【考研类试卷】工商管理硕士入学考试-几何及答案解析.doc

《【考研类试卷】工商管理硕士入学考试-几何及答案解析.doc》由会员分享，可在线阅读，更多相关《【考研类试卷】工商管理硕士入学考试-几何及答案解析.doc（28页珍藏版）》请在麦多课文档分享上搜索。

1、工商管理硕士入学考试-几何及答案解析(总分：315.00，做题时间：90 分钟)一、单项选择题(总题数：63，分数：315.00)1.If the number of square units in the area of a circle is A and the number of 1inear units in the circumference is C, what is the radius of the circle?(1) （分数：5.00）A.B.C.D.E.2.In the figure above, a circle is inscribed in a square wit

2、h side b and a square with side a is inscribed in the circle. What is the area of the square with side b?(1)a=4(2)The radius of the circle is （分数：5.00）A.B.C.D.E.3.A rectangle with dimensions 75 inches by 100 inches is divided into 20 smaller rectangles. If each new rectangle has equal dimensions, ho

3、w many inches of lines are needed to divide the original rectangle?(1)One of the dimensions of each of the rectangles is 15 inches.(2)One of the dimensions of each of the rectangles is 25 inches.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E

4、) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分4. （分数：5.00）A.B.C.D.E.5. （分数：5.00）A.B.C.D.E.6.If each side of ACD above has length 3 and if AB has length 1, what is the area of region BCDF?（分数：5.00）A.B.C.D.E.7. （分数：5.00）A.B.C.D.E.8.If k and are the dimensions of a rectangle that has area 42, and if k and are

5、 integers such that k, what is the total number of possible values of k?（分数：5.00）A.TwoB.ThreeC.FourD.FiveE.(E) Six9.If the area of the circle above is 64, what is the value of k?（分数：5.00）A.B.C.D.E.10. （分数：5.00）A.B.C.D.E.11.What is the volume of a certain rectangular solid?(1)Two adjacent faces of th

6、e solid have areas 15 and 24, respectively.(2)Each of two opposite faces of the solid has area 40.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分12.In the rectangular coordinate system, are the points (r

7、, s) and (u, ) equidistant from the origin?(1)r+s=1(2)u=1-r and =1-s（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分13.A warehouse had a square floor with area 10,000 square meters. A rectangular addition

8、 was built along one entire side of the warehouse that increased the floor area by on-half as much as the original floor are-a. How many meters did the addition extend beyond the original building?（分数：5.00）A.10B.20C.50D.200E.(E) 50014.A straight pipe 1 yard in length was marked off in fourths and al

9、so in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?（分数：5.00）A.B.C.D.E.15.A certain company has records stored with a record-storage firm in 15-inch by 12-inch by 10-inch b

10、oxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.25 per box per month for record storage, what is the total amount that the company pays each month for record storage?（分数：5.00）A.$150B.$300C.$600D.$1，200E.(E) $2,40016. （分数：5.00）A.B.C.D.E.17.What is the length in meter

11、s of a certain rectangular garden?(1)The length of the garden is 6 meters more than twice the width.(2)The length of the garden is 4 times the width.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分18.A py

12、ramidal-shaped box to protect a plant is constructed with 4 lateral faces and an open bottom. What is the lateral area of the box?(1)The base of the pyramid is a polygon with all sides of equal length, and the perimeter of the base is 1 meter.(2)The 1ateral faces are isosceles triangles that have th

13、e same size and shape.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分19. （分数：5.00）A.B.C.D.E.20. （分数：5.00）A.B.C.D.E.21.A circular peg is to be placed in a square hole. What is the perimeter of the hole?(1

14、)The radius of the peg is 4 centimeters(2)Each edge of the hole is tangent to the peg.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分22. （分数：5.00）A.B.C.D.E.23.A rectangle is defined to be “silver“ if and

15、 only if the ratio of its length to its width is2 to 1. If rectangle S is silver, is rectangle R silver?(1)R has the same area as S.(2)The ratio of one side of R to one side of S is 2 to 1.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1

