1. l1, l2 and l3 are three lines in space
The number of points at The number of points at
which lines l1 and l2 intersect which lines l2 and l3 intersect
1。三条任意直线,L1和L2的交点的个数与L2和L3的交点的个数没关。
2. The number of 1/4-inch lengths in 1
a 4-inch length
2,是问4英尺中有多少个1/4英尺,应该是16个,所以是A
3. The maximun number of solid cubes 4
having edges of length 1/2 meter that
can be placed inside a cubical box
having inside edges of length 1 meter
3边长为1的立方体里最多能放下几个边长为1/2的立方体,当然是8个咯
4. Cube C has volume 8 cubic centimeters
The area of one of the faces of cube C 3 square centimeters
4立方体体积是8,那一个面的面积当然是4咯
5. Ms.Smith got an 8 percent cost-of-living raise of $20 per week
Ms.Smith's new weekly salary $260
5 x*0.08=20,那x+20=270>260
6. On a certain number live, 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.-3 E-11
6应该是-11
7. For all real numbers a and b. if a?b=a(a+b), then a?(a?b)=
A. a2+ab B a2+ab+a C a2+a+b D a3+a2b E a3+a2b+a2
注:a2表示a平方,a3表示a立方
7新定义的运算a?b=a(a+b), 那a?(a?b)=a?(aa+ab)=a(a+aa+ab)=aa+aaa+aab
8.secretary typed 6 letters,each of which had either 1 or 2 pages.If the secretary typed 10 pages in all, how many of the letters had 2 pages?
A 1
B 2
C 3
D 4
E 5
答案是D,题目我都看不懂,是啥意思呢?
这是说秘书打六封信,没一封信要1页或者两页。如果秘书总共打了10页,那么有多少封信是两页?
解答:设有x封,则2x+(6-x)=10,解得x=4.
9 how many of the five numbers above are each equal to the product of an integer and an odd integer that greater than 1?
这五个数是:2 6 8 14 16
a.none
b.one
c.two
d.there
e.four
我觉得这道题除了2不可能,其它四个数都有可能.可答案是c,想问大家为什么?
题目意思是这5个数哪些可以是2个>1的数的积,一个是奇数,一个是整数,只有6和14的因数中有奇数,所以C.
10 这句话大家看该怎样列式子呢?这是一道图表题.
what was the approximate percent increase in personal income from 1965 to 1970?
是这样(1970-1965)/1965还是(1970-1965)/1970这样?
是这样:(1970-1965)/1965
1 the sum of two numbers, x and y, equals twice their products. if x=3, what is the value of y?
这道题没大看懂?请问大家是这样么?x+y=2(x+y)
x+y=2xy,求y.
2 if x is an integer and x2(x的平方)<37,what is the greatest possible value of x minus the least possible value of x?
我觉得这道题x的最大值为6,最小值为0,所以选6.
a.5
b.6
c.10
d.12
e.36
选D,最大为6,最小为-6.
3 三角形ABC,角B=X度,X>90 度,比较三角形的周长与3倍AC的长度的大小,答案是B
AC是最大边,所以AB+BC+AC 2.0 比较the greatest value of p(1-p)与1/2的大小,答案是C 答案错了,选B p+(1-p)>=2p(1-p)^1/2 => p(1-p)<=1/4 < 1/2 4 for the line with equation y=ax+b,the x-intercept os twice the y-intercept 比较the slope of the line 与1/2的大小,答案是D,但算出来是-1/2呀 还有截距为零的情况,所以D. 5 a certain moneymarket account that had a balance of $48000 during all of last monthearned $360 in interest for the month. at what simple annual interestrate did the account earn interest last month? 答案是9%,题目没看懂 意思是一个货币市场上个月共结余48000,用它赚了360的利息,问以年单利计算每年利率是多少? 360*12/48000=9% 6 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.1/2 首先这道题我是对multilples of ....不大明白,这是什么意思啊?其次这道题怎么解呢? 在小于360的30的公倍数中,也是12的公倍数的占多少?30N≤360, 得N≤12,所以共有12个数满足题干. 又12与30的最小公倍数为60,其实此题是求是60的倍数又小于等于360所占比例,同理求出为6 所以,6/12=答案E 7 A certain teacher has a total ofat least 110 students enrolled in her classes.if the teachers has anaverage (arithmetic mean) of exactly 27 students enrolled per class.what is the least possible number of classes that the teacher couldhave? a.3 b.4 c.5 d.6 e.7 我觉得这道题就是用110除以27就好了,可是答案是选c的 是呀,110/27=4.04,如果是4个班,那么总人数为108,还剩2个。当然是5个班了。 8 a delivery service charges $0.02 per ounce for the first 16 ounces ofa shipment and $0.15 for each additional ounce of theshipment,(1pound=16ounce) the delivery charges for x shipments weighing a combimed total of the pounds vs 567.00 这道题答案选的是D,不明白怎么会无法确定呢?我是这样算的:16×0.2+(25*16-16)×0.15...这样对么? 因为x是个未知数,所以你无法确定它的值。 9 the cost per gram of carrots if 3 cans of carrots cost $0.90 the costper gram of onions if 5 cans of onions cost $1.50 无法确定,没有告诉1can有多少克? 