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  1. GRE數學重點考察知識點解析

    發布時間:2017-12-22 編輯:少冰

      GRE數學是怎么樣的呢?又有哪些知識點呢?下面是小編為大家整理收集的關于GGRE數學重點考察知識點的相關解析,希望對大家有所幫助。

      Sum of Arithmetic Progression(數列求和)

      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.

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