16、)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分24. （分数：5.00）A.B.C.D.E.25. （分数：5.00）A.B.C.D.E.26.In the figure above, R and Q are points on the x-axis. What is the area of equilateral PQR?(1)The coordinates of point P are (6, （分数：5.00）A.B.C.D.E.27.The shaded region in the figure above represents a rectangular fram

17、e with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in-inches?（分数：5.00）A.B.C.D.E.28. （分数：5

18、.00）A.B.C.D.E.29. （分数：5.00）A.B.C.D.E.30.The outline of a sign for an ice-cream store is made by placing of the circumference of a circle with radius 2 feet on top of an isosceles triangle with height 5 feet, as shown above. What is the perimeter, in feet, of the sign?（分数：5.00）A.B.C.D.E.31.In the fig

19、ure above, square CDEF has area 4. What is the area of ABF?（分数：5.00）A.B.C.D.E.32.In the xy-coordinate system, if(a, b)and(a+3, b+k)are two points on the line defined by the equation x=3y-7, then k（分数：5.00）A.9B.3C.D.1E.(E) 33. （分数：5.00）A.B.C.D.E.34.A certain encyclopedia has 20 volumes, each of which

20、 is inches wide, k inches long and t inches thick. If all of the volumes are to be tightly packaged in one rectangular box that is k inches wide and inches deep inside, could the inside length of the box be less than 35 inches.(1)t=1.5(2)=9 and k=12（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件

21、(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分35. （分数：5.00）A.B.C.D.E.36.Quadrilateral RSTU shown above is a site plan for a parking lot in which side RU is parallel to side ST and RU is longer than ST. What is the area of the parking lot?(1)RU=80 meters

22、(2)TU= （分数：5.00）A.B.C.D.E.37.If the number of square units in the area of circle C is twice the number of linear units in the circumference of C, what is the number of square units in the area?（分数：5.00）A.4B.8C.4D.8E.(E) 1638. （分数：5.00）A.B.C.D.E.39. （分数：5.00）A.B.C.D.E.40. （分数：5.00）A.B.C.D.E.41.The in

23、side dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such cannisters that could be used, what is the radius, in inches, of the one

24、that has maximum volume?（分数：5.00）A.3B.4C.5D.6E.(E) 842.The number of diagonals of a polygon of n sides is given by the formula （分数：5.00）A.B.C.D.E.43. （分数：5.00）A.B.C.D.E.44. （分数：5.00）A.B.C.D.E.45. （分数：5.00）A.B.C.D.E.46.The hexagonal face of the block shown in the figure above has sides of equal lengt

25、h and angles of equal measure. If each lateral face is rectangular, what is the area, in square inches, of one lateral face?（分数：5.00）A.B.C.D.E.47. （分数：5.00）A.B.C.D.E.48. （分数：5.00）A.B.C.D.E.49. （分数：5.00）A.B.C.D.E.50.The figure above shows the dimensions ofa rectangular board that is to be cut into fo

26、ur identical pieces by making cuts at points A, B, and C, as indicated. If x=45, what is the length of AB? (1 foot=12 inches)（分数：5.00）A.B.C.D.E.51.A rectangle with dimensions 24 inches by 42 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the

27、 squares?（分数：5.00）A.4 inchesB.6 inchesC.7 inchesD.8 inchesE.(E) 10 inches52. （分数：5.00）A.B.C.D.E.53.According to the graph above，when x=3, y is most nearly（分数：5.00）A.B.C.D.E.54. （分数：5.00）A.B.C.D.E.55.A ladder 25 feet long is leaning against a wall that is perpendicular to level ground. The bottom of

28、the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?（分数：5.00）A.4B.5C.8D.9E.(E) 1556.A grocer is storing small cereal boxes in large cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of

29、 each small cereal box is 7 inches by 6 inches by 5 inches, then what is the maximum number of small cereal boxes that can be placed in each large carton?（分数：5.00）A.25B.210C.252D.300E.(E) 42057.What is the perimeter of PQR?(1)The measures of PQR, QRP, and RPQ are x, 2x, and 3x, respectively.(2)The a

30、ltitude of PQR from Q to PR is 4.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分58. （分数：5.00）A.B.C.D.E.59. （分数：5.00）A.B.C.D.E.60.A certain club has 237 local branches, one national office, and one social

