High school maths is of all kinds skill of issue answering question and method, be worth to collect!

How do maths is bad, you have

Is bull fond of mathematical achievement? Do you still fear you learn bad maths? Actually the teacher wants to say, want to master the method of study only, maths can promote quickly.

1, solve absolute value problem

Basically include to change brief, the problem such as evaluation, equation, inequality, function, main train of thought is: the question that contains the problem translate into of absolute value not to contain absolute value.

Specific change a method to have:

Does ① classify discussion law: ? Does calamity of  Xi  pound the larva of a tapeworm or the cercaria of a schistosome of  of neon of  fat instrument rank ⒘ of the  that embrace angry scrupulously and respectfully idle of calamity of  of Chong of サ of Wu of ⒏ bold Zhi Xie?

② 0:0 paragraph discussion law: Apply to contain an abecedarian the circumstance of many absolute value.

③ both sides makes the same score a method: Apply to both sides to be not negative equation or inequality.

Law of ④ geometry meaning: Apply to the case that has apparent geometry sense.

2, factorization

Basis several selections method and according to common step the fundamental skill that is success factorization. The common step of factorization is:

Extract fair factor

The choice uses formula

Crossed photograph multiplication

Decompose a law in group

Tear open buy a way

3, recipe law

Use complete square formula to make the same score a posture or partial melt into completely means matchs a method namely, it is the important method in maths and skill. Match main basis of the method to have:

4, change yuan of way

Solution is certain and complex special model equation should be used " change yuan of way " . Changing yuan of law to interpret the general move of equation is:

Set yuan of → to change yuan of → to solve yuan of → deoxidize

5, stay calm coefficient way

Staying calm coefficient way is a kind of means that seeks a target below the condition of foregone object form. Apply to the coordinate that seeks a site, function the settlement of the serious problem such as equation of analytic type, curve. Its interpret problem move is: ① sets ② to list ③ to solve ④ to write

6, complex algebra equality

The use skill of complex algebra equality condition: Left is changed 0, right is out of shape.

① factorization:

① factorization:: -----) (----) two kinds of circumstances are =0 or model

② matchs square model:

② matchs square model:: ----) 2+(----) two kinds of circumstances are 2=0 and model

7, two the greatest train of thought solving a problem in maths

(The train of thought of 1) evaluation lists a desire to be worth abecedarian equation or equation group

(2) begs the train of thought of limits extraction a cost to list inequality of desire limits abecedarian or inequality series

8, change brief 2 radical expression

Main train of thought is: Change √ M into complete square type. Namely:

9, observation law

10, algebraic type evaluation

The method has:

(1) direct generation enters a law

(2) changes brief generation to enter a law

(3) proper anamorphic processes (and accumulate era to enter a law)

Attention: The algebraic type when evaluation is abecedarian " symmetrical type " when, normally can melt into letter " and with accumulate " form, use thereby " and accumulate era to enter a law " evaluation.

11, solution contains ginseng equation

Unknown number has been divided in equation beyond, contained other letter calls parameter, this kind of equation makes contain ginseng equation. Solution contains ginseng equation to want to use commonly ' classified discussion law ' , its principle is:

(1) seeks solution according to the type

(2) discusses according to need

(3) classification draws up conclusion

12, the useful condition that constant establishs equally

(1)ax+b=0 holds water to have countless solution A=0 about the equation Ax+b=0 of X to aleatoric X and B=0.

(＝ of C of ＋ of 2)ax2 ＋ Bx 0 establish the Bx of equation Ax2 ＋ about X to aleatoric X 0 have ＋ C ＝ countless solution A=0, B=0, C=0.

13, constant differs the condition that establish

The concerned conclusion that is R by collect of a yuan of 2 inequality solution gets following constant differs easily the condition that establish:

14, translation rule

The translation rule of image is the important method that studies complex function. Translation rule is:

15, image law

The important method of discussion function property is image law -- see picture, get quality.

Define the share with region corresponding on X axis image

Be worth the share with region corresponding on Y axis image

Monotonicity from left look right, a paragraph of when rise continuously corresponding on X axis interval is to add interval; From left look right, a paragraph of when drop continuously corresponding on X axis interval is to decrease interval.

Most value image apogee is in have maximum, nadir place has picture the least value

Odd even sex about Y axial symmetry be occasionally function, about origin semmetry it is strange function

16, the main concern between function, equation, inequality

The root of equation

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Function image and abscissa of X axis node

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Inequality solves collect end points

17, a yuan of solution of 2 inequality

A yuan 2 times inequality can use n duality of factorization translate into inequality group goes solving, but more complex; Its simple practical solution is a basis " 3 2 " the relation between, the image that uses function 2 times goes solving. Concrete move is as follows:

2 melt into

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Differentiate and extract a root

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The picture shows an intention

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In the cross axle that see market

18, the discussion of root of a yuan of quadratic equation

The symbolic issue of root of a yuan of quadratic equation or M problem can use the relation of the discriminate of the root and root and coefficient to solve, but the average issue of the root, especially the problem of interval root wants a foundation " 3 2 " the relation between, the image that uses function 2 times will solve. "Image law " the general train of thought of the problem that solves root of a yuan of quadratic equation is:

Problem desire

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2 function image

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Inequality group

Inequality group includes: The symbol of A; The circumstance of △ ; The position of symmetrical axis; The symbol that function of interval end points is worth.

19, the basic function value on interval region

The 2 function of the linear function that we had learned, inverse proportion, function function that has a name is basic function. Region of basic function evaluation or most the value has two kinds of cases:

(When 1) defines region to do not have special limitation---Recall law or conclusion way;

(When 2) defines region to have special restriction---Image blocks a way, general train of thought is:

The picture gives picture

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Cut goes out to be broken

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Conclude

20, most the solution of value exercise

In the exercise, involve " another variable when what a variable takes to be worth obtains maximum or the least value " the problem is most value exercise. Solve most the main train of thought of value exercise is function thought law, its interpret problem move is:

Set variable

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Line function

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Beg most value

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Write conclusion

21, the law that wear a line

The law that wear a line is solution tall inequality and the best method of the inequality that distribute form. Its are general train of thought is:

First are changed

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Root of mark of extract a root

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Right on case wear

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Strange wear answer occasionally

Attention: ① is tall methodological melt into that inequality wants to use transpose and factorization above all " left product, right is 0 " form. Inequality of ② cent type cannot be multiplied with both sides commonly go the method of denominator will solve, should pass transpose, reduction of fractions to a common denominator the methodological melt into of amalgamative, factorization " business 0 type " , with solution of the law that wear a line.