3. The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?
4. Rectangular region PQRS shown above is partitioned into ten identical smaller rectangular regions, each of which has width x. What is the perimeter of PQRS in terms Of x?
A.15x
B.25x
C.30x
D.50x
E.It cannot be determined from the information given.
5. 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?
6. 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 the different lengths of the pieces, in fractions of a yard?
A B C D E
D
[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。
7. A certain club has 237 local branches, one national office, and one social 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?
A.482
B.476
C.474
D.239
E.235
A B C D E
A
[解析] 此题的关键在阅读。读懂题意后,很容易得出其官员数如下:237×2+2×4=482人
8. In the figure above, two searchlights S1 and S2 are located 10,000 feet apart, each covers an area of radius 10,000 feet, and each is located 8,000 feet from the railroad track. To the nearest 1,000 feet, what is the total length x of track spanned by the searchlights?
9. 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?
10. The hexagonal face of the block shown in the figure above has sides of equal length and angles of equal measure. If each lateral face is rectangular, what is the area, in square inches, of one lateral face? (A) (B) 12 (C) 20 (D) (E) 24
11. Each step of a staircase is 0.25 meter wide and 0.20 meter high, as shown in the figure above. All angles shown in the figure are right angles. If the height of the staircase is 3.6 meters and the landing at the top of the staircase is 1 meter wide, how long, in meters, is AB?
A.3.0
B.4.25
C.4.5
D.5.25
E.5.5
A B C D E
D
[解析] 因为楼梯的总高度为3.6,则楼梯的总级数为:
又因为楼梯顶端的平台长度为1米,所以AB的长度为:17×0.25+1=5.25m
12. In the figure above, DA=DB=DC, what is the value of x?
13. In the rectangular coordinate system above, the line y=x is the perpendicular bisector of segment AB (not shown), and the x-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (2, 3), what are the coordinates of point C?
14. In the figure above, segments PR and QR are each parallel to one of the rectangular coordinate axes. Is the ratio of the length of QR to the length of PR equal to 1? (1)c=3 and d=4 (2)a=-2 and b=-1
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 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?
A.$150
B.$300
C.$600
D.$1,200
E.$2,400
A B C D E
A
[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600×0.25=150美元。
16. The figure above shows a cord around two circular disks. If the radii of thetwo disks are 80 centimeters and 60 centimeters, respectively, what is the total length, in centimeters, of the cord?
17. A ladder 25 feet long is leaning against a wall that is perpendicular to level ground. The bottom of 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?
18. The shaded region in the figure above represents a rectangular frame 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?
22. The figure above represents the floor of a square foyer with a circular rug partially covering the floor and extending to the outer edges of the floor as shown. What is the area of the foyer that is not covered by the rug? (1)The area of the foyer is 9 square meters. (2)The area 0f the rug is 2.25πsquare meters.
23. In the figure above, line AC represents a seesaw that is touching level ground at point A. If B is the midpoint of AC, how far above the ground is point C? (1)x=30 (2)Point B is 5 feet above the ground.
25. In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a wall. The length of TV is how much greater thanthe length of RV? (1)The 1ength of TU is 10 meters. (2)The length of RV is 5 meters.
26. 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 (2)TU=meters
27. 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.
28. The figure above shows the present position on a radar screen of a sweeping beam that is rotating at a constant rate in a clockwise direction. In which of the four quadrants will the beam lie 30 seconds from now? (1)In each 30-second period, the beam sweeps through 3.690° (2)r=40
29. If the area of the circle above is 64π, what is the value of k?
A B C D E
D
[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:
30. The number of diagonals of a polygon of n sides is given by the formula . If a polygon has twice as many diagonals as sides, how many sides does it have?
A.3
B.5
C.6
D.7
E.8
A B C D E
D
[解析] 根据题意可得:
31. A 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?
32. In the figure above, what is the value of 2x-y7
A.0
B.15
C.30
D.45
E.60
A B C D E
B
[解析] 根据图中的数据及直角三角形的性质很容易求出x=y=15,从而可以得到2x-y=x=15。
33. The figure above shows the shape of a sign to be placed in front of a flower store. The sign has a semicircle on each side of the square. If the sign is 3 centimeters thick and if each side of the square is50 centimeters long, what is the volume, in cubic centimeters, of the sign?
35. 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, ). (2)The coordinates of point Q are (8, 0).
37. What is the perimeter of △PQR? (1)The measures of ∠PQR, ∠QRP, and ∠RPQ are x°, 2x°, and 3x°, respectively. (2)The altitude of △PQR from Q to PR is 4.
38. A pyramidal-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 the same size and shape.
39. In the rectangular coordinate system above, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary lines?
40. In rectangular region PQRS above, T is a point on side PS. If PS=4, what is the area of region PQRS? (1)△QTR is equilateral. (2)Segments PT and TS have equal length.
42. The inside 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 that has maximum volume?
A.3
B.4
C.5
D.6
E.8
A B C D E
B
[解析] 根据题意可知,该圆柱体罐子一定内切于该长方体盒子,圆柱体底面的直径与高直接与该长方体盒子以哪一个面为底有关,长方体有三个不同的底面,所以此题可以分三种情况进行讨论: 圆柱体的体积为:πr2·h (1)当圆柱体的底面与长方体的6 inches by 8 inches面重合时,其体积=90π (2)当圆柱体的底面与长方体的8 inches by 10 inches面重合时,其体积=96π (3)当圆柱体的底面与长方体的6 inches by 10 inches面重合时,其体积=72π 根据以上分析可知,该圆柱体的体积最大时其半径为4时。
43. 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) (2)A>C+3
45. In the figure above, P and S are points on the x-axis. What is the area of square PQRS? (1)The coordinates of point P are (2, 0) (2)The coordinates of point R are (6, 4)
46. What is the volume of a certain rectangular solid? (1)Two adjacent faces of the solid have areas 15 and 24, respectively. (2)Each of two opposite faces of the solid has area 40.
47. Two pulleys are connected by a belt as shown in the drawing above. If pulley Q makes 300 evolutions per minute, how many revolutions per minute does pulley P make? (1)The length of the belt is 12π. (2)The ratio of the radius of pulley P to the radius of pulley Q is 2 to 1.
48. A grocer is storing small cereal boxes in large cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of 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?
50. A portion of a thermometer above is calibrated to show degrees in equal increments. If the temperature indicates a reading at level A, what is the temperature?
51. A circular peg is to be placed in a square hole. What is the perimeter of the hole? (1)The radius of the peg is 4 centimeters. (2)Each edge of the hole is tangent to the peg.
52. A rectangle is defined to be "silver" if and 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.
53. Rectangle WXYZ is inscribed in a circle with center O as shown above. If the diameter of the circle is equal to 16, then what is the area of the shaded region? (1)WZ=OW (2)XW<XY
54. The figure above shows the dimensions ofa rectangular board that is to be cut into four 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) (A) 5 ft 6 in (B) (C) 5 ft 3 in (D) 5 ft (E) 4 ft 9 in
55. 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 the dimensions of each of the rectangles is 25 inches.
56. If k and ω are the dimensions of a rectangle that has area 42, and if k and ω are integers such that k>ω, what is the total number of possible values of k?
57. In the figure above, what is the length of PQ times the length of RS? (1)The length of PQ is 5. (2)The length of OR times the length of PR is equal to 12.
59. In the 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 .
61. A certain encyclopedia has 20 volumes, each of which is ω 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 ω inches deep inside, could the inside length of the box be less than 35 inches. (1)t=1.5 (2)ω=9 and k=12
63. 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 squares?