六年级中英文奥数题3.doc

六年级数学提高练习8姓名 成绩 1、 一个三位数，如果它的每一位数字都不超过另一个三位数对应数位上的数字，那么就称它被另一个三位数“吃掉”。又规定“任何数都可以被它相同的数吃掉”。比如，241被342“吃掉”，123被123“吃掉”，但是240和223互相都不能被“吃掉”。现请你设计出6个三位数，它们中的任何一个都不能被另外5个“吃掉”，并且它们的百位数字只允许取1，2；十位数字只允许取1，2，3；个位数字只允许取1，2，3，4，那么这6个三位数之和是多少？There is a three-digit number. If every digit of it does not exceed its counterpart of another three-digit number, then, we can say that it is eaten by the later three-digit number. It is also the rule that any number can be eaten by itself. For example, 241 is eaten by 342 and 123 is eaten by 123. But 240 and 223 can not be eaten by each other. Now please conceive six three-digit numbers and make sure that none of them can be eaten by the other five. In addition, their hundreds digits can only be 1 or 2, their tens digits can only be 1, 2 or 3, and their ones digits can only be chosen from 1, 2, 3 and 4. Then, what is the sum of the six three-digit numbers?2、 小王骑自行车，小张骑摩托车，他们同时从A、B两地相向而行，在距中点10千米处相遇。已知小王骑车的速度是小张的，求A、B两地间的距离。Xiao Wang is riding a bike and Xiao Zhang is riding a motorcycle. They move face to face from A and B respectively at the same time. They meet at the place which is 10 kilometers away from the midpoint. Given that Xiao Wangs speed is three fifths of that of Xiao Zhang. What is the distance between A and B?3、 小刚骑车从8路汽车的起点站出发，沿着8路车的行驶路线前进。当他骑了1650米时，一辆8路公共汽车从起点站出发，每分钟行450米。这辆汽车在行驶过程中每行5分钟停靠一站，停车时间为1分钟。已知小刚骑车速度是汽车行驶速度的，这辆车出发后多少分钟追上小刚？3. Xiao Gang starts from the origin station of No.8 bus by bike and goes along the route of No.8 bus. When he covers 1650 meters, a No.8 bus sets out from the origin station and moves 450 meters per minute. This bus pulls up for one minute at one bus stop every five minutes. Given that Xiao Gangs speed is two thirds of that of the bus, how many minutes will it take the bus to catch up with Xiao Gang after its departure?4、 甲、乙两筐水果重量相等，如果从甲筐取出6千克水果放入乙筐，这时，甲筐比乙筐少，甲筐原有水果多少千克？4. There are two baskets of fruits, A and B, with the same weight. If one takes out 6 kilograms of fruits from A and put them into B, then, the fruits in A is a quarter less than those in B. How many kilograms of fruits are there in A in the first place?5、 下面的每个图形中的数字都存在一定的规律，请找一找，再算出第四个图形中的“？”表示的数是多少？ 8 13 12 6 22 3 43 5 12 13 14 ? 5 3 4 2 9 5 11 65. There exists a certain regularity of the numbers in the following pictures. Please find the regularity and figure out the number indicated by a question mark in the fourth picture.6、 如果一个整数等于它各个数位上数的和的3倍，那么这个数会是多少？6. If an integer is three times as large as the sum of the figures in its digit positions, then, what is the number?7、 有两个大小不同的正方形A、B，如下图，B的中心与A的一个顶点重合，重叠部分的面积是A面积的，你能知道正方形A的边长是B的多少倍吗？7. Square A and square B are different in size. As is shown in the following picture, the center of B and one of the vertexes of A overlap each other. The area of the overlapped part is one ninth of that of A. Do you know how many times the side of A is as long as that of B?8、 上题中，如果A与B以下图的方式重叠时，那么重叠部分面积又是B面积的几分之几？8. In the above problem, if A and B overlap like the following picture, then, what portion is the area of the overlapped part to that of B in terms of fraction?9、 图1中有8个面积都是4平方厘米的正三角形，依次叠放在同一条直线上，从左到右，每个三角形底边的中点恰好与下一个三角形的一个顶点重合，那么由这8个三角形所盖住的面积是多少平方厘米？9. There are eight identical regular triangles in the following picture. Each area is 4 cm2. They overlap one another on the same straight line. From left to right the midpoint of the base line of every triangle overlaps with one of the vertexes of the next triangle. What is the area covered by the eight triangles in square centimeters? 10、 下图中有10个边长都是2厘米的正方形，依次地排在一条直线上，而且正方形的一个顶点，正好是下一个正方形的中心，那么由这10个正方形所盖住的面积是多少？In the following picture, ten squares with the same side length of 2 cm are arranged on one straight line in order. One of the vertexes of one square is just the center of the next one. What is the area covered by the ten squares?11、 有一个33的方格，能否通过若干次操作，使得方格中的所有数变为0？（其中一次操作是指将表中一行的3个数或一列的3个数同时加上或减去同一个数），如果能请给出一种操作方案，如果不能，请说明理由。11237826711. There is a 33 grid. Can you turn all the numbers in the grid into 0 after several operations? (The operation is to add or minus the same number to or from the three numbers in one row or in one column at the same time.) If you can, please give one plan, and if not, please give your reason.12、 上题中，其他条件不变，能否通过若干次操作，使得方格中的所有数变为1呢？12. In the above problem, if we keep the other conditions unchanged, can you turn all the numbers in the grid into 1 after several operations?13、 将一张长方形纸片连续对折，对折的次数越多，折痕的条数也就越多，请问对折8次后，折痕有多少条？（向同一个方向对折）13. If one folds a piece of rectangular paper continuously, the more times he folds the paper, the more creases there are on the paper. After it has been folded 8 times, how many creases are there on the paper? (Please fold it in the same direction.)必记词汇exceed iksi:d vt. 超过；胜过ones digit 个位数字hundreds digit 百位数字tens digit 十位数字in addition 另外，此外grid rid n. 网格；格子column klm n. 纵队；列；专栏；圆柱 regular triangle 正三角形base line 底边补充词汇counterpart kaunt,p:t n. 副本；配对物；极相似的人或物conceive knsi:v vt. 构思；构想出；想出；怀孕bus stop 公共汽车站origin station 起点站pull up拔起；停下来；阻止in the first place 首先；起初；原先indicate indikeit vt. 表明；指出；预示；象征identical aiden