10 X is an integer, and the remainder when 2X is divided by 4 is 0. The remainder when X is divided by 4 0 选D,当x=2,-2时,余数为2,-2,其它情况为0 1 Let[X]=3, if X is an odd integer; let[X]=6, if X is an even integer. r and s are integers, 3r is odd and 5+s is odd. [r] [s] 3r是奇数说明r为奇数,所以[r]等于3,5+s为奇数,说明s为偶数,所以[s]=6 2 the value of the units' digit in 6^47(6的47次方) the value of the units' digit in 5^77(5的77次方) 比较两个数的个位,6不管多少次方个位都为6,5不管多少次方个位都为5. 3 for all numbers r and s, where s/=(不等于)0, r#s=10r/s. 0.01#0.01 1 0.01#0.01=10*0.01/0.01=10,大于1. 4 1 the sum of the first n odd integers that are greater than zero n^2(n平方)-1 说的是n个大于零的奇数和。 当n=2,1+3=4;n^2-1=3; 当n=3,1+3+5=9;n^2-1=8; 当n=4,1+3+5+7=16;n^2-1=15 所以选A 5 a^7+a^15 a^8+a^14 注是a的7次方,类推呵呵 比较大小题 后-前=a^7(a-1)+a^14(1-a) =(a^7-a^14)(a-1) 然后讨论,最后结果是后-前的差<0,但当a=1时,相等。所以选D. 6 A total of $480 is ina certain cash register. All of the money is in one-dollar and five-dollar bills, and there are 30 more one-dollar bills than five-dollar bills. The sum of 30 and the number of five-dollar bills in the cash register 105 let x be the number of one-dollar bill y be the number of five-dollar bill x+5y=480-----1 x=y+30--------2 subsitute 2 in to 1 6y = 450 so y=75 30+75=105 7 If N is an integer, then the units digit of N平方cannot be b 2 c 4 d 5 e 6 谁能把题目翻译以下?谢谢 就是N^2的个位数不能为几,应该选B吧 8 the value of the units' digit in 6的47次方 the value of the units' digit in 5的77次方 哪个大呀?这种题怎么做呀? 还有,黄皮书的答案是全对的吗?怎么有些明显好怪的,望指点哈~ 这是比较6的47次方的个位数与5的77次方的个位数的大小。 6的多少次方个位数都为6,5的多少次方个位数都为5.所以前面大于后面。选A。 9 two successive discounts of 20percent and 40percent are equavilent tp a single discount of X percent. X 52 同问此题,不明白题目说什莫 我理解的阿:打折20%后再打折40%,结果等于打一个X折,比较X和52的关系 (100-20)*(100-40) = 48 X = 100 - 48 = 52 10.已知:y=x^2-16x+64 比较"the least value of y"和"0"的大小 答案是C, y 没有最小直呀? y=(x-8)^2,所以y的最小值为0. 1 比较"The remainder when a positive odd integer divided by 2"和"The remainder when a positive even integer is divided by 2" 答案是A, 我觉得应该是B呀? 奇数除2余数必为1,偶数除2余数必为零,选A 2 If x,y,and z are consecutive positive integers, with x A.1 B.2 C.4 D.5 E.8 答案是D,如果是D的话,那么3+4+5也不是奇数呀?我觉得C和E怎么都对呀? even是偶数的意思,三个连续的整数相加为偶数,则中间的书必为偶数,两边的就为奇数了。所以选D。 3 In a group of 80 students,2 4 are enrolled in geometry , 40 in biology, and 20 in both. If a student were randomly selected from the 80 students, What is the probability that the strdent selected would NOT be enrolled in either course? 我没头绪没学过概率,怎么办呢? 这里24个学几何,40个学生物,20个全学。问两个都没学占多少比例。 单学几何的有24-20=4个,单学生物的有40-20=20个,所以学了这两门的任何一门的有:20+4+20=44个。所以没学的就是80-44=36个。 所以概率为:36/80=9/20. 4 triangular garden ABC is redesigned by increasing the length of AC by 20 percent to point C' and decreasing the length of AB by 20 percent to B'. the area of the original garden ABC the area of the redesigned garden AB'C' 三角形ABC的面积:AC的长度乘以AB的长度。 三角形AB'C'的面积:1.2AC的长度乘以0.8AB的长度=0.96三角形ABC的面积 所以选A 5 一个三角形的三边分别是11,5,13,怎么判断13的边所对的角是钝角? 假设11,5是两条直角边,斜边的平方等于146小于13的平方,所以13对的边是钝角 Rectangle R has an area of 60 square units and a perimeter of 64 units. The length of the shortest side of R is x and the length of the longest side of R is y. 问x/y大还是1/15大? 这种题怎么算呀,答案是一样大 xy=60 x+y=32.得出:x=30,y=2和x=2,y=30.因为y大于x,所以x=2,y=30 6 Each of the following numbers has two digits blotted out.Which of the numbers could be the numbers 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 P.S. * 代表blotted digit 咋做呀~~ 这是求下面哪个数能被24整除。当尾数为2,6时,倒数第二个数应该为奇数。当尾数为0,4,8时,倒数第二个数为偶数。所以选E。 7 Three solid cubes of lead, each with edges 10 centimeters long, are melted together in a level, rectangular-shaped pan.The base of the pan has inisde dimesions of 20 centimeters by 30 centimeters, and the pan is 15 centimeters deep.If the volume of the solid lead is approximately the same as the volume of the melted lead,approximately how many centimeters deep is the melted lead in the pan? 