六年级奥数题及答案.doc

小升初奥数模拟试卷及答案一、填空题：119971996-19951994+19931992199119909+87654321=_.3在图中的七个圆圈内各填一个数，要求每一条直线上的三个数中，当中的数是两边两个数的平均数，现在已经填好两个数，那么，x=_4把1、2、3、4、5填入下面算式的方格内，使得运算结果最大：+-那么这个最大结果是_.5设上题答数为a，a的个位数字为b，2b的个位数字为c.如图，积的比是_6要把A、B、C、D四本书放到书架上，但是，A不能放在第一层，B不能放在第二层，C不能放在第三层，D不能放在第四层，那么，不同的放法共有_种7从一张长2109毫米，宽627毫米的长方形纸片上，剪下一个边长尽可能大的正方形，如果剩下的部分不是正方形，那么在剩下的纸片上再剪下一个边长尽可能大的正方形，按照上面的过程，不断地重复，最后剪得的正方形的边长是_毫米8龟兔赛跑，全程5.4千米兔子每小时跑25千米，乌龟每小时跑4千米，乌龟不停地跑，但兔子却边跑边玩，它先跑1分，然后玩15分，又跑2分，玩15分再跑3分，玩15分，那么先到达终点的比后到达终点的快_分9从1，2，3，4，5中选出四个数，填入图中的方格内，使得右边的数比左边的数大，下面的数比上面的数大，那么，共有_种填法比女生少人二、解答题：1小明从甲地到乙地，去时每小时走5千米，回来时每小时走7千米，来回共用4小时，小明去时用了多长时间？2有一个长方体，它的正面和上面的面积之和是119，如果它的长、宽、高都是质数，那么这个长方体的体积是多少？3在400米环形跑道上，A、B两点相距100米（如图），甲、乙两人分别从A、B两点同时出发，按逆时针方向跑步，甲每秒跑7米，乙每秒跑5米，他们每人跑100米都停5秒那么，甲追上乙需要多少秒？4五年级三班有26个男生，某次考试全班有30人超过85分，那么女生中超过85分的比男生中未超过85分的多几人？模拟试卷答案一、填空题：11997原式(19971995)(19961994)(19931991)(19921990)(97)(86)(53)(42)12222因为从1至1997共1997个数，所以从2至1997共1996个数，这1996一定相等，所以，9A5B23，A和B都是自然数，先试A1，B1或B2或B3，均不成立；再试A2，B1因此，只有A2，B1时，成立，即：AB3. 314如图，余下的四个圆圈分别用A、B、C、D四个字母来表示，5由每一条直线上三个数的关系可知：从式中知，B比D大2，那么式可写成：D(8D2)2，故D10，所以，C(1012)211，于是，(8x)211，x14最大圆面积为：329，所以阴影部分面积与最大圆面积之比为：69A不能放在第一层，那么A只能放在第二、三、四层，有3种可能情况如果第一层放B，不论第二、三、四哪一层放A、C、D也就可以确定3因此，当第一层放B时，所有可能摆放情况有以下三种：第一层 第二层 第三层 第四层B A D CB D A CB C D A(注意：C不能在第三层，D不能在第四层)当第一个位置放C或D时，也各有3种可能的摆放方法，因此，不同的放法共有339种757由于627的3倍比2109小，因此，开始时的长方形纸片上，可以连剪3个边长为627的正方形：21096273228，剩下的部分是长、宽分别为627和228的长方形，依此类推，有6272282171228171157也就是说，当剩下长171，宽57的长方形时，可以刚好剪成三个边长为57的正方形，所以，最后剪得的正方形边长是57毫米88.04兔子跑完全程(不包括玩的时间)，需要：12.9612342.9612.96分钟分成五段跑完，中间兔子玩了4次，每次15分，共玩了15460(分)，兔子跑完全程共需要12.966072.96(分)而乌龟跑完8172.968.04(分)910先看左上角，它是所填四个数中最小的一个，所以，只能取1或2如果取1，它右边一个空可填2，3或4，当填2时，下面两空有三种情况(3，4)，(3，5)，(4，5)；当填3时，下面两空可填(2，4)，(2，5)，(4，5)；当填4时，下面两空可填(2，5)，(3，5)如果左上角取2，右下角一定取5，3和4可交换，便得到另外两种情况，综上所述，共有10种填法1015(人)，男生比女生少24022515人二、解答题：12小时20分去时速度回来速度57，所以，去时时间回来时间 75，因此，所以，去时用2小时20分2170如图，长方体的正面和上面的面积之和长宽长高长(宽高)119717，那么，有两种可能：(1)长7，宽高17(2)长17，宽高7宽和高必是一个奇质数与一个偶质数2，725，符合要求；17215不符合要求，所以长17，长方体体积2517170365秒甲、乙不停留，甲追上乙需要多少时间？两人同时出发，相差100米，甲每秒比乙快2米，所以100250(秒)就可以追上乙，甲跑507350(米)，在100米， 200米， 300米处共停留5315(秒)，所以甲追上乙需要501565(秒)44人设女生中超过85分的有x人，则男生中超过85分的有(30x)人，那么男生中未超过85分的有26-(30-x)(x-4)(人)，所以女生中超过85分的比男生中未超过85分的多x-(x-4)4(人)Simulation test paper and the answer after mathematical olympiadA, fills up the topic:1.1997 + 1996-1995-1994 + 1993 + 1992-1991-1990 +. + 9 + 8-7-6 + 5 + 4-3-2 + 1 = sight.3. In the graph of the seven circle fill a number in each, each require a line number three, number of is both sides of two Numbers averages, has now fill in the number two, then, x = sight4. 1, 2, 3, 4, 5 in the box below the formula so that the results biggest:- - -+ -so the biggest results is.5. The answer to a question set, a single digits for b, 2 x b for the unit digit of c. as shown in figure,Product than is the sight.6. To put A, B, C, D four books on the shelves, but not in A first layer, B cannot be in the second, and the third layer cannot be in C, D cant on the fourth floor, so, different put method were A sight.7. From a 2109 mm long, wide and 627 mm rectangle on slips of paper, cut a distance as far as possible big square, if the rest of the part is not a square, so that in the rest of the paper, to cut a distance as far as possible big square, according