小学英语奥数 平面图形.doc

平面图形 1. Look at the figure on right,we know the length of the four lines,and two angles is ninety degrees.Can you work out the area of the quadrangle ABCD?2. Look at the figure on right,the length of BD,DE and EC is 2,4 and 2,F is the middle point of line AE,the triangle ABC is 4 high,please calculate the area of triangle DEF.3. In the following diagram, we know the length of the three lines, M is the middle Point of line DE, please calculate the area of quarangle ABMD(the shaded part ).4. As is shown in the diagram,each side of the exact square(正方形) equals 1.please calculate the area of the shaded part(阴影部分)？5. Look at the shadow of the following two parts A and B area.Can you figure out which part is bigger?(the length of sides in rectanglar a are 3,4;and in rectangular B are 2,6 )6. The length of exact squares side equals 1.Please calculate the area of the shaded part.7. The length of the sides in the following grass which is a rectangle are 16,10.And there is two roads in the middle,one is a rectangle one is a parallelogram,then what is the area of the shaded part?8. Seeking the following graphic area.9. In the following diagram,large square area is 10cm2 larger than the small square area.Please calculate the area of the circle.10. Find out which of the following area of two triangles are equal? 11. There is a litter square water pool.It is 5 meters long each side.There is grass around the pool everywhere.There is a goat tied to point A,the rope is 6 meters long.How many square meters of grass can the goat get at most?专题五： 立体图形一、长方体和正方体面积及体积计算：二、典型例题例1：2.1 square meters=( ) square decimeters;2.14 cubic merters=( )cubic decimeters 0.05 cubic merters=( )liters=( ) milliliters.中文意思：_ 答案：_，_，_，_。例2：Please try to figure out the number of surfaces,and the number of the edges in the following diagram.中文意思：_Answer:_,_.解析：surfaces:_,edges _.同学们自己填上中文意思哦。例3：We need _cubes with 5 cm side at least to make a bigger cube.中文意思：_例4：The floor space of a cube is 2 cm2,then its space area is _. 中文意思：_例5：If the edgesed of a cubekju:b increases to three times,then how much times will its area and volume vlju:m increase?中文意思：_ 例6：If we increase the volume of a cube with 2 cm edges by 208 cm3,we get a cube still,then how much centimeters does the edges increse by?中文意思：_例7：The surface area of a cuboid is 33.66 dm2,the length and the side of one surface is 2.3 dm and 2.1 respectively,then what is the volume of the cuboid?中文意思：_例8：If you unfold（展开） the cube on the right,which of the following is possible(可能的)?Answer:_中文意思：_例9：As shownd,there is a cube(456) ,it is made of 120 small cubes ,if we paint(涂) it red,then how much cubes is there with one surface red ,two surfaces red and three surfaces red respectively(分别的)?中文意思：_ 当堂演练：1.The edge of a cube is 6cm,then the sum of its edges are _cm,its surface is _ cm2,and its volume is _ cm3.2.There are five cubes with 2 cm ,we join them to make a cuboid,so the surface of the cuboid is _ cm2, and its volume is _ cm3.3.The stretch out view of the cube is ( )3.As showed,we cut a square with 2 cm side from a rectangle with 13cm length and 9 cm wide,then we fold it along the dotted line(虚线) to make a cuboid container(容器),how much square centimeter is the volume of container?专题五： 练习（立体图形）1.8600 square centimeters=( ) square decimeters;25cubic merters 50 cubic centimeters=( )cubic decimeters=( )cubic centimeters;7.9 cubic decimerters=( )liters=( ) milliliters2.The volume of a finger is about 1 ( ),the volume of a chalk box is about 1( ), the volume of a classroom is about 75( ).（填上合适的体积单位）中文意思：_3.The edge of a cube is 8cm,then the sum of its edges are _cm,its surface is _ cm2,and its volume is _ cm3.中文意思：_4.There are five cubes with 3cm ,we join them to make a cuboid,so the surface of the cuboid is _ cm2, and its volume is _ cm3.中文意思：_5.Please try to figure out the number of surfaces,and the number of the edges in the following diagram.中文意思：_Answer: .6.If the edges of a cube increases to “a” times,then how much times will its area and volume increase to?中文意思：_Answer:_,_.7.If we panit each surface of a cube with one color of the three colors respectively(分别): red,yellow or blue,and every color can paint two surfaces,then how many different ways (方法)we can use at most?中文意思：_Answer:_. 8.There is 30 cubes with 1 cm wide, we put them like this as showed on the right,then wepaint the emerged (露出的)surfaces red,please calculate the red surface area. 中文意思：_Answer:_.9.There is a cube,it has two red,two yellow and two bule surfaces,and there are some apexesepeks (顶点),they are painted with three colors,question:how many apexes like that are there at most?at least?中文意思：_Answer:_,_.专题六： 和差倍分问题一、 知识梳理一般题目中给出的和倍、差倍等关系的问题为和差倍分问题。