这道题实在没大看懂,盼望牛人解释... 三个铅块,每个边长10cm,熔了之后放在一矩形平底锅内.锅的底面积20×30,高15.问这三个熔了的铅块倒进锅了有多深? 8 On Elm Street are 6 houses on oneside of the street and 4 houses on the other.Each pair of houses on Elm Street is connected by exactly one telephone line. The total number of each lines that connect houses on opposite sides of Elm Street 12 这道题我是思÷这么想的:(6-1)+(4-1)=8 而答案选的是A. 你理解错了,题目求连接街道两面的电话线有几根? 24个?,因为有一边就4栋房子啊,4×6. 9 100x 问:1100x y 这道题我是没有什么思路,请大家帮忙. 由上两式知道x 10 三角形RST is isosceles and 角RST=40 问the sum of the measures of the two angles of 三角形RST that have equal measure 和120,哪个大?(题目讲啥?)答案是不能比较 题目告诉了你等腰三角形有一个角是40,问你相等的两个角的和和120比大小 如果40是顶角,那么两个相等角的和是140大于120,如果是底角,那么两个相等角的和是80小于120,所以不能比较 1 d=5.03894,and e is the decimal expression for d rounded to the nearest thousandth. 问the number of decimal places where d and e differ ,和4比较,哪个大?(这个也不晓得题目在讲啥)答案是4大 这道题是问你在哪一位小数位d和e不同,e=5.039,所以是在第三位不同,所以小于四2 n is an odd integer, and S is the finite sequence of consecutive integers1,2,3,4,...,n The number of terms of S that are odd The number of terms of S that are even n为奇数时,S序列中奇数数量多于偶数。 3 ab>0 (a^2+b^2)/a+b a+b (a^2+b^2)/a+b=a+b-2ab/a+b 当a,b都大于零时,前者小于后者;当a,b都小于零时,前者大于后者。 4 图画不出来。。一个三角型,2条边为X,一条边为Y,边Y上的高把三角形分成两半,问一半的面积和xy/4,哪个大? (答案是xy/4大) 设Y上的高为h,一半的面积为:1/2*1/2*y*h=y/4*h.所以比较的就是h和x的大小。因为h是这个三角形的直角边,而x是斜边。所以h小于x,所以xy/4大。 5 The water level in a tank is lowered by 6 inches, then raised by 8 inches, and then lowered by 4 inches. If the water level was x inches before the changes in level, which of the following represents the water level, in inches, after the changes? a. X-1.5 B.X+1.5 C.X-6.5 D. X+6.5 E. X-18.5 答案选A 题目没有说明x的大小。有可能X<6 .而除A外,其他答案都是不可能的。 6 If the cube of n is 180 greater than the square of n, then n=? A. 10 B.9 C.8 D.7 E. 6 答案选E n三次方值比n平方值大180,如果解不出来,一个个带入就行了。 7 一个边长为3 feet 的立方体顶面ABCD由对角线AC将立方体分开两个相等的部分,问分开的一部分每个面的总面积和36 square feet 之间的大小?答案为:A,但是我算出来应该是相等?? 5 个面,应该是大于36,有一边是3sqrt(2) 8 A certain five-number committee must be assembled form a pool of 5 women---A,B,C,D,E, and three men—X,Y,Z, what is the probability that the committee will include B,C,E,Y and Z? A.1/30 B. 1/25 C.2/35 D. 1/15 E.3/32 理解成3:2的组合,就选A 总体几率应该是1/55 9 Diane completed each of her exercise in 25 seconds and rested for 55 seconds between the exercise sets. What is the ratio of the amount of time it took her to complete an exercise set to the amount of time she rested between the sets? (A)5:6 (B) 5:11 (C) 6:11 (D) 11:5 (E) 11:6 答案是B 25/55=5/11 10 Which of the following CANNOT be a factor of 2^i*3^j where i and jare positive integers? (A)6 (B)8 (C) 27 (D) 42 (E) 54 答案是C 这个数必须是个偶数,所以选C。 1. 5 is 1/5 of x 比较x 与1大小? 答案是A 5是X的1/5,所以X=5X5=25 大于1 2. 一个圆上有一点(Z,y),半径是5 The circle above with center O has a radius of 5 圆上的点(Z,y)的y 与20开根号比较 答案是A,因为无论Y 在哪里都坐落于圆上,既它到O的距离为5>根号20 3 which of the following points(x,y)is not on the graph of y<2x? A.(-3,-7) B.(3,3) C.(2,-9) D.(2,2) E.(2,5) 首先是要问大家这是一个什么样子的graph呢?然后是对折刀题没有什么思路... 这道题是说x,y哪个不满足y<2x。这里只有E符合。 4 A bicycle registration costs $2. 5 in city x and $3.0in city y.At these rate, the cost of 4 registration in city x is k percent of the cost of 3 registration in city y k 90 这道题我是这样想的,4×2.5=k*3*3.0,课答案选的是A... 对呀你这样算出来的k=1.1,人家问的是k percent,所以要乘以100,得110.所以选A。 5 In a rectangular coordinate system, line k has x-intercept 4 and slope -2 the y-intercept of k 2 这道题是因为我不能理解x(y)-intercept的意思... 可以列出方程式:y=-2(x-4)=-2x+8,当x=0时,y=8,即在y轴的截距为8.