GRE数学复习要点：Conditional

　　Probability of event A conditioned on the fact that event B has happened is called the conditional probability and written as P(AIB).

　　P(AIB)=Probability Both A and B happens/ Probability B happens.

　　Example:

　　A six-sided die with faces from 1 to 6 is rolled twice. What is the probability that the face 5 turned up on first try given that the sum of the two faces is 9?

　　P(sum of faces is 9)=4/36=1/9.

　　P(face 5 turns up on the first try and sum is 9)=(1/6)*(1/6)=1/36.

　　P(face 5 turned up on first try given sum is 9)=(1/36)*(1/9)=1/4

　　Remember:

　　If P(AIB)=P(A),then two events A and B are independent, that is occurrence of one does not influence the other

　　GRE数学复习要点：Term

　　A product of coefficients and any number of variables with exponents is called a term. Terms that have the same variables with identical exponents for each variables are called like terms.

　　Example:

　　3x,axy,4x2yz are terms. 3x+2 is not term: it is a sum of two terms.

　　3x2y and 7x2y are like terms since both have the same variables x and y with identical exponents: 2 for x and 1 for y.

　　Remember:

　　There cannot be any addition or subtraction in a single term.

　　Since multiplication is associative, rearrangements of variables does not change a term:3xy is same as 3yx.

　　3x2y and 7xyx are like terms.

　　GRE数学复习要点：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.

　　GRE数学复习要点：Algebraic Expression

　　One or many terms connected by algebraic operations is called an algebraic expression. The operations between the terms must be valid to yield an expression.

　　Example

　　(3x+5),(ax2+c),and (xy+a)(x+y) are all algebraic expressions.

　　(2x+5)+·(3x) is not an expression since + followed by· is not a valid sequence of operations.

　　Remember

　　There is no=sign in an expression.

　　GRE数学复习要点：Evaluating Expressions

　　To evaluate an expression, plug in the specific values for the variables and simplify.

　　Example

　　For x=2, the expression 3x+5 evaluates to 3*2+5=11.

　　For x=2 and y=1, the expression xy/(x+y) evaluates to 2*1/(2+1)=2/3.

　　For x=2, the expression 4yx/(y+x) evaluates to 8y/(y+2).

　　Remember

　　After evaluation the expression does not contain the variable in any form.

　　GRE数学复习要点：Total Members

　　Sometimes there are members that do not belong to either set A or B.In that case the total number of members=Size A+Size B-Number of common members+Number of members not in A or B.

　　Example:

　　In an office, 35 people drink coffee, 27 drink tea, 12 drink both, and 4 drink neither. The total number of people in the office = 35+27-12+4=54.

　　In a class of 40 students, 20 study algebra, 15 study geometry, 8 study both.The total number of students that do not study either=40-(20+15-8)=13.

　　Remember:

　　This is a relation between five numbers, and any one can be calculated given the other four.

　　GRE数学复习要点：Adding Monomials

　　To add two monomials of the same variables just add the coefficients.

　　Only two like monomials can be added together.

　　Example:

　　By adding 3x and 4x, we get (3+4)x=7x.

　　By adding 3xy+2xy, we get (3+2)xy=5xy.

　　By adding as and bx, we get ax+bx=(a+b)x.

　　Remember:

　　Monomials can be added only if they have the same variables with identical powers.

　　以上就是楷维留学小编为大家分享的【GRE考试】GRE数学知识点盘点及复习要点详解，希望对大家有所帮助!