二、 典型例题例1驴骡之争How many coins(硬币)do they each have?_(You can write your answer in Chinese!)例2Jane has a RMB 15.00 token.Here are some of the books she would like to buy.Which books will she get if she spends RMB 15.00 exactly?Schoolgirls Life RMB 9.95,Show Jumping RMB 4.50,Pocket Book of Birds RMB 2.95,James and the Pence RMB 1.55,Standard Dictionary RMB 3.50.中文意思：_Answer: _例3景区A BCDEFGH气温（）9/-928/194/-29/512/214/30/-616/4(1)温差最大的景区是（ ） （2）温差最小的景区是（ ）(3)温差相同的景区是（ ）和（ ）例4The students of Grade Five made flowers of 5 kinds of colors.For each color,there are 20 flowers.They used some for decorating the classroom and there are 28 left now.How many flowers did they use for the classroom?中文意思：_Answer: _例5Mrs.Black has some cards in her hand.If Mary,her daughter,gives her 24 more,she will have three times as many as Mrs.Black.If the total of the cards are 120.How many cards did Mrs.Black have in her hand?中文意思：_Answer: _例6Xiao Ming bought 4 pens.Each costs M yuan.He paid 2.5 yuan and got 0.1 back.How much did each pen cost?中文意思：_Answer: _例7A silver fork and silver knife are fifty pence together.If the fork is twenty pence dearer than the knife,How much is the fork and how much is the knife?中文意思：_Answer: _例8.Jim,John,Jerry and Joe together bought a basket of 144 apples.Jim received 10 more apples than John,26 more than Jerry,and 32 more than Joe.How many apples did Jim receive? 中文意思：_Answer: _专题六:练习(和差倍分问题)1. Four times of A are 128.What is A?2.A doctor gives you three pills telling you to take one every half hour.How many minutes would the pills last?3.I am a number,I am greater than the product(积) of 5 and 9.I am less than the difference(差) between 959 and 912.I am an even (偶数的) number.What number am I?4.A shop has some pork in it.5kg is sold,and now 90kg is left.How many kilograms did it have?5.A group has some story-books.It lent to 5 classes with 8 books each.35 books are left now.How many books did it have?6.A shop has some bags of milk.In each bag is 5kg.Now 7 bags of milk are sold,and 80kg is left.How many kilograms did the shop have?7.A construction sit（建筑工地） has got 5 ships of cement（水泥）.In each ship is A tons.When 10 tons are used up,15 tons are left.What is A?8.The students of Grade Five made flowers of 5 kinds of colors.For each color,there are 20 flowers.They used some for decorating the classroom and there are 28 left now.How many flowers did they use for the classroom?9.Two women were doing shopping.One spent60 more than the other,and they spent140 all together.How much did each of them spend?10.A computer and its monitor(监视器)weigh a total(总重量)of 48 pounds.If the monitor weighs twice as much as the computer,how much does each piece(件) of hardware(硬件)weight?11.Trousers on sale for 1/2 off have a green tag,Trouses on sale for 1/4 off have a yellow tag.Stephen bought two green-tagged trouses originally prices at 10 yuan each,and one yellow-tagged trousers originally priced at 16 yuan.How much did he pay for his trousers?专题七 应用题A部分：行程问题基本公式：路程速度时间；一、相遇问题：速度和相遇时间相遇路程 相遇问题：（直线）：甲的路程+乙的路程=总路程相遇问题：（环形）：甲的路程 +乙的路程=环形周长二、追及问题：追及时间速度差路程差追及问题：（直线）：距离差=追者路程-被追者路程=速度差追击时间追及问题：（环形）：快的路程-慢的路程=曲线的周长 三、流水问题：顺水行程（船的静水速度水速）顺水时间 逆水行程（船的静水速度水速）逆水时间 顺水速度=船的静水速度水速 逆水速度船的静水速度水速 静水速度=（顺水速度逆水速度）2 水速=（顺水速度逆水速度）2 四、列车过桥 列车过桥问题：关键是确定物体所运动的路程。总路程=火车长度+桥的长度总时间=总路程火车速度五、钟表问题：（此类问题很多可以转化为追及问题） （1）假设时钟一圈是12格，则时针每小时转1格，分针每小时转12格。 （2）钟面上每两格之间为30（36012=30），时针与分针成某个角度一般都有对称的两种情况。 （3）时针与分针一昼夜重合22次，垂直44次，成180也是22次。六、典型例题例1：The distance between two cities is 405km,two cars start at the same time ,driving towards each other,if the speed of A is 45km/h,and B is two times as fast as A,then how many hours later will the two cars encounter?例2：The distance between two cities (A and B)is 405km, one drive a car from city A to city B for one and a half hour,then one who drive a motocycles starts from city B to city A ,they encounter 5 hours later.If the speed of the car is 40km/h,how many kilometers is the speed of the motorcycles?例3：One person ride a boat between dock A and dock B,when he is in downstream direction,it takes 6 hours;and it takes 2 hours more when he is in countercurrent direction, We know that the waterflow speed is 3 km/h,please calculate the distance between the two docks.例4：Jane walk from station A to station B,when he goes from station A to station B,the speed is 6km/h,but when he back from station B,the speed is 9 km/h.He spends 5 hours for going and backing in all.So how much meters does Jant walk in all?例5：The distance between station A and station B is 450km.An express (快车)starts from station A,with its speed at 65km/h;another car starts from station B,its speed at 85 km/h.(1) The two cars start at the same time,driving towards each other,how many hours later will the two cars encounter(相遇)?