选A. 6 When it was found that 150 more tickets for the school play were sold than the seating capacity of the auditorium.It was decided to have two performances.If the total number of tickets sold was equal to the total number who attended and if the auditorium was 2/3 full for each of the two performances, what is the seating capacity of the auditorium? A.100 B.200 C. 225 D.300 E.450 这道题我没什么思路,请牛人给出解释.主要是读题时头都大了... 这道题的意思是:当学校演出所卖的票比剧院的容量多150个时,需要演两场。如果卖票 数等于参加的人数,那么每场演出的人数为剧院容量的2/3.问剧院的容量? 设剧院容量为x,得:(x+150)/2=2/3 *x,得出x=450,选E. 7 the total area of 18 nonoverlapping circular regions,each having a diameter of 2 inches 36 square inches 答案选A我怎么觉得是D呢? 题目到底是什么意思? 这句话是说:18个不重叠的圆的总面积为多少?每个圆的直径为2. 所以18个圆的面积为:18派,大于36,所以选A 8 the scores reported for a certain mutip;e-choice test were derived by subtracting 1/3 of the number of wrong answers from the number of right answers .On a 40 question test,if none of the questions was omitted and the score reported was 20. how many wrong answers was there? 5 10 15 25 30 选c 设错了X个题,则对了40-X个,总分为40-X(对的题数)-1/3X(错的1/3)=20 解出来X=15 9 The tenths digit of .....是指十位数吗? The tenths digit of为十分位,即小数点后第一位。 10 Olive oil, vinegar, and water were combined to make 10 cups of salad dressing. The oil and vinegar were mixed in the ratio of 2 parts oil to 3 parts vinegar. 10. The number of cups 5 of water used in the salad dressing 这题什么意思? 我的理解是,oil和vinegar的比例是2:3,即放2份的oil要放3份的vinegar,但由于并没有涉及水的比率也并不知道配制1杯sd需要多少oil或vinegar或水,所以无法判断配制10杯sd需要多少杯水。 1 A candy assortment consists of seven flavors of chocolate-coveredcreams packed in two-layered boxes with 27 creams in each layer. Theflavors are always packed in rows so that the flavor varies with eachpiece in the following order, vanilla, orange, cherry, vanilla,raspberry, lime, pecan, cherry, lemon. How many chocolate-coveredvanilla creams are needed to pack 200 boxes of the assortment? (A) 600 (B) 1,200 (C) 1,800 (D) 2,400 (E) 3,600 这题看着晕的要命,不知道怎么回事? 我的理解是,一块box有两层,每层有27creams,题中说口味是packedinrows,又给出了一个9个flavors的排列,我认为这一层是3行这样的排列,按此计算,每层有3*2个vanila,一块box有2*3*2个vanila,所以200boxes有200*2*3*2=2400个vanila的creams。 2一个八边形,内角相等,横边得竖边长都为1,斜边长为根号2,面积是多少.答案是7 八边形的面积分解成一个正方形+4个矩形+4个等边直角三角形,此题那个正方形的面积为为竖边与横边的乘积为1,斜边为根号2,所以直角三角形的两条直角边为1,这样4个三角形的面积为1*1/2*4=2。4个矩形面积为1*1*2+1*1*2=4,所以总面积为7。 3 X是大于1的整数,下面哪个大. 3x+1 ; 4x . (注,答案是无法比较大小) 3x+1-4x=1-x,说明x<1时答案为A,x=1时答案为C,x>1时答案为B 所以选B,答案错误! 4 X>1, Y>1 下面哪个大:1/(1/x+1/y); 1/x+1/y (注,答案是无法比较大小) 第一项太麻烦,化简为xy/(x+y),而第二项合并为(x+y)/xy,由于未知x+y与xy的大小关系,无法比较原题中二者的大小。 5 S is the set of all fractions of the form n/n+1, where n is a positive integer less than 20. The product of all the 1/20 fractions that are in S 这是说1/2*2/3*3/4*.......n/n+1,这里n小于20.所以乘完以后为:1/n+1=1/20.所以相等。 6 A retail business has determined that its net income, in terms of x, the number of items sold, is given by the expression x2+x-380. (第一项是x的平方) The number of items 10 that must be sold for the net income to be zero 这是求x^2+x-380=0,求得x=20.所以选择A 7 w, x, y, and z are consecutive positive integers and w The remainder when (w+x)(x+y)(y+z) 1 答案是C ,不理解。题也不理解,答案也不理解啊! 这道题的解法为:x=w+1,y=w+2,z=w+3.所以(w+x)(x+y)(y+z)=(2w+1)(2w+3)(2w+5),这三个数都为奇数,三个奇数相乘还为奇数。所以除2必余1. 8 新东方数学黄皮书的section65中的第9题 the three small rectangles have the same dimensions, ps/rs 是否大于1/2? 2/3,大于1/2 小矩形设短边长为1,则小矩形的长边长为2; 所以大矩形的短边长PS=小矩形的长边长=2,大矩形的长边长RS=小矩形短边长+小矩形长边长=3; 因此PS/RS=2/3>1/2 9When 9 students took a zoology quiz with a possible score of 0 to 10,inclusive, there average (arithmetic mean) score was 7.5. If a tenthstudent takes the same quiz, what will be the least possible averagescore on the quiz for all 10 students? (A) 6.5 (B) 6.75 (C) 7.0 (D) 7.25 (E) 7.5 KEY:题目是the least( possible average),是问十个人最低能考到的分数,而不是问选项中哪个分数出现的几率最低,如果理解为后者那么选a, 因为a的几率为0,但是题目的本意是前者,所以7.5*9/10=6.75,选B. 10 d=561.165 比较the tenths digit of 100d,和the tenths digit of d/100,答案是一样大。 