1、1GRE 数学第一部分 数学基础知识一、代数 Algebra例 1 比较大小： . The number of distinct positive factors of n 14 比较大小例 2：252 因子的个数是多少？例 3 比较大小：A printer numbered consecutively the pages of a book, beginning with 1 on the first page. In numbering the page, he printed a total of 204 digits.The number of pages in the book 10
2、5例 4 比较大小： In a certain two-digit number, the units digit is twice the tens digit. 5The tens digit例 5 比较大小：二、描述统计 descriptive statistics例 6 比较大小：某长方形的周长为 40，该长方形的最大面积 100例 7 比较大小：空间 5 个点能够构成的直线数目 10例 8：求 3，13，17 的标准方差。三、排列组合 combination、概率 probability 1 排列组合 排列计算公式： ， 组合计算公式： 。2 概率例 9：假如世界杯比赛共有 32 支
3、球队，分成 8 个组，每组 4 个队，每组前两名出线，然后成对进行淘汰赛，直至决赛决出冠军，并且淘汰队不参加比赛，从中间任选出一场比赛观看是半决赛的机会有多大？例 10：有 4 对男女，每对中有 1 男 1 女，从每对中选出 1 人，选出 2 男 2 女的概率是多少？2例 11：有 3 个打字员为 4 家公司服务，如果 4 家公司各有 1 份文件要录入，他们只能找到这 3 个打字员录入，且各公司对打字员的要求是随机的。问每个打字员都收到文件的概率是多少？ 例 12：两个骰子，六面的值分别为 1，2，3，4 ，5，6，投掷这两个骰子，问其中一个骰子的值比另一个的值大 2 的概率为多大?四、几何(
4、Geometry)例 13 比较大小：R is a point in the rectangular coordinate system and OR=5.The x-coordinate of point R 5 4.9例 14 比较大小：(RS)2+(ST)2 (RT)2例 15： According to the graph above, when x=3, y is most nearly:(A) -1 (B) -1/2 (C) 0 (D) 1/2 (E) 1五、文字题(Word Problem)1. 利息问题(interest) 单利 simple interest 复利 compo
5、und interest例 16： If $ 8000 is invested at 6 percent simple annual interest, how much interest is earned after 3 months?例 17：If $ 10,000 is invested at 10 percent simple annual interest, compound semiannually, what is the balance after 1 year?2. 折扣问题(discount)例 18：The price of an item is discounted
6、by 20 percent and then this reduced price is discounted by an additional 30 percent. These two discounts are equal to an overall discount of what percent?3. 英美常识问题3GRE 难题解析例 1：On a certain number line, if -7 is a distance of 4 from n and 7 is a distance of 18 from n ,then n=? (A) 25 (B) 11 (C)- 3 (D
7、) 11 (E)-11例 2：The diagram represents a rectangular garden. The shaded regions are planted in flowers, and the unshaded region is a walk 2 feet wide. All angles are right angles.The sum of the areas of the 2,800 square feetshaded regions 例 3：The map shows the only roads that connect the four towns a
8、nd shows the distance along each road.The road distance between Austen and Seburg The road distance between Coaltown and Woodland例 4：How many positive integers less than 20 are equal to the sum of a positive multiple of 3 and a positive multiple of 4? (A) Two (B) Five (C) Seven (D) Ten (E) Nineteen例
9、 5：Which of the following symbols should be substituted for to make both of the statements true for all integers n such that -2 (E) 4-n 64-n 5例 6：In a soccer league, If there were 10 teams and each team played each of the other teams 16 times, how many games did each team play? (A) 144 (B) 140 (C) 1
10、34 (D) 125 (E) 106例 7：(NOTE: DRAWN TO SCALE)POPULATION OF THE U.S. AGE 55 AND OVER1984 AND PROJECTIONS FOR 1995INCOME DISTRIBUTION FOR POPULATIONOF THE U.S. AGE 55 AND OVER,19844In 1984 median income for a person in the 5564 age category was in which of the following intervals?(A) less than 10,000 (
11、B) 10,00019,999 (C) 20,00024,999 (D) 25,00034,999 (E) 35,00049,999例 8：A sample of employees were tasted on data-entry skills for one hour, and the number of errors (x) they made and the percent of employees (p) making x errors were recorded as follows.Number of error x 0 1 2 3 4 5 6 or morePercent o
12、f employees P 2% 5% 10% 24% 14% 20% 22%what was the median number of errors in the sample?(A) 3 (B) 3.5 (C) 4 (D) 4.5 (E) It cannot be determined from the information given.例 9：d=7.56872 and D is the decimal expression for d rounded to the nearest thousandth.The number of decimal place where d and D