to the above process, repeated, and finally cut of the square is revised sight mm.8. The tortoise and the hare, the 5.4 km. The rabbit run 25 km per hour, the tortoise run four kilometers per hour, the tortoise keep running, but rabbit but were running and playing, it ran 1 minute, then play 15 points, and ran 2 points, playing 15 points. Run again 3 points, playing 15 points,. And then after the first to reach the destination than to cross the finish line fast sight points.9. From 1,2,3,4,5 choose four number, fill in the graph of the square space, make the right number of than the number to the left of the big, the number of large number than the one above, then, a total of sight kind of fill in the law.Less than girls.Second, solution:1. Xiao Ming from point a to point b, every hour to walk 5 km and came back seven kilometers per hour walk, and share four hours, xiao Ming when to how long did it take?2. Have a cuboid, its positive and the area of the above sum is 119, if its length, width and height are prime Numbers, then the volume of the cuboid is how much?3. In the 400 meters and circular runway, A, B two points are 100 meters apart (pictured), the A and B two people separately from A and B two points on at the same time, according to run anti-clockwise direction, A run of seven meters per second, B run five meters per second, each of them ran 100 meters to all stop 5 seconds. So, A catch B need how many seconds?4. Eleven.he 26 a boy, a test the whole class 30 people are more than 85 points, so more than 85 points in girls than boys not more than 85 points in a few more people?Simulation test the answerA, fills up the topic:1.1997The original type = (1997-1995) + (1996-1994) + (1993-1991) + (1992-1990) +. + (9-7) + (8-6) + (5-3) + (4-2) + 1 = 2 + 2 +.+ 2 + 2 +Because from 1 to 1997 1997 number, so from 2 to 1997 the number of 1996, the 1996Must be equal, so, 9 A + 5 B = 23, A and B are natural number, try A = 1, B = 1 or B = 2 or B = 3, are not set up; Try A = 2, B = 1. Therefore, only A = 2, B = 1, set up, namely: A + B = 3.3.14.As shown in figure, the remaining four circle respectively with A, B, C, D four letters to says,5By each a line of the relationship between the three Numbers that:From (1) type of knowledge, B than 2 D, then (2) type can be written as: D = (8 + D + 2) 2, the D = 10, so, C = (10 + 12) 2 = 11, so, (8 + x) 2 = 11, x = 14.Most large circle area of impedance 32 = 9 , so the shaded part area and the ratio of the circle area for:6.9A cannot be in the first layer, then A can only on the second, third, and fourth layer, there are three possible. If the first layer put B, no matter the second, third, and fourth which layer put A, C, D and can determine the 3. Therefore, when the first layer put B, all may have put the following three:The first layer of the second to the third on the fourth floorB A D CB D A CB C D A(note: C cant on the third floor, D in the fourth layer cant).When the first position put C or D, also have each three possible put method, therefore, different put method were 3 by 3 = 9.7.57Because of the 627 three times more than 2109 small, therefore, at the start of the rectangle on slips of paper and can even cut three revised for 627 square: 2109 = 627 x 3 + 228 and the