(2) If the express starts 30 minutes beforehand(先，提前),and the two drive towards each other.Then how many hours later will the two encounter?例6：Two people start from A and B respectivily (分别)to C, the distance between A and B is 7km. Jane walk from B at six oclok in the morning,and Lucy ride a bike from A to catch up with Jane at fifteen past six oclock,then they encounter each other at thirty five past eight oclock. Jane is 1.5 times as fast as Lusy.So how much kilometers does Jane walk per hour?例7：Zhang hua and Li Ming were running along a circle.They started from the same starting point but in the opposite direction(相反方向).When they meet again,Zhang hua had run for 250 meters but Li Ming only 150 meters.The two boys ran at the same speed(速度) along the circle.When Zhang Hua arrived at(到达) the starting point again,how many meters are left(被剩下) for Li Ming to run to get to the starting point again? 专题七A：行程问题练习1.The distance between two places is 214km.At the two ends,A rides a motocycle and B rides a bike,and they ride toward each other.If B rides for 20 minutes earlier,and then B starts,they encounter 5 hours later.And we know that the speed of A is 6 km slower than 3-fold of Bs speed.Please calculate(计算)the speed of B,seeking the speed per hour of B?2.If a boat leaves dock A in downstream direction,it takes 4 hours;and if the boat leaves dock B for dock A in countercurrent direction,it takes 5 hours.We know that the waterflow speed is 3 km/h,please calculate the speed of boat travelling in still water.3.The distance between A and B is 180km,and one is riding a bike from A at the speed of 15km per hour,the other is riding a motocycle from B.As is shown that motorcycles speed is three times faster than bicycle,and their traving direction is the same.If the person who rides the bike starts 2 hours earlier,how long doed the motorcycle need to catch up with the bike?4.X and Y walk along the 400-meter long runway.If they walk in the reverse direction at the same time and spot（点）,they can encounter after 2.5 minutes.And if they walk in the same direction at the same time and spot,X can catch up with Y after 12.5 minutes.So how far does X walk per minute and Y?5.At a constant speed,A,B run in a 400-meter circular track,the two start in the same direction at the same beginning line.The speed of A is 100m/min,B is As 3/2 times.Ask(1)How long will they meet at the first encounter?(2)How long will they meet at the second encounter?6.There is an museum 1000meters away from the school.Now A and B will start from their school to visit it.The speed of A is 80m/min,and Bs speed is 180m/min.B starts 5 minutes later than A.Question:1.How many minutes later will B catch up with A?2.Whats the distance to the museum when B catche up with A?7.There is a bicycle race around the city,35 minutes later the fastest man encounters the lowest man.We know the fastest man is 1.2 times as fast as the lowest man.It is 7km around the city.How much is the speeed of the fastest man and the lowest man?专题七B部分：工程问题一、 基本公式：工作量工作效率工作时间二、 典型例题：例1： 做某件工作，甲单独做要8小时才能完成，乙单独做要12小时才能完成，问：（1） 甲做1小时完成全部工作量的几分之几？_（2） 乙做1小时完成全部工作量的几分之几？_（3） 甲、乙合做1小时完成全部工作量的几分之几？_（4） 甲做x小时完成全部工作量的几分之几？_（5） 甲、乙合做x小时完成全部工作量的几分之几？_（6） 甲先做2小时完成全部工作量的几分之几？_乙后做2小时完成全部工作量的几分之几？_1、 乙再合做x小时完成全部工作量的几分之几？_三次共完成全部工作量的几分之几？_结果完成了工作，则可列出方程：_例2：A bag of rice,Jay need 10 days to eat,Bell need 15 days to eat.Ask:how many days will it take for them to eat the bag of rice?例3：Repair a section of the road,it will take A team 20 days to complete,B team 30 days to complete.Now the two teams start repairing the road at the same time.Question:how many days will it take the two teams to repair three fifths of the road?例4：It takes team A 30 days to complete a project.If done by team B,it will take 40 days to complete.Now the project is undertaken(承担) by team A during the former(前面的) several days,and then by team B,needing 35 days in all.Question:during process,how many days does team A do it?例5：It takes team A 16 days,team B 12 days complete a project alone.Now the project is undertaken(承担) by team B during the former(前面的) 3 days,and the left is done by team A.Ask: How many days will it take for team A? 例6：It takes team A 12 days,team B 16 days,team C 20 days to complete a project alone.Now the project is undertaken(承担) by team A during the first 3 days,and then by team C for 5 days,then how many days will it take for team B to fininsh the left of the project? 专题七B：工程问题练习1.There is a pool and two pipes:A,B.Pipe A needs 10 hours to fill the pool,it opened alone;and B needs 15 hours.Now,if we open the two pipes,how many hours will it take to fill the pool?2.To do some machine part,it will take Mr.Wang 15 hours to complete,Mr. Li 20 hours to complet