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1、数学概念大全(Encyclopedia of mathematical concepts)Junior high school mathematics concept Daquan(with ECNUEdition)Grade seven:Positive and negative:Zero is neither positive nor negative.Positive integer,zero and negative integer called integer,positive fraction and negative fraction fraction collectively.
2、Referred to as integer and fractional rational number.Put some numbers together,form a set of numbers,referred toas the number of sets.All positive integers and zeros number set is called the setof natural numbers.Axis:The provisions of the origin,is the direction and length ofthe line is called the
3、 axis.The number two that is on the axis,the total number of largenumber than the left.Positive numbers are greater than zero,negative numbers areless than zero,positive than negative.Opposite number:Only two the number of different symbols that are opposite,theopposition of zero is zero.Usually in
4、front of a number of add-，said that the numberof opposite number.In front of a number of add that is the number itself.Absolute value:The absolute value of a number of its own,the absolute valueof zero is zero.The absolute value of a negative number is the opposite of it.Size of a rational number:Tw
5、o negative,absolute value is large but small.Rational number addition:The same number of adding two numbers for the same symbol,andthe sum of absolute value.The absolute value of difference is not equal to the sum of thetwo numbers,the larger addend symbol to the absolute value ofabsolute value,and
6、with the larger absolute value of smallerreduction.Opposite number the sum of two numbers zero.A number of zero sum,this number is still the.A rational number by the symbol and the absolute value of twoparts,addition operations,and should pay attention todetermine the symbols and absolute value.Rati
7、onal number addition still satisfies the commutative lawof addition and combination of law.Commutative law of addition:two numbers,exchange addendposition,and invariant,(a+B=B+a)Associative law of addition:three numbers,the first twonumbers,or after the first two numbers,and the same.(a+b)+C=a+(B+C)
8、Subtraction rational number:Subtract a number,plus the opposite number is equal to thenumber.Rational number multiplication:The multiplication,if a factor into its opposite number,theproduct is contrary to the number of original product.The multiplication,the same number of positive,negativedifferen
9、ce,and the absolute value of multiplication.Any number of zero multiplication,all zero.Commutative law of multiplication:two number multiplicationfactor,exchange position,product the same.(AB=BA)Associative law,multiply three numbers,the first two monthsbefore or after the first number multiplicatio
10、n,multiply twonumbers,the same product.(AB)C=a(BC)Not equal to the number multiplied by zero,the number ofproduct symbols with negative factor decision,when thenegative factor is odd when the product is negative;when thenegative factor is even when the product is positive.The number of multiplicatio
11、n,a factor is zero,zero product.Distributive law of multiplication:a number and the two numberand multiplication,equivalent to the lawsuit respectively andthe two number multiplication,the sum of product.A(B+C)=AB+ACRational division:Divided by a number equal to the reciprocal of the number oftimes,
12、(not zero divisor)The number was divided,with different numbers,negative,andthe absolute values.Zero divided by any nonzero number is zero.The rational number:For several of the same factor of product operation,calledpower.The result is called power.An,called a base.The n is called the index.Any pow
13、er of a positive number is positive.Odd power negative is negative,negative even power ispositive.Scientific notation:Using scientific notation a number 10,the index and theoriginal integer bit less.The mixed operation of rational numbers:The first is involution,then calculate the last addition ands
14、ubtraction multiplication and division;The operation,in accordance with the order from left to right;If there are brackets,brackets on the first count,then countin parentheses,and then is in brackets.The approximate number and effective number:Very close to the actual width of the number,called thea
15、pproximate number.From the first one on the left is not 0 numbers,to the lastfigure so far,Effective number of all the numbers called this number.Column type algebra:A single number or a letter is algebraic.(0 is an algebra,algebra without unit.)Algebraic value:The numerical values of the letters in
16、 the algebra,algebraicoperations in relation to the calculation result,calledalgebraic value.Zhengshi:Monomial:algebra consists of product numbers and letters,(asingle number or a letter is a monomial.)The coefficient factor in this digital monomial calledmonomials.A monomial,all letters index and t
17、he number of monomials iscalled.Several monomials and polynomials cal led.Each item is calledmonomial polynomial.Does not contain letters called constant.The degree of the polynomial number of all items and not.Each includes a symbolic polynomial in front of it.Monomials and polynomials are integral