不懂the tenths digit是否指得是十位上的数字? the tenths digit是第十分位的数,100d=56116.5,d/100=5.61165,第一个的十分位为5,第二个的十分位为6。所以选B。 1 If one number is chosen at random from the first 1,000postiveintegers, what is the probability that the number chosen ismultiple ofboth 2 and 8? 从1到1000中选出的同时是2与8的乘积的数概率是多少? 答案是1/125 我的解法是这样的:: 只有满足8*2 8*4...........8*124 可以满足,也就是只有62个,概率就应该是62/1000. 错在哪儿呢? 在1至1000中,8的倍数有125个,因为2和8的最小公倍数为8,则该数是2和8的倍数的概率为:125/1000=1/8. 2. How many 3-digit positeve integers are odd and do not contain the digit " 5" ? How many positive 4-digit integers begin (on the left) with an odd digit and end with an even digit? 一个三位正整数它是奇数,并且没有5:首先第一位有8个数适用,第二位有9个数适用,最后一位有4个数适用。所以总共有9*8*4=288个,一个四位正整数开始的是奇数,末位是偶数“:第一位有5个数适用,第二和第三位有10个数适用,第四位有5个数适用,所以总共有5*10*10*5=2500,所以后者大于前者。 3.A printer numbered consecutively the pages of a book ,beginning with1on the first page .In numbering the pages,he printed a total of189digits. 与100 比较?什么意思呀?看不懂啊,郁闷! 这道题是说:一个打印者数连续的页数,从第一页的1开始.数这些页数,它总共打了189个数。 首先:1-9的单位数一共有9个,所以189-9=180为两位数,180/2=90,说明一共有90个两位数,从10到99.所以比100小。 4 certain integer n is a multiple of both 5 and 9.Which of the following must be true ? I. n is an odd integer. II. n is equal to 45. III. n is a multiple of 15 答案是只有第三个对,第二个为什么不对呢? 这是问的是n是5和9的乘积,但并没有说是几个5和9的乘积,而且还有可能还有其它的数,所以不一定是45. 5 the number of prime numbers the number of prime numbers greater than 10 greater than 40 and less than 50 and less than 20 40到50的质数有:41,43,47. 10到20的质数有:11,13,17,19.所以后者大于前者。Ms.Smith got an 8 percent cost-of-living raise of 20$ per week. 6 Ms.Smith's new weekly salary $260 20/0.08=250,小于260.选B。 71 The sum of the first n odd integers that (n^2)-1 are greater than zero n=2, 前2个大于0的奇数为1、3,所以和为1+3=4 (n^2)-1=3 n=3, 前3个大于0的奇数为1、3、5,所以和为1+3+5=9 (n^2)-1=8 n=4, 前4个大于0的奇数为1、3、5、7,所以和为1+3+5+7=16 (n^2)-1=15 所以前者大于后者。 8 M=3^5*5^3 N=2*3^5*5^3 the value of the units' digit of M the value of the units' digit of N 尾数为3的数的幂的个位数一定以3,9,7,1循环。所以3^5的个位数为3. 5^3的个位数为5. 所以3*5的个位数为5. 所以N的个位数为:2*5的个位数为0. 所以前者大于后者。 9if n is an integer,then the units digit of n^2 cannot be a.0 b.2 c.4 d.5 e.6 答案为b 这题的意思是:如果n为一个整数,那么n的平方的个位数不能是哪个? 因为没有两个相同的数相乘为2,所以选2. 10 Rack A holds 80 pairs ofslackswith prices ranging from $12 to $15 a pair, and rack B holds 60pairs ofslacks with prices ranging from 13$ to 18$ a pair. If all theslacks aresold, what is the greatest amount by which the revenue fromthe slacksof rack A could possibly exceed the revenue from the sale ofslacks onrack B 412 没理解好(80*15-13*60??) 最大的差为:80*15-13*60=420,最小的差为:15*80-18*60=120.所以412在这个范围内。 1. How many 3-digit positeve integers are odd and do not contain the digit " 5" ? How many positive 4-digit integers begin (on the left) with an odd digit and end with an even digit? 一个三位正整数它是奇数,并且没有5:首先第一位有8个数适用,第二位有9个数适用,最后一位有4个数适用。所以总共有9*8*4=288个,一个四位正整数开始的是奇数,末位是偶数“:第一位有5个数适用,第二和第三位有10个数适用,第四位有5个数适用,所以总共有5*10*10*5=2500,所以后者大于前者。 2.A printer numbered consecutively the pages of a book ,beginning with1 on the first page .In numbering the pages,he printed a total of 189digits. 与100 比较?什么意思呀?看不懂啊,郁闷! 这道题是说:一个打印者数连续的页数,从第一页的1开始.数这些页数,它总共打了189个数。 首先:1-9的单位数一共有9个,所以189-9=180为两位数,180/2=90,说明一共有90个两位数,从10到99.所以比100小。 3certain integer n is a multiple of both 5 and 9.Which of the following must be true ? I. n is an odd integer. II. n is equal to 45. III. n is a multiple of 15 答案是只有第三个对,第二个为什么不对呢? 这是问的是n是5和9的乘积,但并没有说是几个5和9的乘积,而且还有可能还有其它的数,所以不一定是45. 中的integer 如果前面没有加positive 或minus OR negative ,是不是都算作是正的整数啊? 不是,没说的话,按整数处理包括正和负 4 Lin and Mark each attempt independently to decode a message. If the probability that Lin will decode the message is 0.80, and the probability that Markwill decode the message is 0.70, find the probability that at least oneof them will decode the messge 这道题是这样解的:问你它们两个至少有一人可以解码的概率。