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新gre數(shù)學(xué)重要考點:Distributive Law
Distributive Law
Like real number, when multiplying a sum or difference of terms, the distributive property of multiplication allows us to distribute the multiplying term among the terms being added or subtracted.
Example:
3*(2x+y)=3*2x+3*y,
3a*(2x+y)=3a*2x+3a*y,
3x*(2x+y)=3x*2x+3x*y.
(3x+4)*(2x+y)=(3x+4)*2x+(3x+4)*y=3x*2x+4*2x+3x*y+4*y.
Remember:
Do not forget to multiply all the terms inside the parenthesis.
For division, the sum and difference in the numerator can be distributed:(x+y)/(2x+y)=x/(2x+y)+y/(2x+y).
For division, the sum and difference in the denominator cannot be distributed :(x+y)/(2x+y)≠(x+y)/2x+(x+y)/y.
新gre數(shù)學(xué)重要考點:Associative Law
Associative Law
Like real numbers, the grouping does not affect the product or sum of 3 or more algebraic terms.
Example:
Sum:2x2+(4y+1)=(2x2+4y)+1,
3x+(2xy+5y+2)=(3x+2xy)+(5y+2)=(3x+2xy+5y)+2.
Product:3x*(2y*4xy)=(3x*2y)*4xy=3x*2y*4xy.
Remember:
Typically, same variable is grouped together in a single term and the product of same variable is expressed as power.
新gre數(shù)學(xué)重要考點:Commutative Law
Commutative Law
Like real numbers, the order does not affect the product or sum of algebraic terms.
Example:
sum:3x+5y=5x+3y,2x2+4y+1=4y+1+2x2,(3x+2)+(y-4)=(y-4)+(3x+2).
product:3x*5y=5y*3x,2x2*4y=4y*2x2,x2yz=yx2z=xzyx,(3x+2)*(y-4)=(y-4)*(3x+2)
Remember:
Subtraction is not commutative:(x+y)-(2x-y) ≠(2x-y)-(x+y)
Division is not commutative:(x+y)/(2x-y) ≠(2x-y)/(x+y)
新gre數(shù)學(xué)重要考點:Substitution
Substitution
Substitution is a method where one or more variables in an expression is replaced by numbers or another set of variables.To evaluate an expression specific numbers are used as substitute. To express in terms of another set of variables, variables are replaced by the new set of variables.
Example:
If x=3, then 2x2+4x+1 can be evaluated by substituting 3 for x.
Replacing all x by 3, we get 2*32+4*3+1=31.
If x=2+y, then x2-3 can be expressed in terms of y by replacing all x by (2+y):(2+y)2-3=y2+4y+1.
Remember:
Do not forget to replace all occurrences of the variable.
After substitution the variable does not appear anywhere in the expression.
由于美國數(shù)學(xué)基礎(chǔ)教育的難度增加導(dǎo)致數(shù)學(xué)考試越來越難,但新gre數(shù)學(xué)復(fù)習(xí)考點都是高中時候?qū)W到的知識點,考生不要過于緊張,把基本概念弄明白,再記住一些新版gre數(shù)學(xué)必備的詞匯,那么相信新版gre數(shù)學(xué)應(yīng)該沒有問題。
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