2011新gre考試實施以來，不僅對寫作部分茫然不知所措，就連我們所擅長的數學也甚是擔憂，相信這其中的原因還是由于考生在新gre數學復習時沒有把基礎打牢。如果新版gre數學基本考點都沒有復習到，如何能拿到分數呢?所以說，想要新版gre數學考好，復習的時候一定要把基本概念和重要考點都弄扎實。
所以，從今天起，針對新版gre數學復習，小編每天給考生整理一個重要考點，這些概念在考試中一定會考到的。希望考生能再接再厲，取得一個好成績，突破新版gre數學難的困境。
新版gre數學復習重要考點：Sum of Arithmetic Progression
The sum of n-numbers of an arithmetic progression is given by
S=nx*dn(n-1)/2
where x is the first number and d is the constant increment.
example:
sum of first 10 positive odd numbers:10*1+2*10*9/2=10+90=100
sum of first 10 multiples of 7 starting at 7: 10*7+7*10*9/2=70+315=385
remember:
For a descending AP the constant difference is negative.
由于美國數學基礎教育的難度增加導致數學考試越來越難，但新gre數學復習考點都是高中時候學到的知識點，考生不要過于緊張，把基本概念弄明白，再記住一些新版gre數學必備的詞匯，那么相信新版gre數學應該沒有問題。
AP
Average of n numbers of arithmetic progression (AP) is the average of the smallest and the largest number of them. The average of m number can also be written as x + d(m-1)/2.
Example:
The average of all integers from 1 to 5 is (1+5)/2=3
The average of all odd numbers from 3 to 3135 is (3+3135)/2=1569
The average of all multiples of 7 from 14 to 126 is (14+126)/2=70
remember:
Make sure no number is missing in the middle.
With more numbers, average of an ascending AP increases.
With more numbers, average of a descending AP decreases.
AP:numbers from sum
given the sum s of m numbers of an AP with constant increment d, the numbers in the set can be calculated as follows:
the first number x = s/m - d(m-1)/2,and the n-th number is s/m + d(2n-m-1)/2.
Example:
if the sum of 7 consecutive even numbers is 70, then the first number x = 70/7 - 2(7-1)/2 = 10 - 6 = 4.
the last number (n=m=7)is 70/7+2(2*7-7-1)/2=10+6=16.the set is the even numbers from 4 to 16.
Remember:
given the first number x, it is easy to calculate other numbers using the formula for n-th number: x+(n-1)
AP:numbers from average
all m numbers of an AP can be calculated from the average. the first number x = c-d(m-1)/2, and the n-th number is c+d(2n-m-1)/2, where c is the average of m numbers.
Example:
if the average of 15 consecutive integers is 20, then the first number x=20-1*(15-1)/2=20-7=13 and the last number (n=m=15) is 20+1*(2*15-15-1)/2=20+7=27.
if the average of 33 consecutive odd numbers is 67, then the first number x=67-2*(33-1)/2=67-32=35 and the last number (n=m=33) is 67+2*(2*33-33-1)/2=67+32=99.
Remember:
sum of the m numbers is c*m,where c is the average.
Sequence of Numbers
A sequence is a set of numbers that follow a fixed pattern.The fixed pattern can be expressed by an equation or by a property.
Example:
A set of consecutive integers: 1,2,3,4,5(Fixed gap)
A set of consecutive even numbers:4,6,8,10,12 (Fixed gap)
A set of consecutive prime: 2,3,5,7,11(Fixed gap)
A set of consecutive power of 2:4,8,16,32,64(Fixed gap)
Remember:
A sequence can be in ascending or desceding order.
Mode
The mode of a set of numbers is the number that repeats the most in the set.
Example:
Mode of the set {1,2,3,2,4,5} is 2.
The set of numbers {1,2,4,1,2,3,6,8}has two modes:1 and 2.
Remember:
There can be more than one number with the highest repeat count. In that case all of them with the highest repeat count are modes.
A set is a collection of objects or things. Each object in a set a member or element of that set.Size of a set is the number of members in the set.
Example:
The set of even numbers between 2 and 10 is of size 5:{2,4,6,8,10}.
The set of primes between 2 and 10 is of size 4:{2,3,5,7}.
Remember:
Each member of set A belongs to A or is in the set A.
A set can not have repeating member:{1,3,1,2}is not a set.
Rearranging the order of the members does not change the set:{1,2,3}is same as{3,2,1}.
Intersection of Sets
Intersection of two sets is another set with only the members that are in both sets. If the two sets do not share any common member, the intersection is the empty set with no member.
Example:
Intersection of {1,2,3} and {2,3,5} is the set {2,3}.
Intersection of the set with all primes and the set with all even numbers is the set {2} since only 2 is both even and prime.
Intersection of {1,2,3} and {4,5,6} is the empty set {}.
Remember:
Intersection contains only the common members.
Two sets are disjoint if they have no member in common, that is they have an empty intersection.
Union of Sets
Union of two sets is another set with all the members from both sets.