31、 service office. If each local branch has 2 officers, and each of the two other offices has 4 officers, how many officers does the club have altogether?（分数：5.00）A.482B.476C.474D.239E.(E) 23561. （分数：5.00）A.B.C.D.E.62. （分数：5.00）A.B.C.D.E.63. （分数：5.00）A.B.C.D.E.工商管理硕士入学考试-几何答案解析(总分：315.00，做题时间：90 分钟)一、

32、单项选择题(总题数：63，分数：315.00)1.If the number of square units in the area of a circle is A and the number of 1inear units in the circumference is C, what is the radius of the circle?(1) （分数：5.00）A. B.C.D.E.解析：解析 设这个圆的半径为 r，则其周长为 2w=C，面积为 r 2=A 所以有：*。根据(1)的*可求出 r=3，所以(1)充分；根据(2)显然不能算出 r 的值，所以(2)不充分。2.In the

33、 figure above, a circle is inscribed in a square with side b and a square with side a is inscribed in the circle. What is the area of the square with side b?(1)a=4(2)The radius of the circle is （分数：5.00）A.B.C.D. E.解析：解析 由 a=4 可求出，内切圆的直径等于*，也即大正方形的边长*，由此可求出其面积等于32，所以(1)充分；由内切圆的半径等于*也可得到大正方形的边长 b=4*，其

34、面积等于 32，所以(2)也是充分的。3.A rectangle with dimensions 75 inches by 100 inches is divided into 20 smaller rectangles. If each new rectangle has equal dimensions, how many inches of lines are needed to divide the original rectangle?(1)One of the dimensions of each of the rectangles is 15 inches.(2)One of t

35、he dimensions of each of the rectangles is 25 inches.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分 E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分解析：解析 根据分割成的 20 个小长方形的面积都相等可得每一个小长方形的面积为(75100)20=375 平方英寸，所以当小长方形的一条边确定时，另一条边的长也是确定的。根据(1)可得每一个小长方形的另

36、一条边长为 25 英寸，所以此时一定是大长方形长为 75 英寸的边被分成 5 段，而长为 100 英寸的边被分成了 4 段，如下图所示：*从图中可以看出这些分割线的长度=4100+753=625 英寸，所以(1)充分；同理可求得(2)也是充分的。4. （分数：5.00）A.B. C.D.E.解析：解析 根据(1)PQ=PR 无法判断 TR 是否平行于 PQ；根据(2)：QR=PRPQR=QPRTR 平分PRSTRS=PRT又根据PRS=TRS+PRT=PQR+QPRTRS=PQRTRPQ(同位角相等，两直线平行)5. （分数：5.00）A.B. C.D.E.解析：解析 由 AB=BC=CD=A

37、D 可得，ABC 和ACD 都是等边三角形，且 ABCD 是菱形，所以 AC 与 BC 互相垂直，因此 x=90-60=30。6.If each side of ACD above has length 3 and if AB has length 1, what is the area of region BCDF?（分数：5.00）A.B. C.D.E.解析：解析 由图可知 BCDF 的面积等于ACD 的面积减去ABF 的面积。因为ACD 是等边三角形，所以A=60，ABF 是直角三角形，所以*，因此ABF 的面积=*；AACD 的面积=*ACADsin*；综上所述 BCDF 的面积为：*

38、。7. （分数：5.00）A.B.C. D.E.解析：解析 由图可知 PR 平行于 x 轴而 QR 平行于 Y 轴，因此 R 点的坐标为(c，b)，所以线段 PR 的长度为 c-a，线段 QR 的长度为 d-b。由以上分析可知，根据(1)中的 c=3 且 d=4 无法得到 PR 与 QR 的长度相同，所以(1)不充分；同理(2)也是不充分的；而(1)+(2)充分，因为在这个条件下 a，b，c，d 的值均已知，所以可以充分地回答题目中的提问，即线段 QR 与线段 PR 的长度之比等于 1。8.If k and are the dimensions of a rectangle that has

39、area 42, and if k and are integers such that k, what is the total number of possible values of k?（分数：5.00）A.TwoB.ThreeC.Four D.FiveE.(E) Six解析：解析 根据 k=42，且 k，可得 k 和 的可能取值如下所示：k=7 =6k=14 =3k=21 =2k=42 =1所以 k 的可能取值的总数为 4。9.If the area of the circle above is 64, what is the value of k?（分数：5.00）A.B.C.D.

