inequality.

One-dimensional linear inequality system;

(1) Several linear inequalities about the same unknown quantity are combined into a linear inequality group.

② The common part of the solution set of each inequality in a linear inequality group is called the solution set of this linear inequality group.

③ The process of finding the solution set of inequality group is called solving inequality group.

3. Function

Variable: dependent variable, independent variable. When using images to represent the relationship between variables, we usually use points on the horizontal axis as independent variables and points on the vertical axis as dependent variables.

Linear function:

(1) If the relationship between two variables X and Y can be expressed as y = kx+b (where B is constant and K is not equal to 0), then Y is said to be a linear function of X..

When B=0, y is said to be a proportional function of X. ..

Linear function image:

① Take the values of the independent variable X and the corresponding dependent variable Y of a function as the abscissa and ordinate of a point respectively, and trace the corresponding point in the rectangular coordinate system. A graph composed of all these points is called an image of a function.

② The image with the proportional function Y=KX is a straight line passing through the origin.

③ In a linear function, when k < 0 and b < 0, it passes through 234 quadrants; When k < 0, b > 0, pass through quadrant124; When k > 0 and b < 0, pass through quadrant134; When k > 0 and b > 0, pass through quadrant 123.

④ When k > 0, y value increases with the increase of x value, and when x < 0, y value decreases with the increase of x value.

Induction of knowledge points in the first volume of mathematics in grade three

Binary linear equations

1. Definition: An integral equation with two unknowns whose degree is 1 is called a binary linear equation.

2. The solution of binary linear equations

(1) substitution method

The equations composed of a quadratic equation and a linear equation are usually solved by method of substitution, which is the basic method of elimination and simplification.

(2) Factor decomposition method

In binary quadratic equation, when at least one equation can be decomposed, it can be solved by factorization, eliminating elements and reducing order.

(3) Matching method

A formula, or a part of a formula, is transformed into a completely flat road or the sum of several completely flat roads through constant deformation.

(4) Vieta's law.

Through the inverse theorem of Vieta's theorem, we can use the sum-product relation of two numbers to construct a quadratic equation with one variable.

(5) Constant elimination method

When the first term is missing in both equations, it can be solved by eliminating the constant term.

Solve a quadratic equation with one variable

The basic idea of solving quadratic equations with one variable is to simplify them into two quadratic equations with one variable.

1, direct Kaiping method:

The equation in the form of (x-m)2=n(n≥0) is solved by direct Kaiping method, and its solution is x = m. 。

Direct Kaiping method is the inverse operation of square, and the result is usually expressed by root sign.

2. Matching method

The method of obtaining the root of a quadratic equation by matching it completely flat. The solution of this unary quadratic equation is called collocation method, and the formula is based on the complete square formula.

(1) transformation: transform the quadratic equation of one variable into the form of ax 2+bx+c = 0 (that is, the general form of the quadratic equation of one variable).

(2) Coefficient 1: convert the quadratic term into 1.

(3) Move the term: move the constant term to the right of the equal sign.

(4) Formula: The left and right sides of the equal sign are added with the square of half of the first coefficient.

(5) Deformation: Write the algebraic expression on the left of the equal sign as a complete square.

(6) Square root: simultaneous square root.

(7) Solution: The root of the original equation can be obtained by sorting.

3. Formula method

Formula method: Convert the quadratic equation of one variable into a general form, and then calculate the value of the discriminant △=b2-4ac. When b2-4ac≥0, substitute the values of the coefficients A, B and C into the formula x=(b2-4ac≥0) to get the root of the equation.

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.

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".

Third grade mathematics people's education edition knowledge point induction related articles;

★ People's Education Edition third grade mathematics knowledge points induction

★ Summary of ninth grade mathematics knowledge points in People's Education Edition

★ ninth grade people's education edition mathematics knowledge point arrangement

★ Summary of Physics Knowledge Points in Grade Three (Full Edition)

★ Outline of Mathematics Review in Volume II of Grade 9 of People's Education Edition

★ Encyclopedia of Mathematics Learning Methods in Different Grades

★ The latest summary of mathematics knowledge points in Grade Three.

★ Summary of ninth grade mathematics knowledge points

★ Review materials of mathematics knowledge in senior high school entrance examination of PEP.

★ Important knowledge points of ninth grade mathematics

var _ HMT = _ HMT | |[]； (function(){ var hm = document . createelement(" script ")； hm.src = "/hm.js？ 3b 57837d 30 f 874 be 5607 a 657 c 67 1896 b "； var s = document . getelementsbytagname(" script ")[0]； s.parentNode.insertBefore(hm，s)； })();