Example:
Union of {2,3,5} and {1,3,4} is the set {1,2,3,4,5}.
Union of {1,2,1} and {1,2} is the set {1,2,1}.
Remember:
The common members do not repeat in the union.
Total Members
所以，從今天起，針對新版gre數學復習，小編每天給考生整理一個重要考點，這些概念在考試中一定會考到的。希望考生能再接再厲，取得一個好成績，突破新版gre數學難的困境。
新版gre數學復習重要考點：Sum of Arithmetic Progression
The sum of n-numbers of an arithmetic progression is given by
S=nx*dn(n-1)/2
where x is the first number and d is the constant increment.
example:
sum of first 10 positive odd numbers:10*1+2*10*9/2=10+90=100
sum of first 10 multiples of 7 starting at 7: 10*7+7*10*9/2=70+315=385
remember:
For a descending AP the constant difference is negative.
由于美國數學基礎教育的難度增加導致數學考試越來越難，但新gre數學復習考點都是高中時候學到的知識點，考生不要過于緊張，把基本概念弄明白，再記住一些新版gre數學必備的詞匯，那么相信新版gre數學應該沒有問題。
AP
Average of n numbers of arithmetic progression (AP) is the average of the smallest and the largest number of them. The average of m number can also be written as x + d(m-1)/2.
Example:
The average of all integers from 1 to 5 is (1+5)/2=3
The average of all odd numbers from 3 to 3135 is (3+3135)/2=1569
The average of all multiples of 7 from 14 to 126 is (14+126)/2=70
remember:
Make sure no number is missing in the middle.
With more numbers, average of an ascending AP increases.
With more numbers, average of a descending AP decreases.
AP:numbers from sum
given the sum s of m numbers of an AP with constant increment d, the numbers in the set can be calculated as follows:
the first number x = s/m - d(m-1)/2,and the n-th number is s/m + d(2n-m-1)/2.
Example:
if the sum of 7 consecutive even numbers is 70, then the first number x = 70/7 - 2(7-1)/2 = 10 - 6 = 4.
the last number (n=m=7)is 70/7+2(2*7-7-1)/2=10+6=16.the set is the even numbers from 4 to 16.
Remember:
given the first number x, it is easy to calculate other numbers using the formula for n-th number: x+(n-1)
AP:numbers from average
all m numbers of an AP can be calculated from the average. the first number x = c-d(m-1)/2, and the n-th number is c+d(2n-m-1)/2, where c is the average of m numbers.
Example:
if the average of 15 consecutive integers is 20, then the first number x=20-1*(15-1)/2=20-7=13 and the last number (n=m=15) is 20+1*(2*15-15-1)/2=20+7=27.
if the average of 33 consecutive odd numbers is 67, then the first number x=67-2*(33-1)/2=67-32=35 and the last number (n=m=33) is 67+2*(2*33-33-1)/2=67+32=99.
Remember:
sum of the m numbers is c*m,where c is the average.
Sequence of Numbers
A sequence is a set of numbers that follow a fixed pattern.The fixed pattern can be expressed by an equation or by a property.
Example:
A set of consecutive integers: 1,2,3,4,5(Fixed gap)
A set of consecutive even numbers:4,6,8,10,12 (Fixed gap)
A set of consecutive prime: 2,3,5,7,11(Fixed gap)
A set of consecutive power of 2:4,8,16,32,64(Fixed gap)
Remember:
A sequence can be in ascending or desceding order.
Mode
The mode of a set of numbers is the number that repeats the most in the set.
Example:
Mode of the set {1,2,3,2,4,5} is 2.
The set of numbers {1,2,4,1,2,3,6,8}has two modes:1 and 2.
Remember:
There can be more than one number with the highest repeat count. In that case all of them with the highest repeat count are modes.
A set is a collection of objects or things. Each object in a set a member or element of that set.Size of a set is the number of members in the set.
Example:
The set of even numbers between 2 and 10 is of size 5:{2,4,6,8,10}.
The set of primes between 2 and 10 is of size 4:{2,3,5,7}.
Remember:
Each member of set A belongs to A or is in the set A.
A set can not have repeating member:{1,3,1,2}is not a set.
Rearranging the order of the members does not change the set:{1,2,3}is same as{3,2,1}.
Intersection of Sets
Intersection of two sets is another set with only the members that are in both sets. If the two sets do not share any common member, the intersection is the empty set with no member.
Example:
Intersection of {1,2,3} and {2,3,5} is the set {2,3}.
Intersection of the set with all primes and the set with all even numbers is the set {2} since only 2 is both even and prime.
Intersection of {1,2,3} and {4,5,6} is the empty set {}.
Remember:
Intersection contains only the common members.
Two sets are disjoint if they have no member in common, that is they have an empty intersection.
Union of Sets
Union of two sets is another set with all the members from both sets.
Example:
Union of {2,3,5} and {1,3,4} is the set {1,2,3,4,5}.
Union of {1,2,1} and {1,2} is the set {1,2,1}.
Remember:
The common members do not repeat in the union.
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