40、 E.解析：解析 从图中可以看出圆的直径为 3k，根据圆的面积公式可得：*10. （分数：5.00）A.B. C.D.E.解析：解析 由 AB=BC，且 BDAC 可推知 D 是线段 AC 的中点，所以 D 点的坐标为*，即为(6, 0)。以因为 BD 与 y 轴平行，所以 B 点的横坐标也是 6，其纵坐标等于线段 AC 的长，|AC|=|20-(-8)|=28，因此B 点的坐标为(6, 28)。11.What is the volume of a certain rectangular solid?(1)Two adjacent faces of the solid have areas 1

41、5 and 24, respectively.(2)Each of two opposite faces of the solid has area 40.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分 D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分解析：解析 设该长方体的 3 条边的长分别为 l，h，则长方体体积为 lh。(1)不充分，因为由(1)只能得到 l=-15，h=24，而无法得到 xyz

42、的值；(2)不充分，因为根据(2)只能得到lh=40，同样得不到该长方体的体积的值；(1)+(2)充分，把上面的 3 个方程联立，可以求得长方体的体积的大小：(l)(h)(lh)=152440(lh) 2=325282lh=12012.In the rectangular coordinate system, are the points (r, s) and (u, ) equidistant from the origin?(1)r+s=1(2)u=1-r and =1-s（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单

43、独都不充分，但条件(1)和条件(2)联合起来充分 D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分解析：解析 (1)不充分，因为(1)中未涉及 u，所以无法判断两点距原点的距离；由(2)可得(u+)=2-(r+s)，同样无法判断 u2+ 2与 r2+s2的大小，所以(2)也不充分；点(r, s)距原点距离为*，点(u, )距原点距离为*，由(2)可得：u 2+ 2=(1-r)2+(1-s)2=r2+s2+2(r+s)+2，再由(1)r+s=1 可得u2+ 2=r2+s2，所以(1)+(2)能充分地回答上面的问题。13.A

44、 warehouse had a square floor with area 10,000 square meters. A rectangular addition was built along one entire side of the warehouse that increased the floor area by on-half as much as the original floor are-a. How many meters did the addition extend beyond the original building?（分数：5.00）A.10B.20C.

45、50 D.200E.(E) 500解析：解析 如下图所示，额外建的房子是图中的阴影部分：*设正方形地板的边长为 a，额外建的房子伸出原房子 b 米，则根据题意可得：a2=10,000a=100 米ab=5,000b=50 米14.A straight pipe 1 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all

46、the different lengths of the pieces, in fractions of a yard?（分数：5.00）A.B.C.D. E.解析：解析 如下图所示，该管子将沿*码处被切开：*由图可知，该管子被切成了六段，其中两两相等，所以共有*三种长度。15.A certain company has records stored with a record-storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If

47、the company pays $0.25 per box per month for record storage, what is the total amount that the company pays each month for record storage?（分数：5.00）A.$150 B.$300C.$600D.$1，200E.(E) $2,400解析：解析 首先应算出该公司共有多少盒的唱片被保管：*所以该公司总共应付的钱为 6000.25=150 美元。16. （分数：5.00）A.B. C.D.E.解析：解析 从图中可以看出该弦覆盖了两圆周长的*，弦中离开两圆的地方分

48、别与两圆相切，切点与圆心的连线组成的四边形是正方形，边长分别等于两圆的半径，因此弦与两圆同时相切的中间两段的切线长为 2(80+60)=280；而覆盖在两圆圆周上的弦的长度为*(2r 1+2r 2)=210。所以此弦的长为2102+280。17.What is the length in meters of a certain rectangular garden?(1)The length of the garden is 6 meters more than twice the width.(2)The length of the garden is 4 times the width.（

49、分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分 D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分解析：解析 设该花园的长为 l，宽为叫，则由(1)可得：l=2+6，根据此式无法求出 l 的值，所以(1)不充分；由(2)可得 l=4，根据此式也无法求出 l18.A pyramidal-shaped box to protect a plant is constructed with 4 lateral faces and an op