18、.A polynomial of the position in accordance with the order ofsize index a letter to order.Descending order:order from big to small order according tothe X index.Ascending order;according to the order from small to large xindex.Rearrange the polynomial,each one must move together with itssymbol.Polyn
19、omial containing two or more than two letters,often inaccordance with one letter arrangement or ascending descendingorder.Adaptive subtraction:Type of addition and subtraction contained the same letter,andthe same letter index were also called equal terms,(the sameletter number of items with the sam
20、e is not much.For example:3a2b3 and 5a3b2)The constant term is all similar itemsThe polynomial of the merger of similar items into one,calledthe merger of similar items.The coefficient of additive terms,the results as a factor,letters and the index remained unchanged.In front of the brackets is put
21、it in front of the bracketsand+removed,the brackets do not change sign.In front of the brackets is-，the brackets and in front ofit-removed,the change of symbols in brackets.So in front of the brackets is including all the same symbolto brackets.So in front of the brackets is 一，including all the symb
22、olsin brackets to change.If there are brackets,then go to the brackets,if there aresimilar items,then the merger of similar items.Three-dimensional graphics:From the front,top and side(left or right)in three directionsat an object,and then describe three see diagram,namely view.From the front to see
23、 the graphics,cal led the view;see fromthe above graph,called the top view;see from the side of thegraph,called the side view.With a three-dimensional graphics,developed in different waysto get the surface development is not the same.The three-dimensional graphics graphic is surrounded by the.Point
24、and line:Usually represents an objects position.The 1ine formed by the two party to the unlimited extension ofthe graph is a straight line.After there is a straight line,and only a straight line.A line is divided into two equal segments,called the midpointof this line.Angle:The angle is composed of
25、two public endpoint ray compositionhungry graphics,can also be regarded as the angle of a rayaround its endpoints and rotate graphics.The endpoint iscalled ray angle vertex,the starting position of ray angle iscalled the initial boundary,the end position is called the endside of the ray angle.Around
26、 the end of the end side and rotate to the angle of theinitial boundary in a straight line,then straight angle.Around the endpoint to the end edge and initial side rotationin time coincidence,this is called as the angle perigon.It was divided into 60 parts,each part is 1 points,denoted1 ;and then pu
27、t the 1 points into 60 equal portions,each oneis 1.Remember,1 1 angle=360 degrees 1 degrees 1 degreesangle=180=60=T 60Put a corner in another corner,making them the verticescoincide,one side and the other side also coincide,two cornersin the edges of the same side.Two corners are added or subtracted
28、,the sum or difference ofangle is.A ray drawn from an angle of the vertex,the angle into two equalangle,the ray is called the angle bisector.Two angles and equal to 90 degrees(rectangular),said the twocomplementary angle angle,referred to as complementary.If the two angles and 180 degrees(boxer),equ
29、al to said thetwo angles are supplementary angles,referred to ascomplementary.Any two vertex of,because they all have the same Bulu,so theyare equal,it can simply say:the angles are equal.When the four corners have a right angle,the other threecorners have become right angle,at this point,the line A
30、B,CD perpendicular to each other,denoted as“AB an CD 0 calledtheir intersection pedal.In the same plane,by line or line point,there is only one 1 ineperpendicular to a given line.Corresponding angles:straight line on the same side,by thesame party line.Alternate angles;straight line on both sides of
31、 the line isinside.The interior angles on the same side:a straight line on thesame side,by the medial line.Parallel lines:Two lines do not intersect in the same plane called parallellines.In the same plane,the two does not coincide with the linearposition relationship only two:intersecting or parall
32、el.After a little known outside the straight line,and only astraight line with a given line in parallel.If the two lines and third lines are parallel,so the two linesare parallel to each other.Corresponding angles are equal,the two parallel lines.Alternate angles are equal,the two parallel lines.Com
33、plementary interior angles on the same side,two parallellines.Two parallel lines,corresponding angles are equal.Two parallel lines,alternate angles are equal.Two parallel lines,complementary interior angles on the sameside.Data collection:The first step:clear survey questions.The second step:determi
