gre数学考试关于几何的重点试题

gre数学考试关于几何的重点试题 1. If the areas of three of the faces of a rectangular solid are 6,10 and 15, what is the volume of the solid? A.30 B.90 C.150 D.300 E.450 ：A 2.△RST lies in the XY-plane and points R and T have (x, y) coordinates (0,0) and (6,0), respectively. The area of △RST is 12. The x-coordinate of R The y-coordinate of S 答案：D 3.What is the maximum number of nonover-lapping regions into which 3 lines can divide the interior of a circle? A.4 B.6 C.7 D.8 E.9 答案:C 4.The rectangular rug shown in the figure above has a floral border 1 foot wide on all sides. What is the area, in square feet, of that portion of the rug that excludes the border? A.28 B.40 C.45 D.48 E.53 答案：A 5. 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 shaded regions 2,800 square feet 答案：D 6.What are the coordinates of point B in the xy-plane above? A.(6,12) B.(6,28) C.(8,20) D.(12,20) E.(14,28) 答案：B 7.If 9 trees are originally planted in a circular pattern as shown above, what is the least number of trees that must be transplanted so that the 9 trees will be in 2 straight rows? A.4 B.5 C.6 D.7 E.8 答案：B 8.If the sum of the measures of two angles is 180o,each angle is a supplement of the other, whereas, if the sum of their measures is 90o, each is a complement of the other. The measure of an angle with a supplement that measures 130o The measure of an angle with a supplement that measures 40o 答案：C 9.If a solid pyramid has 4 vertices and 4 faces, how many edges does the pyramid have? A.2 B.3 C.4 D.6 E.8 答案：D 10.A rectangular floor with an area of 12 square meters is drawn to scale with 2 centimeters representing 1 meter. The area of the scale drawing of the floor 24 square centimeters 答案：A 11.In the rectangular coordinate system, line k passes through the point (0,0) and (4,8); line m passes through the points (0,1) and (4,9). The slope of line k The slope of line m 答案：C 12.In the stop sign shown in the figure above, all sides have equal length and all angles have equal measure. If the figure could be rotated 225 degrees in a clockwise direction, point G would be in the position of point. A.I B.J C.K D.L E.M 答案：B 13.What is the ratio of the perimeter of a pentagon with each side of length 6 to the perimeter of an octagon with each side of length 6? A.5/6 B.4/5 C.3/4 D.2/3 E.5/8 答案：E 14.A circular flower bed is inscribed in a flat, square garden plot that measures x meters on each side. The fraction of the garden plot area that is not part of the flower bed if x=50 meters The fraction of the garden plot area that is not part of the flower bed if x=45 meters 答案：C 15.The dimensions, in centimeters, of rectangular box R are 6 by 8 by 10. Which of the following cannot be the total surface area, in square centimeters, of two faces of R? A.96 B.120 C.128 D.160 E.180 答案：E 16.The figure above shows 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.45 答案：A 17.A certain rectangle has perimeter 54. If the ratio of the length of the rectangle to the width is 5 to 4, what is the length of the rectangle? A.30 B.27 C.24 D.18 E.15 答案：E 18.In the rectangular coordinate system above, the coordinates of points A and B are shown. If the dotted lines represent a second pair of coordinate axes with origin at A, and if the scale is the same on both pairs of axes, what are the coordinates of point B with respect to the second pair of axes? A.(-33,88) B.(33,48) C.(33,-48) D.(97,88) E.(97,-88) 答案：C 19. If the perimeter of the rectangle above is 36, then l= A.9 B.14 C.16 D.28 E.32 答案：B 20.If the perimeter of a triangle is 18, then the length of one of the sides cannot be A.1 B.3 C.6 D.8 E.9 答案：E 21.In the figure above, if ABCD is a parallelogram with A at the origin, what are the coordinates of C? A.(6,5) B.(6,6) C.(7,4) D.(8,5) E.(8,6) 答案：A 22.What fraction of a cubic meter is the volume of a cubic block of stone with edge of length 10 centimeters?(1 meter=100centimeters) A.3/10 B.1/10 C.1/30 D.1/100 E.1/1000 答案：E 23.In the rectangular coordinate system above, for how many of the points that lie inside or on the boundary of the shaded region are both coordinates integers? A.six B.seven C.eight D.nine E.ten 答案：E 24. A rectangular tabletop consists of a piece of laminated wood bordered by a thin metal strip along its four edges. The surface area of the tabletop if x square feet, and the total length of the strip before it was attached was x feet. If the tabletop is 3 feet wide, what is its approximate length, in feet? A.12 B.10 C.9 D.8 E.6 答案：E 25.In the coordinate plane, points A and B are endpoints of a diameter of a circle with center (-2,1). If the coordinates of A are (-5,5), what are the coordinates of B? A.(0,0) B.(3,-2) C.(3,-1) D.(2,-2) E.(1,-3) 答案：E 26.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 inside dimensions 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? A.2.5 B.3 C.5 D.7.5 E.9 答案：C 27.In the figure above, if x, y, and z are integers such that x A.59 and 91 B.59 and 135 C.91 and 178 D.120 and 135 E.120 and 178 答案：C 28.In the rectangular coordinate system above, if P, not shown, is a point AB and if the x-coordinate of P is 1, what is the y-coordinate of P? A.4/3 B.3/2 C.7/3 D.5/2 E.8/3 答案：A 29.There are six marked points on the circle above. How many different lines can be drawn that contain two of the marked points? A.5 B.6 C.12 D.15 E.30 答案：D 30.In the figure above, ABCD is a square. What are the coordinates of point B? A.(-4,2) B.(-2,4) C.(-2,6) D.(4,-6) E.(6,-2) 答案：C