你只要算出他俩都不能解码的概率,然后1减就是答案了。 Lin不能解码的概率为:1-0.8=0.2;Mark不能解码的概率为:1-0.7=0.3 俩人都不能解码的概率为0.2*0.3=0.06 所以至少有一个可以解码的概率为:1-0.06=0.94. GRE数学真题大放送(附答案解析) GRE考试真题是我们备考路上的“好伙伴”,备考初期利用好它,我们的复习将会事半功倍!快来看看2015年7月5日GRE数学真题吧。 1. ABCE is a square, and BCDE is a parallelogram Quantity A: The area of square ABCE Quantity B: The area of parallelogram BCDE A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 参考答案:C。正方形的面积是长乘以宽,平行四边形的面积是长乘以高。一样大。 2. n is an integer. Quantity B: 1 B. Quantity B is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 参考答案:C。如果n是奇数,则负负得正等于1;如果n是偶数,依然是1。 3. The population of Country X for 1980 was p. The population of Country X increased by 3.8 percent in each of the next two years. Quantity A: The population of Country X for 1982. Quantity B: 1.076p A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given. 参考答案:A 4. x≠0 Quantity B: x(x+5) A. Quantity A is greater. 数学词汇 1.数学符号 等于:≡equal to, the same as, is 不等于:>more than <less than ≥ no more than 加:+ add A to B, plus, sum of A and B, total 减:- minus, less, difference, subtract A from B 乘:× multiply,product 除:÷ A divided by B,A divided into B,A divisible by B 绝对值: |…| absolute value X square X2 平方:2 X cube 立方:3 开平方: square root 开立方:3 cube root 平行: // parallel to 垂直:⊥ perpendicular to 2.数字前缀 1:uni, mono, 2: bi, du, di 3: tri, ter 4: tera, quad 5: penta, quint 6: hex, sex 7: sept,hapta 8: oct 9: enn 10: dec, deka 3.方程 Equation 方程 solution 解4.数列和集合 arithmetic progression 等差数列 geometric progression 等比数列 set 集合 term 子集 sequence 序列 term 序列中的项 inclusive 包含序列的首末项 exclusive 不包含序列的首末项 5.排列组合与概率 combination 组合 probability,possibility 概率 6.数论 common division 公约数 common factor 公因子 composite number 合数(质数与1以外的自然数)consecutive integer 连续整数 digit 位 GRE数学词汇表 一、代数部分 1、有关数学运算 普通运算:add,plus 加subtract减difference差multiply / times乘product积divide除dividend被除数quotient商remainder余数 整除:divisible可被整除的divided evenly被整除divisor因子,除数 其他:factorial阶乘power乘方round to / to the nearest四舍五入 2、有关集合 运算:union并集intersection 交集 性质集proper subset真子集solution set解集 3、有关代数式、方程和不等式 代数式:algebraic term 代数项similar terms同类项 literal coefficient字母系数numerical coefficient数字系数 range值域 factorization因式分解 方程:original equation原方程equivalent equation同解方程,等价方程linear equation线性方程 不等式:inequality不等式 4、有关分数和小数 分数:proper fraction 真分数improper fraction假分数common fraction 普通分数mixed number带分数simple fraction简分数complex fraction繁分数 numerator分子denominator分母 (least)common denominator(最小)公分母 quarter四分之一 小数:decimal fraction纯小数infinite decimal无穷小数recurring decimal循环小数places位(thousands’ place,hundreds’ place,tens’ place,units’ place (ones’ digit),tenths’ place,hundredths’ place,thousandths’ place.) 5、基本数学概念 平均数:arithmetic mean 算术平均值geometric mean几何平均数weighted average加权平均值 乘方:exponent指数,幂base乘幂的底数,底边powers幂 cube立方数,立方体square root平方根cube root立方根 数字:digit阿拉伯数字constant常数variable变量 6、有关数论 数:natural number 自然数integer/whole number整数 nonnegative非负的distinct不同的 positive number正数negative number负数 odd integer 奇数even integer偶数 代数部分 1. 有关数学运算 add,plus 加 subtract 减 difference 差 multiply, times 乘 product 积 divide 除 divisible 可被整除的 divided evenly 被整除 dividend 被除数,红利 divisor 因子,除数 quotient 商 remainder 余数 factorial 阶乘 power 乘方 radical sign, root sign 根号 round to 四舍五入 to the nearest 四舍五入 2. 有关集合 union 并集 proper subset 真子集 solution set 解集 3. 有关代数式、方程和不等式 algebraic term 代数项 like terms, similar terms 同类项 numerical coefficient 数字系数 literal coefficient 字母系数 inequality 不等式 triangle inequality 三角不等式 range 值域 original equation 原方程 equivalent equation 同解方程,等价方程 linear equation 线性方程(e.g. 5 x +6=22) 4. 