34、ne the object of investigation.The third step:survey method.The fourth step:investigation.The fifth step:record the results.Step sixth:conclusion.Frequency:the number of times each object of the said.Frequency:ratio of each object and the number of the totalnumber(or percentage)The frequency and fre
35、quency can reflect the degree of eachobject appears frequently.Frequency=absolute data.Frequency=relative data.Solving a linear equation:Both sides of an equation plus or minus the same number or thesame type,invariant solutions of equations.Both sides of an equation or by multiplied by a non-zero n
36、umber,invariant solutions of equations.The equation for some items in changing the sign,from one sideof the equation to the other side of the deformation is calledtransposition.Contains only one unknown,and containing unknown formula isthe number of unknowns is 1 type,and this equation is calleda Yu
37、an linear equation.Two yuan a equation and its solution:Each equation with two unknowns,and the number of unknown itemsare 1,like this equation,we call it two yuan a equation.Thetwo two yuan a equation together to form a two yuan a equationgroup.Two unknowns make two equations two yuan a equation gr
38、oup inthe left and right sides of the value equal to the value of twoyuan,is called a solution of equations.Two yuan for a solution of equations;Through the“substitution eliminate an unknown quantity,theequations are transformed into a linear equation solution,thismethod is called substitution metho
39、d,referred to as thesubstitution method.The two equations(addition or subtraction)eliminate anunknown quantity,the equations are transformed into a linearequation solution,this method is called and elimination,referred to as the addition and subtraction.Understanding inequality:With the sign V or fo
40、rmula,called inequality.The inequality holds the value of the unknown,calledinequalities.All solutions of a set of solutions composed of inequality,theinequality,referred to as the solution set of this inequality.The nature of inequality 1 if a b,then:a+C+C a -b,C bOn both sides of the inequality pl
41、us(or less)with a numberor a whole,same direction of an inequality.The properties of inequality 2 if a b,C 0 and AC be.,then:The properties of inequality 3 if a b,And then:AC C 0,0,y increases with the increase of X,the functionof the image from left to right up;When k 0,the function of the image in
42、 the first,thirdquadrant,in each quadrant,the descending curve from left toright,which is increasing in each quadrant of Y with Xdecreases;When k is less than 0,the function of image in the second,fourth quadrant,in each quadrant,the curve rises from leftto right,which is increasing in each quadrant
43、 with x increasedy.The proposition and theorem to determine whether it is true orfalse sentences called proposition.The correct proposition iscalled true proposition,error is called a false proposition.People summed up in the long-term practice,and take them asthe original judgment based on other tr
44、ue or false,truepropositions such as an axiom.Starting from the axioms or other true proposition by logicalreasoning to prove that they are correct,and can be used asa judgment basis and other propositions,such a theorem calledtrue proposition.Determination of congruent triangles;If a triangle has t
45、wo sides and the angle respectively are equal,then the two congruent triangles,denoted as S.A.S.(or edgeangle).If the two triangle has two angles and the included siderespectively corresponding to the equal,then the two congruenttriangles.Abbreviated as A.S.A.(or corner corner).Two if a triangle has
46、 two angles and one angle on the sidecorresponding to equal,then the two congruent triangles.Abbreviated as A.A.S.(or corner edge).If two of the three sides of the triangle are equal,then thetwo congruent triangles.Abbreviated as S.S.S.(or side toside).If two hypotenuse and a right angle side respec
47、tively,then thetwo congruent right triangles.Abbreviated as H.L.(or bevelangle sides).Inverse and inverse theorem:In proposition two,if the first problem is the proposition ofsecond propositions and conclusions,the first propositionconclusion is proposition second questions,then the twoproposition i
48、s called inverse proposition.If a triangle has two angles are equal,then the two cornersof the edge are equal,(abbreviated as the equiangularequilateral)If one side of the triangle is equal to the square square andthe other two edges,then the triangle is a right triangle.The angle bisector point to
49、a distance equal to the angle onboth sides.To a corner on both sides of the equidistant points in thebisector of the angle.The vertical bisector of the line point to a distance equal totwo ends of this line.To a distance equal to two terminals of a segment of the pointsin this line perpendicular bis
50、ector.Determination of parallelogram:Parallelogram;1.sides parallel to the two groups.The 2.group of two sides respectively.3.a group of parallel and equal.FourThe two diagonal quadri lateral group respectively equalThe 5.diagonal quadrilateral bisect each other.1.:a rectangular corner is angled par