gmat数学.docx

1、gmat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 105例4 比较大小

2、： 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 排列组合 排列计算公式： ， 组合计算公式： 。概率例9：假如世界杯比赛共有32支球队，分成8个组，每组4个队，每组前两名出线，然后成对

3、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？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(Geometry)例13 比较大小：R is a point in the rectangular coordinate

4、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 compound interest例16： If $ 8000 is invested at 6 percent simple annua

5、l 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 by 20 percent and then this reduced price is discounted by an additi

6、onal 30 percent. These two discounts are equal to an overall discount of what percent?3、英美常识问题GRE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) 11 (E)-11例2：The diagram represents a rectangular garden. The shaded re

7、gions 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 and shows the distance along each road.The road distance between Austen and

8、 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5：Which of the following symbols should be substituted for to make both of

9、the statements true for all integers n such that -2 n3? (A) (B) (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) 134 (D) 125 (E) 106例7：(NOTE: DRAWN TO SCALE)POPULATION OF THE U.S.

10、 AGE 55 AND OVER1984 AND PROJECTIONS FOR 1995INCOME DISTRIBUTION FOR POPULATIONOF THE U.S. AGE 55 AND OVER,1984In 1984 median income for a person in the 5564 age category was in which of the following intervals?(A) less than 10,000 (B) 10,00019,999 (C) 20,00024,999 (D) 25,00034,999 (E) 35,00049,999例

11、8：A sample of employees were tested 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 x0123456 or morePercent of employees P2%5%10%24%14%20%22%what was the median number of errors in the

12、 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 differ4例10：In a certain country, a person is born every 3 seconds and a person die

13、s 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 fraction are multiples of 12?(A) 1/6 (B) 1/5 (C) 1/3 (D) 2/5 (E) 1/28inches例12：The figure sho

14、ws a large square formed by fitting three L-shaped tiles and one small square tile together. If a rectangular floor 10 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped tiles will be needed?(A) 810 (B) 405 (C) 270 (D) 135 (E) 458inches例13：The daily rate for a hotel ro

15、om 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 (E) 24例14：A positive integer with exactly two different divisors greater than 1 must be(A) a

16、 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 triangular region ABF and area of triangular region CDEThe area of rectangular region BCEF例19：There a

17、re 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&B, nor C&A?(A)25% (B)30% (C)28% (D)38% (E)40%例20： Out

18、 of 100 ladies attending the church fete, 85 had a white handbag; 75 had black shoes; 60 carried an umbrella; 90 wore 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 polici

19、es having incorrect paper record, 60% also having incorrect electric record; For those policies having incorrect electric record, 75% also having incorrect paper record. 3% of all policies have both incorrect paper and incorrect electric record. If we randomly pick out one policy, whats the probabil

20、ity that the one having both correct paper and correct electric record? (A)0.80 (B)0.94 (C)0.75 (D)0.88 (E)0.92ak100200300400500pk0.100.250.200.250.20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

21、 as a1 p1 + a2 p2 +a3 p3 + a4 p4 + a5p5. For the values and their corresponding probabilities in the table 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,

22、 3, 5, 7, and 9例24：What is the total number of different 5-digit numbers that contain all of the digits 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 th

23、at 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 xyb 2.aifonlyb表示b=a 3.2/3asmanyAasB是:A为B的2/3 4.twiceasmanyAasB是:A为B的2倍 GRE数学常用符号及术语一.数学中常用符号 +: p

24、lus X:multiply -: subtract : divide V: squareroot |.|: absolutevalue =: isequalto =/=: isnotequalto : isgreaterthan =: isgreaterthanorequalto(或nolessthan) =: islessthanorequalto(或nomorethan) 二.表达相应数目的前缀 1:uni-,mono- 2:bi-,du-,di- 3:tri-,ter-, 4:tetra-,quad-, 5:penta-,quint, 6:hex-,sex-, 7:sept-,hapt

25、a-, 8:oct, 9:enn-, 10:dec-,deka-, 三.数学中常用单词术语 abscissa横坐标absolute value绝对值acute angle锐角adjacent angle邻角addition加algebra代数altitude高angle bisector角平分线arc弧 area面积 arithmetic mean算术平均值（总和除以总数）arithmetic progression等差数列（等差级数） arm直角三角形的股at总计（乘法）average平均值base底be contained in位于.上bisect平分center圆心chord弦circl

26、e圆形circumference圆周长circumscribe外切，外接clockwise顺时针方向closest approximation最相近似的combination组合common divisor公约数，公因子common factor公因子complementary angles余角（二角和为90度） Composite number合数（可被除1及本身以外其它的数整除）concentric circle同心圆cone圆锥（体积1/3*r*r*h）congruent全等的consecutive integer连续的整数 coordinate坐标的cost成本counterclockwise逆时针方向cube1.立方数2.立方体（体积a*a*a表面积6*a*a） cylinder圆柱体decagon十边形decimal小数decimal point小数点decreased减少decrease to减少到decrease by减少了degree角度define1.定义 2.化简denominator分母denote代表，表示depreciation折旧distance距离distinct不同的dividend1.被除数 2.红利divided evenly被