有关分数和小数 proper fraction 真分数 improper fraction 假分数 mixed number 带分数 vulgar fraction,common fraction 普通分数 simple fraction 简分数 complex fraction 繁分数 numerator 分子 denominator 分母 (least) common denominator (最小)公分母 quarter 四分之一 decimal fraction 纯小数 infinite decimal 无穷小数 recurring decimal 循环小数 tenths unit 十分位 5. 基本数学概念 arithmetic mean 算术平均值 weighted average 加权平均值 geometric mean 几何平均数 exponent 指数,幂 base 乘幂的底数,底边 cube 立方数,立方体 square root 平方根 cube root 立方根 common logarithm 常用对数 digit 数字 constant 常数 variable 变量 inverse function 反函数 complementary function 余函数 linear 一次的,线性的 factorization 因式分解 absolute value 绝对值,e.g.|-32|=32 round off 四舍五入 6. 有关数论 natural number 自然数 positive number 正数 negative number 负数 odd integer, odd number 奇数 even integer, even number 偶数 integer, whole number 整数 positive whole number 正整数 negative whole number 负整数 consecutive number 连续整数 real number, rational number 实数,有理数 irrational(number)无理数 inverse 倒数 composite number 合数 e.g. 4,6,8,9,10,12,14,15…… prime number 质数e.g. 2,3,5,7,11,13,15…… 注意:所有的质数(2除外)都是奇数,但奇数不一定是质数reciprocal 倒数 common divisor 公约数 multiple 倍数 (least)common multiple (最小)公倍数 (prime) factor (质)因子 common factor 公因子 ordinary scale, decimal scale 十进制 nonnegative 非负的 tens 十位 units 个位 mode 众数 median 中数 common ratio 公比 GRE数学考试范围和内容 GRE全称Graduate Record Examination,是世界各地的大学各类研究生院(除管理类学院,法学院),要求申请者所必须具备的一个考试成绩,也是教授对申请者是否授予奖学金所依据的最重要的标准。因此GRE成绩在留学申请中具有十分重要的地位。但很多同学对GRE数学部分不甚了解。 gre数学考什么?在gre数学的备考过程中,需要复习一下高中数学知识,并且对微分方程、线性代数、初等数论、抽象代数等12个知识点进行归类复习。下面,我们就具体来看一下gre数学考试涉及到的12个知识点。 1、高中知识 各种三角诱导公式,和,差,倍,半公式与和差化积,积化和差公式,平面解析几何。 2、数学分析 极限,连续的概念,单变量微积分(求导法则,积分法则,微商),多边量微积分及其应用,曲线及曲面积分,场论初步。 参考书:张筑生先生的3册《数学分析新讲》,Walter Rudin的Principles of Mathematical Analysis 3、微分方程 基本概念,各种方程的基本解法。 参考书:Wolfgang Walter,Ordinary Differential Equations 说明:以Cracking the GRE Math Test中的相关章节为主,一般不难。 4、线性代数 普通代数,艾森斯坦因法则,行列式,向量空间,多变量方程组解法,特征多项式及特征向量,线形变换及正交变换,度量空间。 参考书:镇系之宝,张贤科老师的《高等代数学》,Seymour Lipschutz的Theory and Problems of Linear Algebra 说明:Cracking the GRE Math Test这本书里面的东西也差不多够了,不过鉴于sub越来越难,大家还是回去翻翻张老师的书吧。 5、初等数论 1、mode(众数) 一堆数中出现频率最高的一个或几个数 e.g. mode of 1,1,1,2,3,0,0,0,5 is 1 and 0 2、range(值域) 一堆数中最大和最小数之差 e.g. range of 1,1,2,3,5 is 5-1=4 3、mean(平均数) arithmatic mean(算术平均数) (不用解释了吧?) geometric mean (几何平均数) n个数之积的n次方根 4、median(中数) 将一堆数排序之后,正中间的一个数(奇数个数字), 或者中间两个数的平均数(偶数个数字) e.g. median of 1,7,4,9,2,2,2,2,2,5,8 is 2 median of 1,7,4,9,2,5 is (5+7)/2=6 5、standard error(标准偏差) 一堆数中,每个数与平均数的差的绝对值之和,除以这堆数的个数(n) e.g. standard error of 0,2,5,7,6 is: (0-4+2-4+5-4+7-4+6-4)/5=2.4 6、standard variation 一堆数中,每个数与平均数之差的平方之和,再除以n e.g. standard variation of 0,2,5,7,6 is: s _ 2 2 2 2 2_ _(0-4) +(2-4)+(5-4)+(7-4)+(6-4)_/5=6.8 7、standard deviation ?òè¥ 就是standard variation的平方根 标准方差的公式:d^2=[(a1-a)^2+(a2-a)^2+....+(an-a)^2 ]/n d 为标准方差 8、三角形 余玄定理C^2=A^2+B^2-2ABCOSt t为AB两条线间的夹角 9、Y=k1X+B1,Y=k2X+B2,两线垂直的条件为K1K2=(-1) 10、三的倍数的特点:所有位数之和可被3整除 11、N的阶乘公式: N!=1*2*3*....(N-2)*(N-1)*N 且规定0!=1 例如 8!=1*2*3*4*5*6*7*8 12、 熟悉一下根号2、3、5的值 sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236 13. ...2/3 as many A as B: A=2/3*B ...twice as many... A as B: A=2*B 14. a if only b: b-a 15. 数学常用术语 主要符号 数的概念和特性 *几个GRE 最常用的概念: 偶数(even number):能被2整除的整数; 奇数(odd number):不能被2整除的数; 质数(prime number):大于1的整数,除了1和它本身外,不能被其他正整数所整除的,称为质数。也叫素数;(学过数论的同学请注意,这里的质数概念不同于数论中的概念,GRE 里的质数不包括负整数) 倒数(reciprocal):一个不为零的数为x,则它的倒数为1/x 。 *最重要的性质: 奇偶性:偶加偶为偶,偶减偶为偶,偶乘偶为偶; 奇加奇为偶,奇减奇为偶,奇乘奇为奇; 奇加偶为偶,奇减偶为偶,奇乘偶为偶。 等差数列 GRE 数学中绝大部分是等差数列,d n a a n )1(1-+=,形式主要为应用题。题目会说三年稳步增长第一年的产量是x,第三年的产量是y,问你的二年的产量。 数理统计 *众数(mode) 一组数中出现频率最高的一个或几个数。 例:mode of 1,1,1,2,3,0,0,0,5 is 1 and 0。 *值域(range) 一组数中最大和最小数之差。 例:range of 1,1,2,3,5 is 5-1=4 *平均数(mean ) 算术平均数(arithmetic mean ) *几何平均数(geometric mean ) n 个数之积的n 次方根。 *中数(median) 对一组数进行排序后,正中间的一个数(数字个数为奇数), 或者中间两个数的平均数(数字个数为偶数)。