13、 differ 4例 10： In a certain country, a person is born every 3 seconds and a person dies every 10 seconds. Therefore, the birth and death rates account for a population growth rate of one person every例 11： Of the positive integers that are multiples of 30 and are less than or equal to 360, what fract
14、ion are multiples of 12?(A) 1/6 (B) 1/5 (C) 1/3 (D) 2/5 (E) 1/2例 12： The figure shows a large square formed by fitting three L-shaped tiles and one small square tile together. If 8inches8inches5a rectangular floor 10 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped t
15、iles will be needed?(A) 810 (B) 405 (C) 270 (D) 135 (E) 45例 13： The daily rate for a hotel room that sleeps 4 people is $39 for one person and x dollars for each additional person. If 3 people take the room for one day and each pays $21 for the room, what is the value of x? (A) 6 (B) 8 (C) 12 (D) 13
16、 (E) 24例 14： A positive integer with exactly two different divisors greater than 1 must be(A) a prime (B) an even integer (C) a multiple of 3 (D) the square of a prime (E) the square of an odd integer例 15： xz, yz x + y z例 16： xy and xy0 (x + y)/x (x + y)/y例 17： 2AF=AB=BD=DE=AEThe sum of the area of
17、triangular region ABF and area of triangular region CDEThe area of rectangular region BCEF例 18： Each of the following numbers has two digits blotted out. Which of the numbers could be the number of hours in x days, where x is an integer?(A)25 , 06 (B)50 , 26 (C)56 , 02 (D)62 , 50 (E)65 , 20例 19： The
18、re are 1200 represents to a poll, each favoring their preference for candidates A, B, and C. 54% favored A, 48% favored B, and 42% favored C, and there is 30% favored both A and B. Whats the largest possible number of represents favoring c, but not C 75 had black shoes; 60 carried an umbrella; 90 wo
19、re a ring, How many ladies must have had all four items?(A)15 (B)35 (C)5 (D)10 (E)25例 21： In an insurance company, each policy has a paper record and an electric record. For those policies having incorrect paper record, 60% also having incorrect electric record; For those policies having incorrect e
20、lectric record, 75% also having incorrect paper record. 3% of all policies have both incorrect paper and incorrect electric record. If we randomly pick out 6one policy, whats the probability that the one having both correct paper and correct electric record?(A)0.80 (B)0.94 (C)0.75 (D)0.88 (E)0.92ak
21、100 200 300 400 500pk 0.10 0.25 0.20 0.25 0.20例 22： If in an experiment the probabilities of obtaining the values a1,a2,a3,a4,a5 are p1,p2,p3,p4,p5 , respectively, then the expected value is defined as a1 p1 + a2 p2 +a3 p3 + a4 p4 + a5p5. For the values and their corresponding probabilities in the t
22、able above, what is the expected value? (A)350 (B)320 (C)300 (D)270 (E)250 例 23：The standard deviation of the sample measurements 0, 2, 4, 6, and 8The standard deviation of the sample measurements 1, 3, 5, 7, and 9例 24： What is the total number of different 5-digit numbers that contain all of the di
23、gits 2, 3,4,7 and 9 and in which none of the even digits occur next to each other?(A)72 (B)100 (C)120 (D)60 (E)48 例 25： Water is to be poured at a rate of 2.5 gallons per minute into a 500-gallon tank that initially contains 50 gallons of water.The percent of the tanks capacity that will befilled 1 hour after water begins to be poured in60 percent例 26： In the figure, if x, y, and z are integers such that x: is greater than =: is greater than or equal to (或 no less than) b 2. a if only b 表示 b=a 3. 2/3 as many A as B 是: A 为 B 的 2/3 4. twice as many A as B 是: A 为 B 的 2 倍