例: median of 1,7,4,9,2,5,8 is 5 median of 1,7,4,9,2,5 is (5+7)/2=6 ps: GRE 经常考察众数与数的个数的积和这组数的和的大小。 *标准偏差(standard error) 一组数中,每个数与平均数的差的绝对值之和,再除以这组数的个数n 例:standard error of 0,2,5,7,6 is: (|0-4|+|2-4|+|5-4|+|7-4|+|6-4|)/5=2.4 *standard variation (方差) 一组数中,每个数与平均数之差的平方和,再除以这组数的个数n 例: standard variation of 0,2,5,7,6 is: _ 2 2 2 2 2_ |_(0-4) +(2-4)+(5-4)+(7-4)+(6-4)_|/5=6.8 *标准差(standard deviation) standard deviation 等于standard variation 的平方根 ps :GRE 经常让你比较众数或中数与数的个数的乘积和这组数的和的大小,可以举几个极限情况的例子验证一下。还有一种题型是给你两组数的平均值,方差,比较他们的中数大小;要注意中数的大小和那两个值是没有必然联系的,无法比较。 2020年新GRE数学模拟考试试题及答案 1. A,B,C,D,E,F排在1,2,3,4,5,6六个位置上,问A不在1, B不在2, C不在3的情况下,共有多少种排法? (A) 720 (B) 450 (C) 180 (D) 216 (E) 320 2. 一直线L过点A(5,0), B(0,2), 坐标原点为O, 点P(X,Y)为三角形OAB中一点, 问:Y (A) 1/4 (B) 3/8 (C) 1/2 (D) 5/8 (E) 3/4 3. 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 policies having incorrect electric record, 75% also having incorrect paper record. 3% of all policies have both incorrect paper and incorrect electric records. If we randomly pick out one policy,what’s the probability that the one having both correct paper and correct electric records? (A) 0.80 (B) 0.94 (C) 0.75 (D) 0.88 (E) 0.92 4. If Bob can do a job in 20 days and Jane can do the job in 30 days, they work together to do this job and in this period, Bob stop work for 2.5 days and Jane stop work for x days, and the job be finished for 14 days, what is x? (A) 1.6 (B) 3.2 (C) 1.5 (D) 1.25 (E) 1.15 5. The probability of A is 60% and the probability of B is 50%, what is the most possible probability that neither A nor B would happen? (A) 0.80 (B) 0.40 (C) 0.75 (D) 0.55 (E) 0.68 1.有关数学运算add,plus加 subtract减 difference差 multiply,times乘 product积 divide除 divisible可被整除的 divided evenly被整除 dividend被除数,红利 divisor因子,除数 quotient商 remainder余数 factorial阶乘 power乘方 radicalsign, rootsign根号 round to四舍五入 to the nearest四舍五入 2. 有关集合 union并集 proper subset真子集 solution set解集 3. 有关代数式、方程和不等式algebraic term代数项 like terms, similar terms同类项 numerical coefficient数字系数 literal coefficient字母系数 inequality不等式 triangle inequality三角不等式 range值域 original equation原方程 equivalent equation同解方程,等价方程 linear equation线性方程(e.g.5x+6=22) 4. 有关分数和小数 proper fraction真分数 improper fraction假分数 mixed number带分数 vulgar fraction,common fraction普通分数 simple fraction简分数 complex fraction繁分数 numerator分子 denominator分母 (least)common denominator(最小)公分母 quarter四分之一 decimal fraction纯小数 infinite decimal无穷小数 recurring decimal循环小数 tenths unit十分位 5. 基本数学概念 arithmetic mean算术平均值 weighted average加权平均值 geometric mean几何平均数 exponent指数,幂 GRE数学部分读不懂题解决方法 在做GRE数学部分的时候,很多考生单词都认识,但是连在一起就读不懂题怎么办呢?在这种情况下,题目里面的生词已经解决了,但是还是读不懂,到底怎么回事呢? 举个例子先:Of the positive integers that are multiples of 30 and are less than or equal to 360, what fraction are multiples of 12? 其实呢,如果没有这个倒装,应该没有任何问题:What fraction of the positive intergers that are multiples of 30 and are less than or equal to 360 are multiples of 12?主要就是一个阅读的问题:A占B的几分之几用英文解释是:what fraction of B are A .因此,这个问题就归结于阅读问题,而这个阅读的问题不在于单词,而在于这么一点:不仅仅是单词,一些数学里面很口语化的内容用英文怎么表达? 提供一种解决的方法:在 题目里面遇到了这样的说法,自己翻译出来,然后再用同样的语言来造句和自己出题给自己做。 比如,遇到了fraction这个结构以后,自己给自己出个 题目:of the positive integers that are less than or equal to 100, what fraction are prime numbers? 以下一些口语化的数学语言,希望同学们自己完成练习:A和B成比例 A和B相似 A打了八折 G R E数学真题大放送(附答案解析) 真题是我们备考路上的“好伙伴”,备考初期利用好它,我们的复习将会事半功倍!快来看看2015年7月5日GRE数学真题吧。 ,andBCDEisaparallelogram QuantityA:TheareaofsquareABCE QuantityB:TheareaofparallelogramBCDE . . . 参考答案:C。正方形的面积是长乘以宽,平行四边形的面积是长乘以高。一样大。 . QuantityB:1 .最新GRE数学真题大放送(附答案解析)资料
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GRE数学单词表
GRE数学部分术语总汇
GRE数学考试范围和内容
最新GRE数学基本概念汇编
新GRE数学词汇手册
2020年新GRE数学模拟考试试题及答案
GRE数学词汇大汇总(全!!)
GRE数学部分读不懂题解决方法
GRE数学真题大放送附答案解析